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1

Fourier Transform Quantum State Tomography  

E-print Network

We propose a technique for performing quantum state tomography of photonic polarization-encoded multi-qubit states. Our method uses a single rotating wave plate, a polarizing beam splitter and two photon-counting detectors per photon mode. As the wave plate rotates, the photon counters measure a pseudo-continuous signal which is then Fourier transformed. The density matrix of the state is reconstructed using the relationship between the Fourier coefficients of the signal and the Stokes' parameters that represent the state. The experimental complexity, i.e. different wave plate rotation frequencies, scales linearly with the number of qubits.

Mohammadreza Mohammadi; Agata M. Branczyk; Daniel F. V. James

2012-11-06

2

The Fourier Transform on Quantum Euclidean Space  

E-print Network

We study Fourier theory on quantum Euclidean space. A modified version of the general definition of the Fourier transform on a quantum space is used and its inverse is constructed. The Fourier transforms can be defined by their Bochner's relations and a new type of q-Hankel transforms using the first and second q-Bessel functions. The behavior of the Fourier transforms with respect to partial derivatives and multiplication with variables is studied. The Fourier transform acts between the two representation spaces for the harmonic oscillator on quantum Euclidean space. By using this property it is possible to define a Fourier transform on the entire Hilbert space of the harmonic oscillator, which is its own inverse and satisfies the Parseval theorem.

Kevin Coulembier

2011-05-03

3

Quantum Fourier Transform Over Galois Rings  

E-print Network

Galois rings are regarded as "building blocks" of a finite commutative ring with identity. There have been many papers on classical error correction codes over Galois rings published. As an important warm-up before exploring quantum algorithms and quantum error correction codes over Galois rings, we study the quantum Fourier transform (QFT) over Galois rings and prove it can be efficiently preformed on a quantum computer. The properties of the QFT over Galois rings lead to the quantum algorithm for hidden linear structures over Galois rings.

Yong Zhang

2009-04-16

4

The classical and quantum Fourier transform Ronald de Wolf  

E-print Network

The classical and quantum Fourier transform Ronald de Wolf February 22, 2011 1 The classical Fourier transform 1.1 The discrete Fourier transform The Fourier transform occurs in many different to complexity theory. For our purposes, the Fourier transform is going to be an N Ã? N unitary matrix, all

de Wolf, Ronald

5

On Admissible States of Quantum Fourier Transform  

E-print Network

We present a general methodology to obtain the basis of qudits which are admissible to Quantum Fourier Transform (QFT). We first study this method for qubits to characterize the ensemble that works for the Hadamard transformation (QFT for two dimension). In this regard we identify certain incompleteness in the result of Maitra and Parashar (IJQI, 2006). Next we characterize the ensemble of qutrits for which QFT is possible. Further, some theoretical results related to higher dimensions are also discussed.

Arpita Maitra; Santanu Sarkar

2011-09-21

6

Purple bacteria and quantum Fourier transform  

E-print Network

The LH-II of purple bacteria Rhodospirillum (Rs.) molischianum and Rhodopseudomonas (Rps.) acidophila adopts a highly symmetrical ring shape, with a radius of about 7 nm. In the case of Rps. acidophila the ring has a ninefold symmetry axis, and in LH-II from Rs. molischianum the ring has an eightfold symmetry axis. These rings are found to exibit two bands of excitons. A simplified mathematical description of the exciton states is given in Hu, X. & Schulten, K. (1997) Physics Today 50, 28-34. Using this description, we will show, by suitable labeling of the lowest energy (Qy) excited states of individual BChls, that the resulting exciton states are the quantum Fourier transform of the BChls excited states. For Rs. molischianum ring exciton states will be modeled as the four qubit quantum Fourier transform and the explicit circuit will be derived. Exciton states for Rps. acidophila ring cannot be modeled with an integer number of qubits. Both quantum Fourier transforms are instances of the hidden subgroup problem and this opens up a possibility that both purple bacteria implement an efficient quantum circuit for light harvesting.

Samir Lipovaca

2007-02-22

7

Fourier-transform quantum state tomography  

NASA Astrophysics Data System (ADS)

We propose a technique for performing quantum state tomography of photonic polarization-encoded multiqubit states. Our method uses a single rotating wave plate, a polarizing beam splitter, and two photon-counting detectors per photon mode. As the wave plate rotates, the photon counters measure a pseudocontinuous signal which is then Fourier transformed. The density matrix of the state is reconstructed using the relationship between the Fourier coefficients of the signal and the Stokes’ parameters that represent the state. The experimental complexity, i.e., different wave plate rotation frequencies, scales linearly with the number of qubits.

Mohammadi, Mohammadreza; Bra?czyk, Agata M.; James, Daniel F. V.

2013-01-01

8

The Discrete or Quantum Fourier Transform Frank Rioux  

E-print Network

The Discrete or Quantum Fourier Transform Frank Rioux The continuous-variable Fourier transformsx x dx p p dp we can write the following generic Fourier transforms. andp p x x dx x x p p dp By analogy a discrete Fourier transform between the k and j indices can be created. 1 0 N j k k j j were

Rioux, Frank

9

Quantum Mechanics and the Fourier Transform Frank Rioux  

E-print Network

Quantum Mechanics and the Fourier Transform Frank Rioux Wave-particle duality as expressed and momentum, and energy and time. The vehicle for this extension will turn out to be the Fourier transform examples of Fourier transforms. They are dictionaries for translating between two different languages

Rioux, Frank

10

Quantum operation, quantum Fourier transform and semi-definite programming  

E-print Network

We analyze a class of quantum operations based on a geometrical representation of $d-$level quantum system (or qudit for short). A sufficient and necessary condition of complete positivity, expressed in terms of the quantum Fourier transform, is found for this class of operations. A more general class of operations on qudits is also considered and its completely positive condition is reduced to the well-known semi-definite programming problem.

Runyao Duan; Zhengfeng Ji; Yuan Feng; Mingsheng Ying

2003-04-22

11

Cavity QED implementation of the discrete quantum Fourier transform  

E-print Network

We present a scheme for the implementation of the discrete quantum Fourier transform using cavity quantum electrodynamics. In the proposed scheme a series of atoms whose atomic coherence carries the input state passes through a series of cavities...

Scully, Marlan O.; Zubairy, M. Suhail

2002-01-01

12

Quantum Fourier transform and tomographic Renyi entropic inequalities  

E-print Network

Renyi entropy associated with spin tomograms of quantum states is shown to obey to new inequalities containing the dependence on quantum Fourier transform. The limiting inequality for the von Neumann entropy of spin quantum states and a new kind of entropy associated with quantum Fourier transform are obtained. Possible connections with subadditivity and strong subadditivity conditions for tomographic entropies and von Neumann entropies are discussed.

M. A. Man'ko; V. I. Man'ko

2009-02-25

13

Quantum process tomography of the quantum Fourier transform.  

PubMed

The results of quantum process tomography on a three-qubit nuclear magnetic resonance quantum information processor are presented and shown to be consistent with a detailed model of the system-plus-apparatus used for the experiments. The quantum operation studied was the quantum Fourier transform, which is important in several quantum algorithms and poses a rigorous test for the precision of our recently developed strongly modulating control fields. The results were analyzed in an attempt to decompose the implementation errors into coherent (overall systematic), incoherent (microscopically deterministic), and decoherent (microscopically random) components. This analysis yielded a superoperator consisting of a unitary part that was strongly correlated with the theoretically expected unitary superoperator of the quantum Fourier transform, an overall attenuation consistent with decoherence, and a residual portion that was not completely positive-although complete positivity is required for any quantum operation. By comparison with the results of computer simulations, the lack of complete positivity was shown to be largely a consequence of the incoherent errors which occurred over the full quantum process tomography procedure. These simulations further showed that coherent, incoherent, and decoherent errors can often be identified by their distinctive effects on the spectrum of the overall superoperator. The gate fidelity of the experimentally determined superoperator was 0.64, while the correlation coefficient between experimentally determined superoperator and the simulated superoperator was 0.79; most of the discrepancies with the simulations could be explained by the cumulative effect of small errors in the single qubit gates. PMID:15446906

Weinstein, Yaakov S; Havel, Timothy F; Emerson, Joseph; Boulant, Nicolas; Saraceno, Marcos; Lloyd, Seth; Cory, David G

2004-10-01

14

Quantum Fourier transform, Heisenberg groups and quasiprobability distributions  

E-print Network

This paper aims to explore the inherent connection among Heisenberg groups, quantum Fourier transform and (quasiprobability) distribution functions. Distribution functions for continuous and finite quantum systems are examined first as a semiclassical approach to quantum probability distribution. This leads to studying certain functionals of a pair of "conjugate" observables, connected via the quantum Fourier transform. The Heisenberg groups emerge naturally from this study and we take a rapid look at their representations. The quantum Fourier transform appears as the intertwining operator of two equivalent representation arising out of an automorphism of the group. Distribution functions correspond to certain distinguished sets in the group algebra. The marginal properties of a particular class of distribution functions (Wigner distributions) arise from a class of automorphisms of the group algebra of the Heisenberg group. We then study the reconstruction of Wigner function from the marginal distributions via inverse Radon transform giving explicit formulas. We consider applications of our approach to quantum information processing and quantum process tomography.

Manas K. Patra; Samuel L. Braunstein

2010-04-30

15

Efficient classical simulation of the approximate quantum Fourier transform  

E-print Network

We present a method for classically simulating quantum circuits based on the tensor contraction model of Markov and Shi (quant-ph/0511069). Using this method we are able to classically simulate the approximate quantum Fourier transform in polynomial time. Moreover, our approach allows us to formulate a condition for the composability of simulable quantum circuits. We use this condition to show that any circuit composed of a constant number of approximate quantum Fourier transform circuits and log-depth circuits with limited interaction range can also be efficiently simulated.

Nadav Yoran; Anthony J. Short

2006-11-23

16

CS294-4: Fourier Transforms and Theoretical Computer Science Spring 1999 Lecture 11: Quantum Algorithms  

E-print Network

CS294-4: Fourier Transforms and Theoretical Computer Science Spring 1999 Lecture 11: Quantum of the major quantum algorithms. We will discuss the next algorithms: #15; Computation of Fourier Transform #15 Computation of Fourier Transform We consider two kinds of Fourier Transforms: #15; Fourier Transform over ZZ N

Vazirani, Umesh

17

Quantum fast Fourier transform using multilevel atoms ASHOK MUTHUKRISHNAN and C. R. STROUD, JR.  

E-print Network

Quantum fast Fourier transform using multilevel atoms ASHOK MUTHUKRISHNAN and C. R. STROUD, JR of the quantum fast Fourier transform algorithm in an entangled system of multilevel atoms. The Fourier transform packets amounts to a discrete quantum Fourier transform within each atom. The algorithm then reduces

Stroud, Carlos R.

18

An approximate Fourier transform useful in quantum factoring  

Microsoft Academic Search

We define an approximate version of the Fourier transform on $2^L$ elements, which is computationally attractive in a certain setting, and which may find application to the problem of factoring integers with a quantum computer as is currently under investigation by Peter Shor. (1994 IBM Internal Report)

D. Coppersmith

2002-01-01

19

Quantum Discrete Fourier Transform with Classical Output for Signal Processing  

E-print Network

Discrete Fourier transform (DFT) is the base of modern signal or information processing. 1-Dimensional fast Fourier transform (1D FFT) and 2D FFT have time complexity O(NlogN) and O(N^2logN) respectively. Quantum 1D and 2D DFT algorithms with classical output (1D QDFT and 2D QDFT) are presented in this paper. And quantum algorithm for convolution estimation is also presented in this paper. Compared with FFT, QDFT has two advantages at least. One of advantages is that 1D and 2D QDFT has time complexity O(sqrt(N)) and O(N) respectively. The other advantage is that QDFT can process very long signal sequence at a time. QDFT and quantum convolution demonstrate that quantum signal processing with classical output is possible.

Chao-Yang Pang; Ben-Qiong Hu

2007-06-17

20

Quantum control in two-dimensional Fourier-transform spectroscopy  

SciTech Connect

We present a method that harnesses coherent control capability to two-dimensional Fourier-transform optical spectroscopy. For this, three ultrashort laser pulses are individually shaped to prepare and control the quantum interference involved in two-photon interexcited-state transitions of a V-type quantum system. In experiments performed with atomic rubidium, quantum control for the enhancement and reduction of the 5P{sub 1/2}{yields} 5P{sub 3/2} transition was successfully tested in which the engineered transitions were distinguishably extracted in the presence of dominant one-photon transitions.

Lim, Jongseok; Lee, Han-gyeol; Lee, Sangkyung; Ahn, Jaewook [Department of Physics, KAIST, Daejeon 305-701 (Korea, Republic of)

2011-07-15

21

Discrete quantum Fourier transform in coupled semiconductor double quantum dot molecules  

E-print Network

In this Letter, we present a physical scheme for implementing the discrete quantum Fourier transform in a coupled semiconductor double quantum dot system. The main controlled-R gate operation can be decomposed into many simple and feasible unitary transformations. The current scheme would be a useful step towards the realization of complex quantum algorithms in the quantum dot system.

Ping Dong; Ming Yang; Zhuo-Liang Cao

2007-04-17

22

On the Fourier Transform Approach to Quantum Error Control  

E-print Network

Quantum codes are subspaces of the state space of a quantum system that are used to protect quantum information. Some common classes of quantum codes are stabilizer (or additive) codes, non-stabilizer (or non-additive) codes obtained from stabilizer codes, and Clifford codes. These are analyzed in a framework using the Fourier transform on finite groups, the finite group in question being a subgroup of the quantum error group considered. All the classes of codes that can be obtained in this framework are explored, including codes more general than Clifford codes. The error detection properties of one of these more general classes ("direct sums of translates of Clifford codes") are characterized. Examples codes are constructed, and computer code search results presented and analysed.

Hari Dilip Kumar

2012-08-24

23

Fast Quantum Fourier Transforms for a Class of non-abelian Groups  

E-print Network

Fast Quantum Fourier Transforms for a Class of non-abelian Groups Markus Puschel 1 , Martin R@ira.uka.de Abstract. An algorithm is presented allowing the construction of fast Fourier transforms for any solvable, fast quantum Fourier transforms for all 4 classes of non- abelian 2-groups with cyclic normal subgroup

Püschel, Markus

24

The Amplified Quantum Fourier Transform: solving the local period problem  

E-print Network

This paper creates and analyses a new quantum algorithm called the Amplified Quantum Fourier Transform (Amplified-QFT) for solving the following problem: The Local Period Problem: Let L = {0,1...N-1} be a set of N labels and let A be a subset of M labels of period P, i.e. a subset of the form A = {j : j = s + rP; r = 0,1...M-1} where P {0,1} which is 1 on A and 0 elsewhere, find the local period P. A separate algorithm finds the offset s. The first part of the paper defines the Amplified-QFT algorithm. The second part of the paper summarizes the main results and compares the Amplified-QFT algorithm against the Quantum Fourier Transform (QFT) and Quantum Hidden Subgroup (QHS) algorithms when solving the local period problem. It is shown that the Amplified-QFT is, on average, quadratically faster than both the QFT and QHS algorithms. The third part of the paper provides the detailed proofs of the main results, describes the method of recovering P from an observation y and describes the method for recovering the offset s.

David J. Cornwell

2010-09-30

25

The Fourier transform of the Hadamard transform: Multifractals, Sequences and Quantum Chaos  

E-print Network

We introduce a class of functions that limit to multifractal measures and which arise when one takes the Fourier transform of the Hadamard transform. This introduces generalizations of the Fourier transform of the well-studied and ubiquitous Thue-Morse sequence, and introduces also generalizations to other intriguing sequences. We show their relevance to quantum chaos, by displaying quantum eigenfunctions of the quantum bakers map that are approximated well by such measures, thereby extending our recent work where we pointed to the existence of ``Thue-Morse'' states.

N. Meenakshisundaram; Arul Lakshminarayan

2005-10-05

26

Quantum Pseudo-fractional Fourier Transform and its application to quantum phase estimation  

E-print Network

- In this paper we present a method to compute the coefficients of the fractional Fourier transform (FrFT) on a quantum computer using quantum gates of polynomial complexity of the order O(n^3). The FrFt, a generalization of the DFT, has wide applications in signal processing and is particularly useful to implement the Pseudopolar and Radon transforms. Even though the FrFT is a non-unitary operation, to develop its quantum counterpart, we develop a unitary operator called the quantum Pseudo-fraction Fourier Transform (QPFrFT) in a higher-dimensional Hilbert space, in order to computer the coefficients of the FrFT. In this process we develop a unitary operator denoted U by which is an essential step to implement the QPFrFT. We then show the application of the operator U in the problem of quantum phase estimation.

Srinivas V. Parasa; K. Eswaran

2009-06-05

27

Evolution of a Human-Competitive Quantum Fourier Transform Algorithm Using Genetic Programming  

E-print Network

Evolution of a Human-Competitive Quantum Fourier Transform Algorithm Using Genetic Programming Paul, UK, YO10 5DD {psm111 | jac | susan}@cs.york.ac.uk ABSTRACT In this paper, we show how genetic-competitive Quantum Fourier Transform (QFT) algorithm evolved by GP. Categories and Subject Descriptors D.1.m

Fernandez, Thomas

28

Matching-pursuit/split-operator Fourier-transform simulations of nonadiabatic quantum dynamics  

E-print Network

for simulations of adiabatic quantum dynamics in multidimensional systems. The MP/SOFT propagation schemeMatching-pursuit/split-operator Fourier-transform simulations of nonadiabatic quantum dynamics March 2005 A rigorous and practical approach for simulations of nonadiabatic quantum dynamics

Wu, Yinghua

29

Scale invariance and efficient classical simulation of the quantum Fourier transform  

E-print Network

We provide numerical evidence that the quantum Fourier transform can be efficiently represented in a matrix product operator with a size growing relatively slowly with the number of qubits. Additionally, we numerically show that the tensors in the operator converge to a common tensor as the number of qubits in the transform increases. Together these results imply that the application of the quantum Fourier transform to a matrix product state with $n$ qubits of maximum Schmidt rank $\\chi$ can be simulated in $O(n (log(n))^2 \\chi^2)$ time. We perform such simulations and quantify the error involved in representing the transform as a matrix product operator and simulating the quantum Fourier transform of periodic states.

Kieran J. Woolfe; Charles D. Hill; Lloyd C. L. Hollenberg

2014-06-04

30

Large quantum Fourier transforms are never exactly realized by braiding conformal blocks  

SciTech Connect

Fourier transform is an essential ingredient in Shor's factoring algorithm. In the standard quantum circuit model with the gate set {l_brace}U(2), controlled-NOT{r_brace}, the discrete Fourier transforms F{sub N}=({omega}{sup ij}){sub NxN}, i,j=0,1,...,N-1, {omega}=e{sup 2{pi}}{sup i} at {sup {approx}}{sup sol{approx}} at {sup N}, can be realized exactly by quantum circuits of size O(n{sup 2}), n=ln N, and so can the discrete sine or cosine transforms. In topological quantum computing, the simplest universal topological quantum computer is based on the Fibonacci (2+1)-topological quantum field theory (TQFT), where the standard quantum circuits are replaced by unitary transformations realized by braiding conformal blocks. We report here that the large Fourier transforms F{sub N} and the discrete sine or cosine transforms can never be realized exactly by braiding conformal blocks for a fixed TQFT. It follows that an approximation is unavoidable in the implementation of Fourier transforms by braiding conformal blocks.

Freedman, Michael H. [Microsoft Project Q, Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106-4030 (United States); Wang, Zhenghan [Microsoft Project Q, Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106-4030 (United States); Department of Mathematics, Indiana University, Bloomington, Indiana 47405 (United States)

2007-03-15

31

Analysis of electronic structures of quantum dots using meshless Fourier transform k·p method  

NASA Astrophysics Data System (ADS)

We develop a complete Fourier transform k.p method and present its application for a theoretical investigation on electronic structures of quantum dots with consideration of the built-in strain effects. The Fourier transform technique is applied to the periodic position-dependent Hamiltonian, and a simple and neat expression of the Hamiltonian matrix in the Fourier domain is formulated due to the orthogonality of exponential functions. Spurious solutions can be avoided due to the truncation of high Fourier frequencies. A kinetic Hamiltonian matrix in momentum domain is formulated by entering the analytical Fourier transform of the quantum-dot shape function into the neat Hamiltonian matrix easily, which allows meshless numerical implementation. The formulation of strain Hamiltonian matrix is done by convolution of Fourier series of strain components and Fourier series of the quantum-dot shape functions. Therefore, an original Fourier transform-based k.p approach is developed by combining the kinetic Hamiltonian matrix and the strain Hamiltonian. This approach is adopted to study the dimension effect and strain effect on the ground states of electrons and holes of pyramidal quantum dots that are truncated to different heights. The ground-state energy variation shows that the electron state is the most sensitive to these effects and the strain effect on E1, LH1, and HH1 is more prominent for sharperquantum dots. This investigation shows that band mixing between the conduction band and valence band, and band mixing between heavy-hole and light-hole bands are reduced due to the strain effect, whereas this effect is more prominent for nontruncated pyramidal quantum dots due to the stress concentration. Among the three ground states, light-hole states are more weakly confined in the nonpyramidal quantum dot and shift to the tip of the pyramid due to the strain.

Zhao, Qiuji; Mei, Ting

2011-03-01

32

The fractional order Fourier transform and its application to quantum mechanics  

Microsoft Academic Search

The concept of Fourier transforms of fractional order is introduced, the ordinary Fourier transform being of order 1. The integral representation of this transform can be used to construct a table of fractional order Fourier transforms. A generalized operational calculus is developed, paralleling the familiar one for the ordinary transform. Its application provides a convenient technique for solving certain classes

VICTOR NAMIAS

1980-01-01

33

Fourier Transform Pairs The Fourier transform transforms a function of  

E-print Network

Fourier Transform Pairs The Fourier transform transforms a function of time, f(t), into a function of frequency, F(s): F {f(t)}(s) = F(s) = Z - f(t)e- j2st dt. The inverse Fourier transform transforms a func. The inverse Fourier transform of the Fourier trans- form is the identity transform: f(t) = Z - Z - f()e- j2s

Masci, Frank

34

Efficient classical simulation of the semi-classical Quantum Fourier Transform  

E-print Network

A number of elegant approaches have been developed for the identification of quantum circuits which can be efficiently simulated on a classical computer. Recently, these methods have been employed to demonstrate the classical simulability of the quantum Fourier transform (QFT). In this note, we show that one can demonstrate a number of simulability results for QFT circuits in a straightforward manner using Griffiths and Niu's semi-classical QFT construction [Phys. Rev. Lett. 76, 3228 (1996)]. We then discuss the consequences of these results in the context of Shor's factorisation algorithm.

Daniel E. Browne

2006-12-03

35

Analyzing Signals Fourier transform  

E-print Network

Page 1 1 Analyzing Signals Fourier transform s frequency content s linear combination of sin frequency analysis s windowed Fourier transform 6 #12;Page 4 7 Gabor Transform function to analyze window Gabor Transform Spatial domain Gabor domain b #12;Page 5 9 Gabor Transform Problems s discrete version

Sweldens, Wim

36

Detection and measurement of electroreflectance on quantum cascade laser device using Fourier transform infrared microscope  

SciTech Connect

We demonstrate the use of a Fourier Transform Infrared microscope system to detect and measure electroreflectance (ER) from mid-infrared quantum cascade laser (QCL) device. To characterize intersubband transition (ISBT) energies in a functioning QCL device, a microscope is used to focus the probe on the QCL cleaved mirror. The measured ER spectra exhibit resonance features associated to ISBTs under applied electric field in agreement with the numerical calculations and comparable to observed photocurrent, and emission peaks. The method demonstrates the potential as a characterization tool for QCL devices.

Enobio, Eli Christopher I.; Ohtani, Keita; Ohno, Yuzo; Ohno, Hideo, E-mail: ohno@riec.tohoku.ac.jp [Laboratory for Nanoelectronics and Spintronics, Research Institute of Electrical Communication, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577 (Japan)] [Laboratory for Nanoelectronics and Spintronics, Research Institute of Electrical Communication, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577 (Japan)

2013-12-02

37

Discrete Fourier Series & Discrete Fourier Transform Chapter Intended Learning Outcomes  

E-print Network

Discrete Fourier Series & Discrete Fourier Transform Chapter Intended Learning Outcomes (i) Understanding the relationships between the transform, discrete-time Fourier transform (DTFT), discrete Fourier series (DFS), discrete Fourier transform (DFT) and fast Fourier transform (FFT) (ii) Understanding

So, Hing-Cheung

38

Wavelet transforms versus Fourier transforms  

Microsoft Academic Search

This note is a very basic introduction to wavelets. It starts with an orthogonal basis of piecewise constant functions, constructed by dilation and translation. The ``wavelet transform'' maps each $f(x)$ to its coefficients with respect to this basis. The mathematics is simple and the transform is fast (faster than the Fast Fourier Transform, which we briefly explain), but approximation by

Gilbert Strang

1993-01-01

39

Migration by Fourier transform  

Microsoft Academic Search

Wave equation migration is known to be simpler in principle when the horizontal coordinate or coordinates are replaced by their Fourier conjugates. Two practical migration schemes utilizing this concept are developed. One scheme extends the Claerbout finite difference method, greatly reducing dispersion problems usually associated with this method at higher dips and frequencies. The second scheme effects a Fourier transform

R. H. Stolt

1978-01-01

40

Imaging Fourier transform spectrometer  

SciTech Connect

This invention is comprised of an imaging Fourier transform spectrometer having a Fourier transform infrared spectrometer providing a series of images to a focal plane array camera. The focal plane array camera is clocked to a multiple of zero crossing occurrences as caused by a moving mirror of the Fourier transform infrared spectrometer and as detected by a laser detector such that the frame capture rate of the focal plane array camera corresponds to a multiple of the zero crossing rate of the Fourier transform infrared spectrometer. The images are transmitted to a computer for processing such that representations of the images as viewed in the light of an arbitrary spectral ``fingerprint`` pattern can be displayed on a monitor or otherwise stored and manipulated by the computer.

Bennett, C.L.

1993-09-13

41

Fourier Transform Mass Spectrometry  

PubMed Central

This article provides an introduction to Fourier transform-based mass spectrometry. The key performance characteristics of Fourier transform-based mass spectrometry, mass accuracy and resolution, are presented in the view of how they impact the interpretation of measurements in proteomic applications. The theory and principles of operation of two types of mass analyzer, Fourier transform ion cyclotron resonance and Orbitrap, are described. Major benefits as well as limitations of Fourier transform-based mass spectrometry technology are discussed in the context of practical sample analysis, and illustrated with examples included as figures in this text and in the accompanying slide set. Comparisons highlighting the performance differences between the two mass analyzers are made where deemed useful in assisting the user with choosing the most appropriate technology for an application. Recent developments of these high-performing mass spectrometers are mentioned to provide a future outlook. PMID:21742802

Scigelova, Michaela; Hornshaw, Martin; Giannakopulos, Anastassios; Makarov, Alexander

2011-01-01

42

ENVIRONMENTAL ANALYSIS BY AB INITIO QUANTUM MECHANICAL COMPUTATION AND GAS CHROMATOGRAPHY/FOURIER TRANSFORM INFRARED SPECTROMETRY.  

EPA Science Inventory

Computational chemistry, in conjunction with gas chromatography/mass spectrometry/Fourier transform infrared spectrometry (GC/MS/FT-IR), was used to tentatively identify seven tetrachlorobutadiene (TCBD) isomers detected in an environmental sample. Computation of the TCBD infrare...

43

Fourier Transform Spectrometer  

NASA Technical Reports Server (NTRS)

Understanding the global atmospheric changes is difficult with today's current technology. However, with high resolution and nearly continuous observations from a satellite, it's possible to transform our understanding of the atmosphere. To enable the next generation of atmospheric science, a new class of orbiting atmospheric sensors is being developed. The foundation of this advanced concept is the Fourier Transform Spectrometer, or FTS.

1998-01-01

44

Coherent excitonic resonances of natural quantum dots studied with optical 2D Fourier transform spectroscopy  

NASA Astrophysics Data System (ADS)

Electronic structure and dynamics can be captured by optical 2D-Fourier-transform spectroscopy (2DFTS), which tracks the phase of the nonlinear signal during two time delays of a multi-pulse excitation sequence. We use optical 2DFTS [1] to study the coherent response of an ensemble of interfacial ``natural'' GaAs quantum dots (QD) [2], found within the monolayer fluctuations of a quantum well (QW). Low temperature (˜6K) spectra show excitonic resonances from both the QD and the QW. We simultaneously extract homogenous and inhomogeneous linewidths of both QW and QD states, indicating slow dephasing and size distribution in the QDs. Additionally, variation of the population time delay and lattice temperature reveals a coupling from the QW states to the lower energy QD mediated by incoherent phonon interactions. [1] S. T. Cundiff, T. Zhang, A. D. Bristow, D. Karaiskaj, X. Dai, Acc. Chem. Res. 42, 1423 (2009). [2] D. Gammon, E.S. Snow, B.V. Shanabrook, D.S. Katzer, and D. Park, PRL 76, 3005 (1996).

Siemens, Mark; Moody, Galan; Bristow, Alan; Dai, Xingcan; Karaiskaj, Denis; Cundiff, Steven; Bracker, Allan; Gammon, Daniel

2010-03-01

45

Fourier Transforms, Fourier Series and the FFT  

NSDL National Science Digital Library

The goal of this module is to give students an understanding of the one-dimensional Fourier Transform, both mathematically and computationally, with a focus on finding periodicity in data. To motivate the study of the Fourier Transform, the students will be presented with certain application areas, such as searching for periodic patterns in CO2 data and differentiating between two sound signals using their power spectra. Students will explore some computational issues and challenges of the Discrete and Fast Fourier Transforms.

De Pillis, Lisette; Radunskaya, Ami

46

The discrete fractional Fourier transform  

Microsoft Academic Search

We propose and consolidate a definition of the discrete fractional Fourier transform that generalizes the discrete Fourier transform (DFT) in the same sense that the continuous fractional Fourier transform generalizes the continuous ordinary Fourier transform. This definition is based on a particular set of eigenvectors of the DFT matrix, which constitutes the discrete counterpart of the set of Hermite-Gaussian functions.

Çagatay Candan; M. Alper Kutay; Haldun M. Ozaktas

2000-01-01

47

Discrete Fourier Transform Javier Montoya  

E-print Network

Discrete Fourier Transform Javier Montoya Photogrammetry and Remote Sensing ETH Zurich March 16, 2012 1 Introduction The Discrete form of the Fourier transform is known as Discrete Fourier Transform domain using the Inverse Discrete Fourier Transform (IDFT): f(x) = 1 N N-1 x=0 F(u)ej 2 N ux for u = 0, 1

Giger, Christine

48

Properties of the Fourier Transform  

E-print Network

Properties of the Fourier Transform 24.2 Introduction ' & $ % Prerequisites Before starting to . . . #12;1. Linearity Properties of the Fourier Transform (i) If f(t), g(t) are functions with transforms F Transform of the resulting function is simply the sum of the individual Fourier Transforms. (ii) If k is any

Vickers, James

49

Fourier Transform I  

NSDL National Science Digital Library

Created by Lang Moore for the Connected Curriculum Project, the purpose of this module is to study the Fourier transform and use it to describe solutions of the heat equation on an infinite rod. This is one of a much larger set of learning modules hosted by Duke University.

Moore, Lang

2010-07-02

50

Fourier Transform Mass Spectrometry.  

ERIC Educational Resources Information Center

Discusses the nature of Fourier transform mass spectrometry and its unique combination of high mass resolution, high upper mass limit, and multichannel advantage. Examines its operation, capabilities and limitations, applications (ion storage, ion manipulation, ion chemistry), and future applications and developments. (JN)

Gross, Michael L.; Rempel, Don L.

1984-01-01

51

Fourier Transform Infrared (FTIR) Spectroscopy  

E-print Network

Fourier Transform Infrared (FTIR) Spectroscopy Klaus Gerwert, Lehrstuhl fu¨r Biophysik, Ruhr Transform IR by Johannes Orphal. Fourier transform infrared (FTIR) spectroscopy is an experimental technique. Introduction The underlying principle of a Fourier transform infrared (FTIR) spectrometer is the separation

Gerwert, Klaus

52

Quantum Physics and Signal Processing in Rigged Hilbert Spaces by means of Special Functions, Lie Algebras and Fourier and Fourier-like Transforms  

E-print Network

Quantum Mechanics and Signal Processing in the line R, are strictly related to Fourier Transform and Weyl-Heisenberg algebra. We discuss here the addition of a new discrete variable that measures the degree of the Hermite functions and allows to obtain the projective algebra io(2). A Rigged Hilbert space is found and a new discrete basis in R obtained. The operators {O[R]} defined on R are shown to belong to the Universal Enveloping Algebra UEA[io(2)] allowing, in this way, their algebraic discussion. Introducing in the half-line a Fourier-like Transform, the procedure is extended to R^+ and can be easily generalized to R^n and to spherical reference systems.

Celeghini, Enrico

2014-01-01

53

Some Special Fourier Transform Pairs  

E-print Network

Some Special Fourier Transform Pairs 24.3 Introduction ' & $ % Prerequisites Before starting period. For a non-periodic real signal f(t) with Fourier Transform F() the corresponding result is - f2): Workbook Level 2 24.3: Some Special Fourier Transform Pairs 2 #12;Wehave F()=F{e-t u(t)}= 1 1+i , so |F()|2

Vickers, James

54

Continuous boundary local Fourier transform  

NASA Astrophysics Data System (ADS)

The Local Fourier Transform (LFT) provides a nice tool for concentrating both a signal and its Fourier transform. But there are certain properties of this algorithm that make it unattractive for various applications. In this paper, some of these disadvantages are explored, and a new approach to localized Fourier analysis is proposed, the continuous boundary local Fourier transform (CBLFT), which attempts to correct some of these shortcomings. Results ranging from segmentation to representation cost to compression are also presented.

Larson, Brons M.; Saito, Naoki

2001-12-01

55

Rainbow Fourier Transform  

NASA Technical Reports Server (NTRS)

We present a novel technique for remote sensing of cloud droplet size distributions. Polarized reflectances in the scattering angle range between 135deg and 165deg exhibit a sharply defined rainbow structure, the shape of which is determined mostly by single scattering properties of cloud particles, and therefore, can be modeled using the Mie theory. Fitting the observed rainbow with such a model (computed for a parameterized family of particle size distributions) has been used for cloud droplet size retrievals. We discovered that the relationship between the rainbow structures and the corresponding particle size distributions is deeper than it had been commonly understood. In fact, the Mie theory-derived polarized reflectance as a function of reduced scattering angle (in the rainbow angular range) and the (monodisperse) particle radius appears to be a proxy to a kernel of an integral transform (similar to the sine Fourier transform on the positive semi-axis). This approach, called the rainbow Fourier transform (RFT), allows us to accurately retrieve the shape of the droplet size distribution by the application of the corresponding inverse transform to the observed polarized rainbow. While the basis functions of the proxy-transform are not exactly orthogonal in the finite angular range, this procedure needs to be complemented by a simple regression technique, which removes the retrieval artifacts. This non-parametric approach does not require any a priori knowledge of the droplet size distribution functional shape and is computationally fast (no look-up tables, no fitting, computations are the same as for the forward modeling).

Alexandrov, Mikhail D.; Cairns, Brian; Mishchenko, Michael I.

2012-01-01

56

ContentsContents2424Fourier 1. The Fourier transform  

E-print Network

ContentsContents2424Fourier transforms 1. The Fourier transform 2. Properties of the Fourier Transform 3. Some Special Fourier Transform Pairs Learning outcomes needs doing Time allocation You mathematical topics this time may vary considerably. 1 #12;The Fourier Transform 24.1 Introduction

Vickers, James

57

Imaging Fourier Transform Spectrometer  

SciTech Connect

The operating principles of an Imaging Fourier Transform Spectrometer (IFTS) are discussed. The advantages and disadvantages of such instruments with respect to alternative imaging spectrometers are discussed. The primary advantages of the IFTS are the capacity to acquire more than an order of magnitude more spectral channels than alternative systems with more than an order of magnitude greater etendue than for alternative systems. The primary disadvantage of IFTS, or FTS in general, is the sensitivity to temporal fluctuations, either random or periodic. Data from the IRIFTS (ir IFTS) prototype instrument, sensitive in the infrared, are presented having a spectral sensitivity of 0.01 absorbance units, a spectral resolution of 6 cm{sup {minus}1} over the range 0 to 7899 cm{sup {minus}1}, and a spatial resolution of 2.5 mr.

Bennett, C.L.; Carter, M.R.; Fields, D.J.; Hernandez, J.

1993-04-14

58

Fractional Fourier processing of quantum light.  

PubMed

We have extended Fourier transform of quantum light to a fractional Fourier processing, and demonstrated that a classical optical fractional Fourier processor can be used for the shaping of quantum correlations between two or more photons. Comparing the present method with that of Fourier processing, we find that fractional Fourier processing for quantum light possesses many advantages. Based on such a method, not only quantum correlations can be shaped more rich, but also the initial states can be easily identified. Moreover, the twisted phase information can be recovered and quantum states are easily controlled in performing quantum information experiments. Our findings open up new avenues for the manipulation of correlations between photons in optical quantum information processing. PMID:24515032

Sun, Yifan; Tao, Ran; Zhang, Xiangdong

2014-01-13

59

Quadratic discrete Fourier transform and mutually unbiased bases  

E-print Network

The present chapter [submitted for publication in "Fourier Transforms, Theory and Applications", G. Nikolic (Ed.), InTech (Open Access Publisher), Vienna, 2011] is concerned with the introduction and study of a quadratic discrete Fourier transform. This Fourier transform can be considered as a two-parameter extension, with a quadratic term, of the usual discrete Fourier transform. In the case where the two parameters are taken to be equal to zero, the quadratic discrete Fourier transform is nothing but the usual discrete Fourier transform. The quantum quadratic discrete Fourier transform plays an important role in the field of quantum information. In particular, such a transformation in prime dimension can be used for obtaining a complete set of mutually unbiased bases.

Maurice Robert Kibler

2010-10-28

60

Fast Numerical Nonlinear Fourier Transforms  

E-print Network

The nonlinear Fourier transform, which is also known as the forward scattering transform, decomposes a periodic signal into nonlinearly interacting waves. In contrast to the common Fourier transform, these waves no longer have to be sinusoidal. Physically relevant waveforms are often available for the analysis instead. The details of the transform depend on the waveforms underlying the analysis, which in turn are specified through the implicit assumption that the signal is governed by a certain evolution equation. For example, water waves generated by the Korteweg-de Vries equation can be expressed in terms of cnoidal waves. Light waves in optical fiber governed by the nonlinear Schr\\"dinger equation (NSE) are another example. Nonlinear analogs of classic problems such as spectral analysis and filtering arise in many applications, with information transmission in optical fiber, as proposed by Yousefi and Kschischang, being a very recent one. The nonlinear Fourier transform is eminently suited to address them ...

Wahls, Sander

2014-01-01

61

Fourier transforms of UD integrals  

E-print Network

UD integrals published by N. Usyukina and A. Davydychev in 1992-1993 are integrals corresponding to ladder-type Feynman diagrams. The results are UD functions $\\Phi^{(L)},$ where $L$ is the number of loops. They play an important role in N=4 supersymmetic Yang-Mills theory. The integrals were defined and calculated in the momentum space. In this paper the position space representation of UD functions is investigated. We show that Fourier transforms of UD functions are UD functions of space-time intervals but this correspondence is indirect. For example, the Fourier transform of the second UD integral is the second UD integral.

Igor Kondrashuk; Anatoly Kotikov

2008-02-23

62

Multi-dimensional real Fourier transform  

NASA Technical Reports Server (NTRS)

Four subroutines compute one-dimensional and multi-dimensional Fourier transforms for real data, multi-dimensional complex Fourier transforms, and multi-dimensional sine, cosine and sine-cosine transforms. Subroutines use Cooley-Tukey fast Fourier transform. In all but one-dimensional case, transforms are calculated in up to six dimensions.

Krogh, F. T.

1971-01-01

63

A Fast Fourier Transform Compiler  

Microsoft Academic Search

The FFTW library for computing the discrete Fourier transform (DFT) has gained a wide acceptance in both academia and industry, because it provides excellent performance on a variety of machines (even competitive with or faster than equivalent libraries supplied by vendors). In FFTW, most of the performance-critical code was generated automatically by a special-purpose compiler, called genfft, that outputs C

Matteo Frigo

1999-01-01

64

Fractional Fourier Transform and Geometric Quantization  

E-print Network

Generalized Fourier transformation between the position and the momentum representation of a quantum state is constructed in a coordinate independent way. The only ingredient of this construction is the symplectic (canonical) geometry of the phase-space: no linear structure is necessary. It is shown that the "fractional Fourier transform" provides a simple example of this construction. As an application of this techniques we show that for any linear Hamiltonian system, its quantum dynamics can be obtained exactly as the lift of the corresponding classical dynamics by means of the above transformation. Moreover, it can be deduced from the free quantum evolution. This way new, unknown symmetries of the Schr\\"odinger equation can be constructed. It is also argued that the above construction defines in a natural way a connection in the bundle of quantum states, with the base space describing all their possible representations. The non-flatness of this connection would be responsible for the non-existence of a quantum representation of the complete algebra of classical observables.

Witold Chmielowiec; Jerzy Kijowski

2010-02-20

65

A Short Biography of Joseph Fourier and Historical Development of Fourier Series and Fourier Transforms  

ERIC Educational Resources Information Center

This article deals with a brief biographical sketch of Joseph Fourier, his first celebrated work on analytical theory of heat, his first great discovery of Fourier series and Fourier transforms. Included is a historical development of Fourier series and Fourier transforms with their properties, importance and applications. Special emphasis is made…

Debnath, Lokenath

2012-01-01

66

Fourier Transform, Riemann Surfaces and Indefinite Metric  

E-print Network

Fourier Transform, Riemann Surfaces and Indefinite Metric P. G. Grinevich, S.P.Novikov Zakharov Park, College Park, USA #12;What is Fourier Transform in Riemann Surfaces? Which Problems need it. Continuous Fourier Transform on Riemann Surfaces was con- structed in our work (GN, 2003). As we found

Fominov, Yakov

67

Introduction to the Discrete Fourier Transform  

E-print Network

Introduction to the Discrete Fourier Transform Lucas J. van Vliet www.ph.tn.tudelft.nl/~lucas TU Discrete Fourier Transform 2 TU Delft Pattern Recognition Group Linear Shift Invariant System A discrete and h impulse at position n amplitude at position n #12;Discrete Fourier Transform 3 TU Delft Pattern

van Vliet, Lucas J.

68

Birefringent Fourier-transform imaging spectrometer  

E-print Network

Birefringent Fourier-transform imaging spectrometer Andrew Robert Harvey and David William Fletcher.r.Harvey@hw.ac.uk http://www.ece.eps.hw.ac.uk/~arharvey Abstract: Fourier-transform imaging spectrometers offer important, for application in harsh environments, deployment of Fourier-transform instruments based on traditional moving

Harvey, Andy

69

Lecture 2: Fourier transforms and frequency response  

E-print Network

Lecture 2: Fourier transforms and frequency response Course at a glance Discrete-time signals and systems Fourier-domain representation DFT/FFT System structures Filter structures Filter design Filter z-transform Sampling and reconstruction System analysis System Fourier transforms and frequency response Frequency

Fan, Xingzhe

70

Comparison theorem between Fourier transform and Fourier transform with compact support  

E-print Network

Comparison theorem between Fourier transform and Fourier transform with compact support Christine Huyghe December 4, 2012 Abstract We prove a comparison theorem between Fourier transform without support and and Fourier transform with compact support in the context of arithmetic D-modules. R´esum´e Nous d

Paris-Sud XI, Université de

71

JPL Fourier transform ultraviolet spectrometer  

NASA Technical Reports Server (NTRS)

The Fourier Transform Ultraviolet Spectrometer (FTUVS) is a new high resolution interferometric spectrometer for multiple-species detection in the UV, visible and near-IR. As an OH sensor, measurements can be carried out by remote sensing (limb emission and column absorption), or in-situ sensing (long-path absorption or laser-induced fluorescence). As a high resolution detector in a high repetition rate (greater than 10 kHz) LIF system, OH fluorescence can be discriminated against non-resonant background emission and laser scatter, permitting (0, 0) excitation.

Cageao, R. P.; Friedl, R. R.; Sander, Stanley P.; Yung, Y. L.

1994-01-01

72

Fourier Transform Mass Spectrometry Lab  

NSDL National Science Digital Library

This Web site discusses Boston University's Fourier Transform Mass Spectrometry (FTMS) Lab's devotion to the improvement of FTMS instrumentation and methods for its everyday biochemical functions. After discovering the importance of FTMS, visitors can find out about the lab's work in the enhancement of electrospray ion source and Cryogenic FTMS. Students can learn about the modern biochemistry's utilization of both traditional instrumentation such as gel electrophoresis and the latest devices including high performance chromatography, nuclear magnetic resonance, and X-ray crystallography. By downloading the Boston University Data Analysis (B.U.D.A.), researchers can participate in the development of analysis software for FTMS.

73

The Fast Fourier Transform Telescope  

E-print Network

We propose an all-digital telescope for 21 cm tomography, which combines key advantages of both single dishes and interferometers. The electric field is digitized by antennas on a rectangular grid, after which a series of Fast Fourier Transforms recovers simultaneous multifrequency images of up to half the sky. Thanks to Moore's law, the bandwidth up to which this is feasible has now reached about 1 GHz, and will likely continue doubling every couple of years. The main advantages over a single dish telescope are cost and orders of magnitude larger field-of-view, translating into dramatically better sensitivity for large-area surveys. The key advantages over traditional interferometers are cost (the correlator computational cost for an N-element array scales as N log N rather than N^2) and a compact synthesized beam. We argue that 21 cm tomography could be an ideal first application of a very large Fast Fourier Transform Telescope, which would provide both massive sensitivity improvements per dollar and mitigate the off-beam point source foreground problem with its clean beam. Another potentially interesting application is cosmic microwave background polarization.

Max Tegmark; Matias Zaldarriaga

2008-05-29

74

Tunable fractional-order Fourier transformer  

SciTech Connect

A fractional two-dimensional Fourier transformer whose orders are tuned by means of optical quadrupoles is described. It is shown that in the optical scheme considered, the Fourier-transform order a element of [0,1] in one of the mutually orthogonal planes corresponds to the transform order (2-a) in another plane, i.e., to inversion and inverse Fourier transform of the order a. (laser modes and beams)

Malyutin, A A [A.M. Prokhorov General Physics Institute, Russian Academy of Sciences, Moscow (Russian Federation)

2006-01-31

75

Frequency and impulse responses Are a Fourier transform pair  

E-print Network

Frequency and impulse responses Are a Fourier transform pair Fourier transform is periodic Sufficient condition for Fourier transform Condition for the convergence of the infinite sum X[n] is absolutely summable, then its Fourier transform exists (sufficient condition

Fan, Xingzhe

76

Laser Field Imaging Through Fourier Transform Heterodyne  

SciTech Connect

The authors present a detection process capable of directly imaging the transverse amplitude, phase, and Doppler shift of coherent electromagnetic fields. Based on coherent detection principles governing conventional heterodyned RADAR/LADAR systems, Fourier Transform Heterodyne incorporates transverse spatial encoding of the reference local oscillator for image capture. Appropriate selection of spatial encoding functions allows image retrieval by way of classic Fourier manipulations. Of practical interest: (1) imaging may be accomplished with a single element detector/sensor requiring no additional scanning or moving components, (2) as detection is governed by heterodyne principles, near quantum limited performance is achievable, (3) a wide variety of appropriate spatial encoding functions exist that may be adaptively configured in real-time for applications requiring optimal detection, and (4) the concept is general with the applicable electromagnetic spectrum encompassing the RF through optical.

Cooke, B.J.; Laubscher, B.E.; Olivas, N.L.; Galbraith, A.E.; Strauss, C.E.; Grubler, A.C.

1999-04-05

77

Large Fourier transforms never exactly realized by braiding conformal blocks  

E-print Network

Fourier transform is an essential ingredient in Shor's factoring algorithm. In the standard quantum circuit model with the gate set $\\{\\U(2), \\textrm{CNOT}\\}$, the discrete Fourier transforms $F_N=(\\omega^{ij})_{N\\times N},i,j=0,1,..., N-1, \\omega=e^{\\frac{2\\pi i}{N}}$, can be realized exactly by quantum circuits of size $O(n^2), n=\\textrm{log}N$, and so can the discrete sine/cosine transforms. In topological quantum computing, the simplest universal topological quantum computer is based on the Fibonacci (2+1)-topological quantum field theory (TQFT), where the standard quantum circuits are replaced by unitary transformations realized by braiding conformal blocks. We report here that the large Fourier transforms $F_N$ and the discrete sine/cosine transforms can never be realized exactly by braiding conformal blocks for a fixed TQFT. It follows that approximation is unavoidable to implement the Fourier transforms by braiding conformal blocks.

Michael H. Freedman; Zhenghan Wang

2006-09-18

78

Digital computation of the fractional Fourier transform  

Microsoft Academic Search

An algorithm for efficient and accurate computation of the fractional Fourier transform is given. For signals with time-bandwidth product N, the presented algorithm computes the fractional transform in O(NlogN) time. A definition for the discrete fractional Fourier transform that emerges from our analysis is also discussed

Haldun M. Ozaktas; O. Arikan; M. Alper Kutay; G. Bozdagt

1996-01-01

79

Fourier Analysis and Structure Determination: Part I: Fourier Transforms.  

ERIC Educational Resources Information Center

Provides a brief introduction with some definitions and properties of Fourier transforms. Shows relations, ways of understanding the mathematics, and applications. Notes proofs are not included but references are given. First of three part series. (MVL)

Chesick, John P.

1989-01-01

80

Quantum Algorithms, Symmetry, and Fourier Analysis  

NASA Astrophysics Data System (ADS)

I describe the role of symmetry in two quantum algorithms, with a focus on how that symmetry is made manifest by the Fourier transform. The Fourier transform can be considered in a wider context than the familiar one of functions on Rn or Z/nZ ; instead it can be defined for an arbitrary group where it is known as representation theory.. The first quantum algorithm solves an instance of the hidden subgroup problem—distinguishing conjugates of the Borel subgroup from each other in groups related to PSL(2; q). I use the symmetry of the subgroups under consideration to reduce the problem to a mild extension of a previously solved problem. This generalizes a result of Moore, Rockmore, Russel and Schulman by switching to a more natural measurement that also applies to prime powers. In contrast to the first algorithm, the second quantum algorithm is an attempt to use naturally continuous spaces. Quantum walks have proved to be a useful tool for designing quantum algorithms. The natural equivalent to continuous time quantum walks is evolution with the Schrödinger equation, under the kinetic energy Hamiltonian for a massive particle. I take advantage of quantum interference to find the center of spherical shells in high dimensions. Any implementation would be likely to take place on a discrete grid, using the ability of a digital quantum computer to simulate the evolution of a quantum system. In addition, I use ideas from the second algorithm on a different set of starting states, and find that quantum evolution can be used to sample from the evolute of a plane curve. The method of stationary phase is used to determine scaling exponents characterizing the precision and probability of success for this procedure.

Denney, Aaron

81

H. C. So Page 1 Semester B 2011-2012 Discrete Fourier Series & Discrete Fourier Transform  

E-print Network

H. C. So Page 1 Semester B 2011-2012 Discrete Fourier Series & Discrete Fourier Transform Chapter Intended Learning Outcomes (i) Understanding the relationships between the transform, discrete-time Fourier transform (DTFT), discrete Fourier series (DFS), discrete Fourier transform (DFT) and fast Fourier transform

So, Hing-Cheung

82

The Fourier Transform The Fourier transform is crucial to any discussion of time series analysis, and this chapter discusses the  

E-print Network

The Fourier Transform The Fourier transform is crucial to any discussion of time series analysis: Fourier Series Fourier Transform Example and Interpretation Oddness and Evenness The Convolution Theorem Discrete Fourier Transforms Definitions Example Implementation Author Ã? Fourier Series Recall the Fourier

Masci, Frank

83

Fourier transform channeled spectropolarimetry in the MWIR  

E-print Network

forms of spectroscopic measurement, such as a diffraction grating spectrometer, in the MWIR. Luo, et al, "Polarization acquisition using a commercial Fourier transform spectrometer in the MWIR. Chapman et al, "Data processing pipeline for a time-sampled imaging Fourier transform spectrometer

Dereniak, Eustace L.

84

The Fourier Transform -A Primer Hagit Shatkay  

E-print Network

The Fourier Transform - A Primer Hagit Shatkay Department of Computer Science Brown University Department of Computer Science Brown University Providence, RI 02912 1 Introduction The Fourier transform applications is covered in numerous, stout books (such as Bra65, OS75, Wea83, BP85, Jac90]), and this paper can

Learned, John

85

Fourier transform and related integral transforms in superspace  

E-print Network

In this paper extensions of the classical Fourier, fractional Fourier and Radon transforms to superspace are studied. Previously, a Fourier transform in superspace was already studied, but with a different kernel. In this work, the fermionic part of the Fourier kernel has a natural symplectic structure, derived using a Clifford analysis approach. Several basic properties of these three transforms are studied. Using suitable generalizations of the Hermite polynomials to superspace (see [H. De Bie, F. Sommen, Hermite and Gegenbauer polynomials in superspace using Clifford analysis, J. Phys. A 40 (2007) 10441-10456]) an eigenfunction basis for the Fourier transform is constructed.

Hendrik De Bie

2008-05-13

86

The fractional Fourier transform and applications  

NASA Technical Reports Server (NTRS)

This paper describes the 'fractional Fourier transform', which admits computation by an algorithm that has complexity proportional to the fast Fourier transform algorithm. Whereas the discrete Fourier transform (DFT) is based on integral roots of unity e exp -2(pi)i/n, the fractional Fourier transform is based on fractional roots of unity e exp -2(pi)i(alpha), where alpha is arbitrary. The fractional Fourier transform and the corresponding fast algorithm are useful for such applications as computing DFTs of sequences with prime lengths, computing DFTs of sparse sequences, analyzing sequences with noninteger periodicities, performing high-resolution trigonometric interpolation, detecting lines in noisy images, and detecting signals with linearly drifting frequencies. In many cases, the resulting algorithms are faster by arbitrarily large factors than conventional techniques.

Bailey, David H.; Swarztrauber, Paul N.

1991-01-01

87

On the positivity of Fourier transforms  

E-print Network

Characterizing in a constructive way the set of real functions whose Fourier transforms are positive appears to be yet an open problem. Some sufficient conditions are known but they are far from being exhaustive. We propose two constructive sets of necessary conditions for positivity of the Fourier transforms and test their ability of constraining the positivity domain. One uses analytic continuation and Jensen inequalities and the other deals with Toeplitz determinants and the Bochner theorem. Applications are discussed, including the extension to the two-dimensional Fourier-Bessel transform and the problem of positive reciprocity, i.e. positive functions with positive transforms.

Bertrand G. Giraud; Robi Peschanski

2014-05-13

88

The Geostationary Fourier Transform Spectrometer  

NASA Technical Reports Server (NTRS)

The Geostationary Fourier Transform Spectrometer (GeoFTS) is an imaging spectrometer designed for an earth science mission to measure key atmospheric trace gases and process tracers related to climate change and human activity. The GeoFTS instrument is a half meter cube size instrument designed to operate in geostationary orbit as a secondary "hosted" payload on a commercial geostationary satellite mission. The advantage of GEO is the ability to continuously stare at a region of the earth, enabling frequent sampling to capture the diurnal variability of biogenic fluxes and anthropogenic emissions from city to continental scales. The science goal is to obtain a process-based understanding of the carbon cycle from simultaneous high spatial resolution measurements of carbon dioxide (CO2), methane (CH4), carbon monoxide (CO), and chlorophyll fluorescence (CF) many times per day in the near infrared spectral region to capture their spatial and temporal variations on diurnal, synoptic, seasonal and interannual time scales. The GeoFTS instrument is based on a Michelson interferometer design with a number of advanced features incorporated. Two of the most important advanced features are the focal plane arrays and the optical path difference mechanism. A breadboard GeoFTS instrument has demonstrated functionality for simultaneous measurements in the visible and IR in the laboratory and subsequently in the field at the California Laboratory for Atmospheric Remote Sensing (CLARS) observatory on Mt. Wilson overlooking the Los Angeles basin. A GeoFTS engineering model instrument is being developed which will make simultaneous visible and IR measurements under space flight like environmental conditions (thermal-vacuum at 180 K). This will demonstrate critical instrument capabilities such as optical alignment stability, interferometer modulation efficiency, and high throughput FPA signal processing. This will reduce flight instrument development risk and show that the GeoFTS design is mature and flight ready.

Key, Richard; Sander, Stanley; Eldering, Annmarie; Miller, Charles; Frankenberg, Christian; Natra, Vijay; Rider, David; Blavier, Jean-Francois; Bekker, Dmitriy; Wu, Yen-Hung

2012-01-01

89

The Geostationary Fourier Transform Spectrometer  

NASA Technical Reports Server (NTRS)

The Geostationary Fourier Transform Spectrometer (GeoFTS) is an imaging spectrometer designed for a geostationary orbit (GEO) earth science mission to measure key atmospheric trace gases and process tracers related to climate change and human activity. GEO allows GeoFTS to continuously stare at a region of the earth for frequent sampling to capture the variability of biogenic fluxes and anthropogenic emissions from city to continental spatial scales and temporal scales from diurnal, synoptic, seasonal to interannual. The measurement strategy provides a process based understanding of the carbon cycle from contiguous maps of carbon dioxide (CO2), methane (CH4), carbon monoxide (CO), and chlorophyll fluorescence (CF) collected many times per day at high spatial resolution (2.7kmx2.7km at nadir). The CO2/CH4/CO/CF measurement suite in the near infrared spectral region provides the information needed to disentangle natural and anthropogenic contributions to atmospheric carbon concentrations and to minimize uncertainties in the flow of carbon between the atmosphere and surface. The half meter cube size GeoFTS instrument is based on a Michelson interferometer design that uses all high TRL components in a modular configuration to reduce complexity and cost. It is self-contained and as independent of the spacecraft as possible with simple spacecraft interfaces, making it ideal to be a "hosted" payload on a commercial communications satellite mission. The hosted payload approach for measuring the major carbon-containing gases in the atmosphere from the geostationary vantage point will affordably advance the scientific understating of carbon cycle processes and climate change.

Key, Richard; Sander, Stanley; Eldering, Annmarie; Blavier, Jean-Francois; Bekker, Dmitriy; Manatt, Ken; Rider, David; Wu, Yen-Hung

2012-01-01

90

Lagrange-mesh calculations and Fourier transform  

SciTech Connect

The Lagrange-mesh method is a very accurate procedure for computing eigenvalues and eigenfunctions of a two-body quantum equation written in the configuration space. Using a Gauss quadrature rule, the method only requires the evaluation of the potential at some mesh points. The eigenfunctions are expanded in terms of regularized Lagrange functions, which vanish at all mesh points except one. Using the peculiarities of the method, it is shown that the Fourier transform of the eigenfunctions, computed in the configuration space, can easily be obtained with good accuracy in the physical domain of the momentum space. Also, observables in this space can easily be computed with good accuracy only using matrix elements and eigenfunctions computed in the configuration space.

Lacroix, Gwendolyn; Semay, Claude [Service de Physique Nucleaire et Subnucleaire, Universite de Mons-UMONS, Academie universitaire Wallonie-Bruxelles, Place du Parc 20, B-7000 Mons (Belgium)

2011-09-15

91

Lecture 16 Appendix B (Fourier Transform) First load the Fourier package  

E-print Network

Lecture 16 Appendix B (Fourier Transform) First load the Fourier package In[24]:= FourierSeries` Ex-axis with multiples of and the Exclusions command to show the vertical lines. Now find the Fourier transform using the built-in functions In[27]:= g _ : FourierTransform f1 x , x, , FourierParameters 0, 1 In[28]:= g Out[28

Ellis, Steve

92

Demystification of the geometric Fourier transforms  

NASA Astrophysics Data System (ADS)

As it will turn out in this paper, the recent hype about most of the Clifford Fourier transforms is not thoroughly worth the pain. Almost every one that has a real application is separable and these transforms can be decomposed into a sum of real valued transforms with constant multivecor factors. This fact makes their interpretation, their analysis, and their implementation almost trivial.

Bujack, Roxana; Scheuermann, Gerik; Hitzer, Eckhard

2013-10-01

93

PROJECTIONS OF CONVEX BODIES AND THE FOURIER TRANSFORM  

E-print Network

PROJECTIONS OF CONVEX BODIES AND THE FOURIER TRANSFORM A of the Fourier transform of the curvature function. 1. Introduction as their section counterparts. The Fourier transform approach to sections of convex bodies is based on certain

Ryabogin, Dmitry

94

PARALLEL COMPUTATION OF THE INTERLEAVED FAST FOURIER TRANSFORM WITH MPI  

E-print Network

PARALLEL COMPUTATION OF THE INTERLEAVED FAST FOURIER TRANSFORM WITH MPI A Thesis Presented FOURIER TRANSFORM WITH MPI Ameen Baig Mirza Thesis Approved: Accepted _______________________ _______________________ Committee Member Date Dr. Wolfgang Pelz #12;iii ABSTRACT Fourier Transforms have wide range of applications

O'Neil, Tim

95

GENERALIZED FOURIER TRANSFORMATIONS: THE WORK OF BOCHNER AND CARLEMAN  

E-print Network

GENERALIZED FOURIER TRANSFORMATIONS: THE WORK OF BOCHNER AND CARLEMAN-1949) presented gen- eralizations of the Fourier transform of functions defined on the real axis* *. While Bochner's idea was to define the Fourier transform as a (formal) derivative* * of high order

Kiselman, Christer

96

FOURIER TRANSFORM INFRARED SPECTROMETRY OF AMBIENT AEROSOLS  

EPA Science Inventory

Fourier transform infrared (FTIR) spectrometry has been evaluated as a method for determining the concentration of selected species present in ambient aerosols collected on Teflon filters. The filters are analyzed by transmission measurements after collection of the fine fraction...

97

Parallel FFT & Isoefficiency 1 The Fast Fourier Transform in Parallel  

E-print Network

Parallel FFT & Isoefficiency 1 The Fast Fourier Transform in Parallel the Fastest Fourier Transform / 25 #12;Parallel FFT & Isoefficiency 1 The Fast Fourier Transform in Parallel the Fastest Fourier & Isoefficiency L-14 14 February 2014 2 / 25 #12;the Discrete Fourier Transform (DFT) A periodic function f(t) can

Verschelde, Jan

98

Transforming quantum operations: quantum supermaps  

E-print Network

We introduce the concept of quantum supermap, describing the most general transformation that maps an input quantum operation into an output quantum operation. Since quantum operations include as special cases quantum states, effects, and measurements, quantum supermaps describe all possible transformations between elementary quantum objects (quantum systems as well as quantum devices). After giving the axiomatic definition of supermap, we prove a realization theorem, which shows that any supermap can be physically implemented as a simple quantum circuit. Applications to quantum programming, cloning, discrimination, estimation, information-disturbance trade-off, and tomography of channels are outlined.

G. Chiribella; G. M. D'Ariano; P. Perinotti

2008-04-01

99

Real-valued fast Fourier transform algorithms  

Microsoft Academic Search

This tutorial paper describes the methods for constructing fast algorithms for the computation of the discrete Fourier transform (DFT) of a real-valued series. The application of these ideas to all the major fast Fourier transform (FFT) algorithms is discussed, and the various algorithms are compared. We present a new implementation of the real-valued split-radix FFT, an algorithm that uses fewer

H. V. Sorensen; D. L. Jones; M. T. Heideman; C. S. Burrus

1987-01-01

100

Topics In Chemical Instrumentation: Fourier Transformations for Chemists Part I. Introduction to the Fourier Transform.  

ERIC Educational Resources Information Center

This paper explores how Fourier Transform (FT) mimics spectral transformation, how this property can be exploited to advantage in spectroscopy, and how the FT can be used in data treatment. A table displays a number of important FT serial/spectral pairs related by Fourier Transformations. A bibliography and listing of computer software related to…

Glasser, L.

1987-01-01

101

Quantifying momenta through the Fourier transform  

E-print Network

Integral transforms arising from the separable solutions to the Helmholtz differential equation are presented. Pairs of these integral transforms are related via Plancherel theorem and, ultimately, any of these integral transforms may be calculated using only Fourier transforms. This result is used to evaluate the mean value of momenta associated to the symmetries of the reduced wave equation. As an explicit example, the orbital angular momenta of plane and elliptic-cylindrical waves is presented.

Rodr\\'\\iguez-Lara, B M

2011-01-01

102

A Primer of Fourier Transform NMR.  

ERIC Educational Resources Information Center

Fourier transform nuclear magnetic resonance (NMR) is a new spectroscopic technique that is often omitted from undergraduate curricula because of lack of instructional materials. Therefore, information is provided to introduce students to the technique of data collection and transformation into the frequency domain. (JN)

Macomber, Roger S.

1985-01-01

103

Spacevariant Fourier Analysis: the Exponential Chirp Transform  

E-print Network

of the fast exponential chirp algorithm on a data­base of images in a template matching task, and also­Variant Image Processing, Fourier Analysis, Non­Uniform Sampling, Real­Time Imaging, Warped Template Matching to the Mellin­ Transform) provides a fast exponential chirp transform. This provides size and rotation

Schwartz, Eric L.

104

Fingerprint segmentation based on local fourier transform  

NASA Astrophysics Data System (ADS)

The segmentation of fingerprint images plays an important role in fingerprint recognition. A new algorithm based on Local Fourier Transform (LFT) for the fingerprint segmentation is proposed in this paper. Firstly, we perform the Local Fourier Transform on image to get eight independent Local Fourier coefficients per pixel. Then, block features are extracted by calculating the 2nd, 4th, 6th order moments of the local Fourier coefficients of every pixel in the block. After that, a Fisher linear discriminant classifier is trained for the classification per block. Finally, mathematical morphology and region boundary smoothing is applied as postprocessing to obtain compact clusters and to reduce the number of classification errors. The experimental results on the databases of FVC2004 demonstrate the robustness and the efficiency of the proposed method.

Fan, Dongjin; Feng, Jufu

2007-11-01

105

LOCAL FOURIER TRANSFORMS AND RIGIDITY FOR SPENCER BLOCH AND H  

E-print Network

LOCAL FOURIER TRANSFORMS AND RIGIDITY FOR D-MODULES SPENCER BLOCH AND H #19; EL #18; ENE ESNAULT To Armand Borel, in memoriam Abstract. Local Fourier transforms, analogous to the `-adic local Fourier transforms to prove an invariance result for the rigidity index under global Fourier transform. A key

Bloch, Spencer

106

Ubung 2. Fast Fourier Transform in image April 27, 2005  

E-print Network

Ubung 2. Fast Fourier Transform in image processing April 27, 2005 1 Background Fourier Transform, the contribution of Fourier Transformation states that any function can be expressed as the integral of sines and in a Fourier transform, can be reconstructed (recovered) completely via an inverse process. This important

Kjellström, Hedvig

107

An Efficient Hamiltonian for Discrete Fractional Fourier Transform  

Microsoft Academic Search

Fractional Fourier Transform, which is a generalization of the classical Fourier Transform, is a powerful tool for the analysis of transient signals. The discrete Fractional Fourier Transform Hamiltonians have been proposed in the past with varying degrees of correlation between their eigenvectors and Hermite Gaussian functions. In this paper, we propose a new Hamiltonian for the discrete Fractional Fourier Transform

Sukrit Shankar; Chetana Shanta Pats; Jaydev Sharma

2008-01-01

108

Fast Fourier Transform algorithm design and tradeoffs  

NASA Technical Reports Server (NTRS)

The Fast Fourier Transform (FFT) is a mainstay of certain numerical techniques for solving fluid dynamics problems. The Connection Machine CM-2 is the target for an investigation into the design of multidimensional Single Instruction Stream/Multiple Data (SIMD) parallel FFT algorithms for high performance. Critical algorithm design issues are discussed, necessary machine performance measurements are identified and made, and the performance of the developed FFT programs are measured. Fast Fourier Transform programs are compared to the currently best Cray-2 FFT program.

Kamin, Ray A., III; Adams, George B., III

1988-01-01

109

Fast Fourier Transform in the West (FFTW)  

NSDL National Science Digital Library

Despite its curious name, Fast Fourier Transform in the West (FFTW) is a powerful, free "C subroutine library for computing the discrete Fourier transform (DFT) in one or more dimensions, of both real and complex data, and of arbitrary input size." Developed by researchers from the Massachusetts Institute of Technology, FFTW purportedly has outstanding performance when compared with other DFT algorithms. This statement is supported by experimental results from extensive speed and accuracy benchmarks. FFTW can be downloaded directly from this site, along with substantial documentation and three research papers stemming from its development.

Frigo, Matteo; Johnson, Steven G.

110

Delta potentials revisited via Fourier transform  

E-print Network

The problem of bound states in delta potentials is revisited by means of Fourier transform approach. The problem in a simple delta potential sums up to solve an algebraic equation of degree one for the Fourier transform of the eigenfunction and the problem for more than one delta function also reveals itself to be a simple matter. Quite differently from direct methods, no knowledge about the jump discontinuity of the first derivative of the eigenfunction is required to determine the solution of the problem.

A. S. de Castro

2012-09-30

111

Fast Fourier Transform Spectral Analysis Program  

NASA Technical Reports Server (NTRS)

Fast Fourier Transform Spectral Analysis Program is used in frequency spectrum analysis of postflight, space vehicle telemetered trajectory data. This computer program with a digital algorithm can calculate power spectrum rms amplitudes and cross spectrum of sampled parameters at even time increments.

Daniel, J. A., Jr.; Graves, M. L.; Hovey, N. M.

1969-01-01

112

Ultrafast Fourier-transform parallel processor  

SciTech Connect

A new, flexible, parallel-processing architecture is developed for a high-speed, high-precision Fourier transform processor. The processor is intended for use in 2-D signal processing including spatial filtering, matched filtering and image reconstruction from projections.

Greenberg, W.L.

1980-04-01

113

Fourier Transform and Reflective Imaging Pyrometry  

SciTech Connect

A stationary Fourier transform pyrometer was used to record mid-wavelength IR spectra in dynamic shock experiments. The gated-IR camera used with this system was also used to record images of light produced and light reflected from shocked metals in order to constrain the dynamic emissivity and provide temperature estimates. This technique will be referred to as reflective imaging pyrometry.

Stevens, G. D.

2011-07-01

114

On Computing the Discrete Fourier Transform  

Microsoft Academic Search

New algorithms for computing the Discrete Fourier Transform of n points are described. For n in the range of a few tens to a few thousands these algorithms use substantially fewer multiplications than the best algorithm previously known, and about the same number of additions.

Shmuel Winograd

1976-01-01

115

Fourier Transform Spectroscopy, Eleventh International Conference. Proceedings  

SciTech Connect

These proceedings represent the papers presented at the Eleventh International Conference on Fourier Transform Spectroscopy held in August, 1997 in Athens, Georgia, USA. The Conference provided an atmosphere for people of diverse backgrounds to congregate and exchange information. The topics discussed included applications of Fourier transform spectroscopy to surface science, biological systems, atmospheric science, forensics and textiles, etc. Biochemical and biomedical studies utilizing Fourier Transform infrared spectroscopy formed a large section of the Conference Applications to semiconductor industry, namely monitoring of CVD processes and photoresists were also discussed. Most of the applications were in the near and mid infrared, with a few extending to the far infrared and visible regions of the electromagnetic spectrum. In the Keynote Address, Fourier Transform Ion Cyloctron Resonance Spectroscopy was reviewed by Professor Alan G. Marshall of the National High Magnetic Field Laboratory in Florida. Altogether 152 papers were presented at the Conference and out of these, 15 have been abstracted for the Energy, Science and Technology database. (AIP)

de Haseth, J.A. [Department of Chemistry, University of Georgia, Atlanta, GA 30602-2556 (United States)

1998-05-01

116

Complex signal recovery from multiple fractional Fourier-transform intensities  

E-print Network

Complex signal recovery from multiple fractional Fourier-transform intensities M. Günhan Ertosun the magnitudes of any number of its fractional Fourier transforms at any set of fractional orders is addressed domain and its Fourier transform resides in the frequency domain, the ath-order fractional Fourier

Barshan, Billur

117

An algorithm for the basis of the finite Fourier transform  

NASA Technical Reports Server (NTRS)

The Finite Fourier Transformation matrix (F.F.T.) plays a central role in the formulation of quantum mechanics in a finite dimensional space studied by the author over the past couple of decades. An outstanding problem which still remains open is to find a complete basis for F.F.T. In this paper we suggest a simple algorithm to find the eigenvectors of F.T.T.

Santhanam, Thalanayar S.

1995-01-01

118

Electro-optic imaging Fourier transform spectrometer  

NASA Technical Reports Server (NTRS)

An Electro-Optic Imaging Fourier Transform Spectrometer (EOIFTS) for Hyperspectral Imaging is described. The EOIFTS includes an input polarizer, an output polarizer, and a plurality of birefringent phase elements. The relative orientations of the polarizers and birefringent phase elements can be changed mechanically or via a controller, using ferroelectric liquid crystals, to substantially measure the spectral Fourier components of light propagating through the EIOFTS. When achromatic switches are used as an integral part of the birefringent phase elements, the EIOFTS becomes suitable for broadband applications, with over 1 micron infrared bandwidth.

Chao, Tien-Hsin (Inventor); Znod, Hanying (Inventor)

2009-01-01

119

Electro-optic Imaging Fourier Transform Spectrometer  

NASA Technical Reports Server (NTRS)

JPL is developing an innovative compact, low mass, Electro-Optic Imaging Fourier Transform Spectrometer (E-0IFTS) for hyperspectral imaging applications. The spectral region of this spectrometer will be 1 - 2.5 pm (1000 -4000 cm-') to allow high-resolution, high-speed hyperspectral imaging applications [l-51. One application will be theremote sensing of the measurement of a large number of different atmospheric gases simultaneously in the sameairmass. Due to the use of a combination of birefiingent phase retarders and multiple achromatic phase switches toachieve phase delay, this spectrometer is capable of hyperspectral measurements similar to that of the conventionalFourier transform spectrometer but without any moving parts. In this paper, the principle of operations, systemarchitecture and recent experimental progress will be presen.

Chao, Tien-Hsin

2005-01-01

120

Electro-optic Imaging Fourier Transform Spectrometer  

NASA Technical Reports Server (NTRS)

JPL is developing an innovative compact, low mass, Electro-Optic Imaging Fourier Transform Spectrometer (E-O IFTS) for hyperspectral imaging applications. The spectral region of this spectrometer will be 1 - 2.5 micron (1000-4000/cm) to allow high-resolution, high-speed hyperspectral imaging applications. One application will be the remote sensing of the measurement of a large number of different atmospheric gases simultaneously in the same airmass. Due to the use of a combination of birefringent phase retarders and multiple achromatic phase switches to achieve phase delay, this spectrometer is capable of hyperspectral measurements similar to that of the conventional Fourier transform spectrometer but without any moving parts. In this paper, the principle of operations, system architecture and recent experimental progress will be presented.

Chao, Tien-Hsin

2005-01-01

121

An Imaging Fourier Transform Spectrometer for NGST  

E-print Network

Due to its simultaneous deep imaging and integral field spectroscopic capability, an Imaging Fourier Transform Spectrograph (IFTS) is ideally suited to the Next Generation Space Telescope (NGST) mission, and offers opportunities for tremendous scientific return in many fields of astrophysical inquiry. We describe the operation and quantify the advantages of an IFTS for space applications. The conceptual design of the Integral Field Infrared Spectrograph (IFIRS) is a wide field (5'.3 x 5'.3) four-port imaging Michelson interferometer.

James R. Graham

1999-07-18

122

Simple and practical algorithm for sparse fourier transform  

E-print Network

We consider the sparse Fourier transform problem: given a complex vector x of length n, and a parameter k, estimate the k largest (in magnitude) coe fficients of the Fourier transform of x. The problem is of key interest ...

Hassanieh, Haitham

123

Programs for high-speed Fourier, Mellin and Fourier-Bessel transforms  

NASA Technical Reports Server (NTRS)

Several FORTRAN program modules for performing one-dimensional and two-dimensional discrete Fourier transforms, Mellin, and Fourier-Bessel transforms are described along with programs that realize the algebra of high speed Fourier transforms on a computer. The programs can perform numerical harmonic analysis of functions, synthesize complex optical filters on a computer, and model holographic image processing methods.

Ikhabisimov, D. K.; Debabov, A. S.; Kolosov, B. I.; Usikov, D. A.

1979-01-01

124

On Superoscillations Longevity: A Windowed Fourier Transform Approach  

NASA Astrophysics Data System (ADS)

In this paper we prove that the evolution of a superoscillating sequence of functions Y N (x), which we take as the initial value of the Schrödinger equation, remains superoscillating for all values of the time tFourier transform approach. [Editor's note: for a video of the talks given by Prof. Aharonov at the Aharonov-80 conference in 2012 at Chapman University, see http://quantum.chapman.edu/talk-3 and http://quantum.chapman.edu/talk-30. For the subject of super-oscillations, the editors also recommend the video of the talk given by Prof. Berry at the Aharonov-80 conference in 2012 at Chapman University, see http://quantum.chapman.edu/talk-6 along with the talk by Prof. Casher, see http://quantum.chapman.edu/talk-21.

Aharonov, Y.; Colombo, F.; Sabadini, I.; Struppa, D. C.; Tollaksen, J.

125

Color Object Recognition Based On Clifford Fourier Transform  

E-print Network

Color Object Recognition Based On Clifford Fourier Transform Jose Mennesson, Christophe Saint recognition, both using the recently defined color Clifford Fourier transform. The first one deals with so, Christophe Saint-Jean and Laurent Mascarilla of existing methods based on a Fourier transform. Clearly

Paris-Sud XI, Université de

126

Doppler spectrum estimation by Ramanujan-Fourier Transform (RFT)  

E-print Network

Doppler spectrum estimation by Ramanujan-Fourier Transform (RFT) Mohand Lagha, Messaoud Bensebti of the power spectral density PSD by using Fourier transforms. We introduces a new tool of signal processing to the order q of resonances. New results will be supplied by the use of Ramanujan Fourier Transform (RFT

Paris-Sud XI, Université de

127

Coupling Capillary Electrochromatography with Electrospray Fourier Transform Mass  

E-print Network

Coupling Capillary Electrochromatography with Electrospray Fourier Transform Mass Spectrometry spectrometry (Fourier transform ion cyclotron resonance). Contour plots have been generated from the mixtures-pressure capillary liquid chro- matography (CLC) to Fourier transform (FT) MS in high- throughput proteomics5-7 has

Clemmer, David E.

128

Fourier transforms of fractional order and their optical interpretation  

Microsoft Academic Search

Fourier transforms of fractional order a are defined in a manner such that the common Fourier transform is a special case with order a=1. An optical interpretation is provided in terms of quadratic graded index media and discussed from both wave and ray viewpoints. Fractional Fourier transforms can extend the range of spatial filtering operations.

Haldun M. Ozaktas; David Mendlovic

1993-01-01

129

Spinor Fourier Transform for Image Processing Thomas Batard, Michel Berthier  

E-print Network

1 Spinor Fourier Transform for Image Processing Thomas Batard, Michel Berthier Abstract--We propose in this paper to introduce a new spinor Fourier transform for both grey-level and color image processing. Our Fourier transform may be used to perform frequency filtering that takes into account the Riemannian

Paris-Sud XI, Université de

130

Heisenberg Uncertainty Principle for the q-Bessel Fourier transform  

E-print Network

Heisenberg Uncertainty Principle for the q-Bessel Fourier transform Lazhar Dhaouadi Abstract further variant of Heisen- bergs uncertainty principle. Let f be the Fourier transform of f defined by f entropy argument de give an un- certainty inequality for the q-Bessel Fourier transform (also called q

Paris-Sud XI, Université de

131

Fourier Transform Heterodyne Spectroscopy of Liquid Interfaces A thesis presented  

E-print Network

Fourier Transform Heterodyne Spectroscopy of Liquid Interfaces A thesis presented by Doo Soo Chung Abstract This thesis describes the application of a novel Fourier transform heterodyne spectroscopy of fluid interfaces 3 1.4 Organization of this thesis 5 2 Fourier Transform Heterodyne Spectroscopy 7 2

Mazur, Eric

132

Fast Clifford Fourier Transformation for Unstructured Vector Field Data  

E-print Network

Fast Clifford Fourier Transformation for Unstructured Vector Field Data Michael Schlemmer 1 Ingrid analysis used the Clifford Fourier transform for efficient pattern recognition for vector field data this approach with a fast Fourier transform to handle unstructured scalar data [6]. Our extension enables us

Hamann, Bernd

133

SIGNAL APPROXIMATION VIA THE GOPHER FAST FOURIER TRANSFORM  

E-print Network

SIGNAL APPROXIMATION VIA THE GOPHER FAST FOURIER TRANSFORM By I. Ben Segal and M.A. Iwen IMA-626-7370 URL: http://www.ima.umn.edu #12;Signal Approximation via the Gopher Fast Fourier Transform I. Ben this problem [1, 2]. These methods were implemented as the Ann Arbor Fast Fourier Transform (AAFFT

134

The Effects of Temporally Changing Sources on Fourier Transform Spectrometers  

E-print Network

The Effects of Temporally Changing Sources on Fourier Transform Spectrometers Herbert J. Mitchell ABSTRACT A Michelson Fourier Transform Spectrometer senses an object/material in the time domain, producing an interferogram. To produce a spectrum, the interferogram is Fourier transformed into the spectral domain. Unless

Salvaggio, Carl

135

Fourier transform of a Gaussian measure on the Heisenberg group  

E-print Network

Fourier transform of a Gaussian measure on the Heisenberg group M´aty´as Barczy and Gyula Pap University of Debrecen, Hungary Abstract An explicit formula is derived for the Fourier transform measure. 1 Introduction Fourier transforms of probability measures on a locally compact topological group

Barczy, Mátyás

136

ON THE FOURIER TRANSFORM OF THE SYMMETRIC DECREASING REARRANGEMENTS  

E-print Network

ON THE FOURIER TRANSFORM OF THE SYMMETRIC DECREASING REARRANGEMENTS PHILIPPE JAMING R families of rearrangement inequalities for the Fourier transform. More precisely, we show that the L2 behavior of a Fourier transform of a function over a small set is con- trolled by the L2 behavior

Paris-Sud XI, Université de

137

Certifying the Fast Fourier Transform with Coq Venanzio Capretta  

E-print Network

Certifying the Fast Fourier Transform with Coq Venanzio Capretta Computing Science Institute+24+3652647, fax: +31+24+3553450 Abstract. We program the Fast Fourier Transform in type theory, using the tool Coq. We prove its correctness and the correctness of the Inverse Fourier Transform. A type of trees

Capretta, Venanzio

138

LOCAL FOURIER TRANSFORMS AND RIGIDITY FOR D-MODULES  

E-print Network

LOCAL FOURIER TRANSFORMS AND RIGIDITY FOR D. Local Fourier transforms, analogous to the `-adic local Fourier transforms [14], are constructed is shown to be rigid, i.e. determined by local data at the singularities, if and only if a certain

Bloch, Spencer

139

Quality Factor Variation with Transform Order in Fractional Fourier Domain  

Microsoft Academic Search

Fractional Fourier Transform is a powerful tool, which is a generalization of the classical Fourier Transform. This paper provides a mathematical relation relating the span in Fractional Fourier domain with the amplitude and phase functions of the signal, which is further used to study the variation of quality factor with different values of the transform order. It is seen that

Sukrit Shankar; Chetana Shanta; K. Pardha Saradhi; Jaydev Sharma

2007-01-01

140

Stationary Wave Integrated Fourier Transform Spectrometer (SWIFTS)  

NASA Astrophysics Data System (ADS)

The size and the weight of current spectrometers is a serious issue regarding various applications, however the technologies used in existing spectrometers prevent them from substantial improvement. SWIFTS (Stationary Wave Integrated Fourier Transform Spectrometer) is a new familyof spectrometers based on a verypromising technology. It is based on an original wayto fully sample the Fourier interferogram obtained in a waveguide byeither a reflection (SWIFTS Lippmann) or counter-propagative (SWIFTS Gabor) interference phenomenon. The sampling can be simultaneouslydone without anymo ving part thanks to "nano-detectors" located in the evanescent field of the waveguide. It allows a dramatic reduction of the size and the weight of spectrometers while improving their performances (high stabilityand high resolution ?? < 1cm-1). Here, we present the development status of the SWIFTS Gabor and the results obtained (resolution of 4cm-1) with existing technical solutions for the "nano-detectors" in visible and near infrared.

Ferrand, Jérôme; Custillon, Guillaume; Leblond, Gregory; Thomas, Fabrice; Moulin, Thibault; le Coarer, Etienne; Morand, Alain; Blaize, Sylvain; Gonthiez, Thierry; Benech, Pierre

2010-02-01

141

The PROSAIC Laplace and Fourier Transform  

SciTech Connect

Integral Transform methods play an extremely important role in many branches of science and engineering. The ease with which many problems may be solved using these techniques is well known. In Electrical Engineering especially, Laplace and Fourier Transforms have been used for a long time as a way to change the solution of differential equations into trivial algebraic manipulations or to provide alternate representations of signals and data. These techniques, while seemingly overshadowed by today`s emphasis on digital analysis, still form an invaluable basis in the understanding of systems and circuits. A firm grasp of the practical aspects of these subjects provides valuable conceptual tools. This tutorial paper is a review of Laplace and Fourier Transforms from an applied perspective with an emphasis on engineering applications. The interrelationship of the time and frequency domains will be stressed, in an attempt to comfort those who, after living so much of their lives in the time domain, find thinking in the frequency domain disquieting.

Smith, G.A.

1994-11-01

142

Analysis method for Fourier transform spectroscopy  

NASA Technical Reports Server (NTRS)

A fast Fourier transform technique is given for the simulation of those distortion effects in the instrument line shape of the interferometric spectrum that are due to errors in the measured interferogram. The technique is applied to analyses of atmospheric absorption spectra and laboratory spectra. It is shown that the nonlinear least squares method can retrieve the correct information from the distorted spectrum. Analyses of HF absorption spectra obtained in a laboratory and solar CO absorption spectra gathered by a balloon-borne interferometer indicate that the retrieved amount of absorbing gas is less than the correct value in most cases, if the interferogram distortion effects are not included in the analysis.

Park, J. H.

1983-01-01

143

Noise figure of amplified dispersive Fourier transformation  

SciTech Connect

Amplified dispersive Fourier transformation (ADFT) is a powerful tool for fast real-time spectroscopy as it overcomes the limitations of traditional optical spectrometers. ADFT maps the spectrum of an optical pulse into a temporal waveform using group-velocity dispersion and simultaneously amplifies it in the optical domain. It greatly simplifies spectroscopy by replacing the diffraction grating and detector array in the conventional spectrometer with a dispersive fiber and single-pixel photodetector, enabling ultrafast real-time spectroscopic measurements. Following our earlier work on the theory of ADFT, here we study the effect of noise on ADFT. We derive the noise figure of ADFT and discuss its dependence on various parameters.

Goda, Keisuke; Jalali, Bahram [Electrical Engineering Department, University of California, Los Angeles, California 90095 (United States)

2010-09-15

144

Fourier transform infrared studies of coal oxidation  

SciTech Connect

Fourier transform infrared spectroscopy was combined with chemical methods of analysis to determine changes in hydroxyl and ether groups upon oxidation. Samples were acetylated in order to determine hydroxyl groups and reacted with potassium in tetrahydrofuran in order to cleave ether bonds. The conclusions are: in the early stages of coal oxidation the principal products appear to be carbonyl and carboxyl groups; oxidation at 150/sup 0/C appears to result in a slight loss of phenolic OH, possibly through condensation reactions to give ethers.

Painter, P.; Rhoads, C.

1981-03-29

145

Variant fractional Fourier transformer for optical pulses.  

PubMed

We demonstrate that it is possible to perform a fractional Fourier transform of an incident pulse with a continuously variable degree of fractionality, using a dispersive and nonlinear Kerr medium. This medium acts as a linear waveguide for the optical pulse if its intensity is small and if the refractive index is nonlinearly time-dependently modified by a simultaneously launched bright soliton. For optical pulses the dispersive and nonlinear medium is perfectly equivalent to a graded-index refractive medium for optical beams. PMID:18073900

Dragoman, D; Dragoman, M; Brenner, K H

1999-07-15

146

Fourier Transforms Simplified: Computing an Infrared Spectrum from an Interferogram  

ERIC Educational Resources Information Center

Fourier transforms are used widely in chemistry and allied sciences. Examples include infrared, nuclear magnetic resonance, and mass spectroscopies. A thorough understanding of Fourier methods assists the understanding of microscopy, X-ray diffraction, and diffraction gratings. The theory of Fourier transforms has been presented in this "Journal",…

Hanley, Quentin S.

2012-01-01

147

Fast Fourier Transform of Sparse Spatial Data to Sparse Fourier Data W. C. Chew* and J.M. Song  

E-print Network

1 Fast Fourier Transform of Sparse Spatial Data to Sparse Fourier Data W. C. Chew* and J.M. Song-3]. However, not much has been written on Fourier transforming sparse spatial data where the Fourier transform to the Fourier transform of the scatterers. In many instances, the scatterer is describable by a few scattering

Lanterman, Aaron

148

Fourier Transforms for Chemists Part III. Fourier Transforms in Data Treatment.  

ERIC Educational Resources Information Center

Discusses the factors affecting the behavior of a spectral function. Lists some important properties of Fourier transform (FT) pairs that are helpful when using the FT. Notes that these properties of the mathematical formulation have identical counterparts in the physical behavior of FT systems. (TW)

Glasser, L.

1987-01-01

149

Cauchy transforms of measures viewed as some functionals of Fourier transforms  

E-print Network

Cauchy transforms of measures viewed as some functionals of Fourier transforms Zbigniew J. Jurek to the imaginary axis can be viewed as the Fourier transform of some corresponding measures. Thus this allows 60E10, 46L54; sec- ondary 42B10 30E05. Key words and phrases: Cauchy transform; Fourier transform

Jurek, Zbigniew J.

150

Surface Inspection using fourier transform infrared spectroscopy  

SciTech Connect

The use of reflectance Fourier transform infrared (FTIR) spectroscopy as a tool for surface inspection is described. Laboratory instruments and portable instruments can support remote sensing probes that can map chemical contaminants on surfaces. Detection limits under the best of conditions are in the subnanometer range (i.e., near absolute cleanliness), excellent performance is obtained in the submicrometer range, and useful performance may exist for films tens of microns thick. Identifying and quantifying contamination such as mineral oils and greases, vegetable oils, and silicone oils on aluminum foil, galvanized sheet steel, smooth aluminum tubing, and gritblasted 7075 aluminum alloy and D6AC steel are described. The ability to map in time and space the distribution of oil stains on metals is demonstrated. Techniques for quantitatively applying oils to metals, subsequently verifying the application, and nonlinear relationships between reflectance and the quantity of oil are discussed.

Powell, G.L.; Smyrl, N.R.; Williams, D.M.; Meyers, H.M. III [Martin Marietta Energy Systems, Inc., TN (United States). Oak Ridge Y-12 Plant; Barber, T.E.; Marrero-Rivera, M. [Oak Ridge Institute for Science and Education, Oak Ridge, TN (United States)

1994-08-08

151

Fourier Cosine and Sine Transform on fractal space  

E-print Network

In this paper, we establish local fractional Fourier Cosine and Sine Transforms on fractal space, considered some properties of local fractional Cosine and Sine Transforms, show applications of local fractional Fourier Cosine and Sine transform to local fractional equations with local fractional derivative.

Guang-Sheng Chen

2011-10-21

152

On Fourier transforms of radial functions and distributions  

E-print Network

We find a formula that relates the Fourier transform of a radial function on $\\mathbf{R}^n$ with the Fourier transform of the same function defined on $\\mathbf{R}^{n+2}$. This formula enables one to explicitly calculate the Fourier transform of any radial function $f(r)$ in any dimension, provided one knows the Fourier transform of the one-dimensional function $t\\to f(|t|)$ and the two-dimensional function $(x_1,x_2)\\to f(|(x_1,x_2)|)$. We prove analogous results for radial tempered distributions.

Loukas Grafakos; Gerald Teschl

2011-12-22

153

Application of Fourier Transform Infrared Spectrophotometry in Pharmaceutical Drugs Analysis  

Microsoft Academic Search

This review provides some background to infrared spectroscopy including Fourier transform infrared spectroscopy. It is not meant to be complete or exhaustive but to provide the reader with sufficient background for selected applications in pharmaceutical analysis. Fourier transform infrared spectroscopy (FTIR) is a fast and nondestructive analytical method. Associated with chemometrics, it can become a powerful tool for the pharmaceutical

Andrei A. Bunaciu; Hassan Y. Aboul-Enein; Serban Fleschin

2010-01-01

154

Determination of Fourier Transforms on an Instructional Analog Computer  

ERIC Educational Resources Information Center

An analog computer program to find and display the Fourier transform of some real, even functions is described. Oscilloscope traces are shown for Fourier transforms of a rectangular pulse, a Gaussian, a cosine wave, and a delayed narrow pulse. Instructional uses of the program are discussed briefly. (DT)

Anderson, Owen T.; Greenwood, Stephen R.

1974-01-01

155

Fractional Fourier transforms and their optical implementation. II  

Microsoft Academic Search

Fourier transforms of fractional order a are defined in a manner such that the common Fourier transform is a special case with order a = 1. An optical interpretation is provided in terms of quadratic graded index media and discussed from both wave and ray viewpoints. Several mathematical properties are derived. 1. MOTIVATION It is often the case that an

Haldun M. Ozaktas; David Mendlovic

1993-01-01

156

On the Fast Fourier Transform of Functions with Singularities  

Microsoft Academic Search

We consider a simple approach for the fast evaluation of the Fourier transform of functions with singularities based on projecting such functions on a subspace of Multiresolution Analysis. We obtain an explicit approximation of the Fourier Transform of generalized functions and develop a fast algorithm based on its evaluation. In particular, we construct an algorithm for the Unequally Spaced Fast

G. Beylkin

1995-01-01

157

The fractional Fourier transform and time-frequency representations  

Microsoft Academic Search

The functional Fourier transform (FRFT), which is a generalization of the classical Fourier transform, was introduced a number of years ago in the mathematics literature but appears to have remained largely unknown to the signal processing community, to which it may, however, be potentially useful. The FRFT depends on a parameter ? and can be interpreted as a rotation by

Luis B. Almeida

1994-01-01

158

Communication Interlaced Fourier transformation of ultrafast 2D NMR data  

E-print Network

Communication Interlaced Fourier transformation of ultrafast 2D NMR data Mor Mishkovsky, Lucio in ultrafast 2D NMR is discussed and exemplified, based on the interlaced Fourier transformation. This approach- and heteronuclear ultrafast 2D NMR acquisitions, and found systematically fulfilled. The robustness and conditions

Frydman, Lucio

159

Linear Response Theory 15.0.1 Fourier Transform  

E-print Network

Chapter 15 Linear Response Theory 15.0.1 Fourier Transform A function of time f(t) which (15.5) F(!) is the Fourier transform of f(t). Note that if f(t) = (t) such thatR (t)dt = 1, then F is periodic with period T can be written as a Fourier series f(t) = 1X n= 1 cnein!ot (15.1) where !o = 2 =T

Palffy-Muhoray, Peter

160

Stepwise Iterative Fourier Transform: The SIFT  

NASA Technical Reports Server (NTRS)

A program, designed specifically to study the respective effects of some common data problems on results obtained through stepwise iterative Fourier transformation of synthetic data with known waveform composition, was outlined. Included in this group were the problems of gaps in the data, different time-series lengths, periodic but nonsinusoidal waveforms, and noisy (low signal-to-noise) data. Results on sinusoidal data were also compared with results obtained on narrow band noise with similar characteristics. The findings showed that the analytic procedure under study can reliably reduce data in the nature of (1) sinusoids in noise, (2) asymmetric but periodic waves in noise, and (3) sinusoids in noise with substantial gaps in the data. The program was also able to analyze narrow-band noise well, but with increased interpretational problems. The procedure was shown to be a powerful technique for analysis of periodicities, in comparison with classical spectrum analysis techniques. However, informed use of the stepwise procedure nevertheless requires some background of knowledge concerning characteristics of the biological processes under study.

Benignus, V. A.; Benignus, G.

1975-01-01

161

Imaging Fourier transform spectrometry of chemical plumes  

NASA Astrophysics Data System (ADS)

A midwave infrared (MWIR) imaging Fourier transform spectrometer (FTS), the Telops FIRST-MWE (Field-portable Imaging Radiometric Spectrometer Technology - Midwave Extended) has been utilized for the standoff detection and characterization of chemical plumes. Successful collection and analysis of MWIR hyperspectral imagery of jet engine exhaust has allowed us to produce spatial profiles of both temperature and chemical constituent concentrations of exhaust plumes. Successful characterization of this high temperature combustion event has led to the collection and analysis of hyperspectral imagery of lower temperature emissions from industrial smokestacks. This paper presents MWIR data from remote collection of hyperspectral imagery of methyl salicilate (MeS), a chemical warfare agent simulant, during the Chemical Biological Distributed Early Warning System (CBDEWS) test at Dugway Proving Grounds, UT in 2008. The data did not contain spectral lines associated with emission of MeS. However, a few broad spectral features were present in the background-subtracted plume spectra. Further analysis will be required to assign these features, and determine the utility of MWIR hyperspectral imagery for analysis of chemical warfare agent plumes.

Bradley, Kenneth C.; Gross, Kevin C.; Perram, Glen P.

2009-05-01

162

Fourier transform spectroscopy to study planetary atmospheres.  

NASA Astrophysics Data System (ADS)

Motivated by the selection of MATMOS for the ExoMars Trace Gas Orbiter (withdrawn), we have been working on algorithms for retrieving information about the Martian atmosphere using infrared spectroscopy.The Mars Atmospheric Trace Molecule Occultation Spectrometer (MATMOS) was a joint Canadian Space Agency (CSA) and Jet Propulsion Laboratory (JPL) mission to send a high-resolution Fourier transform spectrometer to Mars, similar to the CSA's Atmospheric Chemistry Experiment (ACE) FTS. The ACE-FTS, currently in Earth orbit, is a solar-occultation instrument measuring the solar spectrum between 750-4400 cm (-1) at a spectral resolution of 0.02 cm (-1) . We present an algorithm to retrieve temperatures and pressures from measured spectra, accurate knowledge of which is vital for inferring volume mixing ratios of trace gases. The effects of high dust quantities on spectra have been simulated using synthetic spectra of the Martian atmosphere and a method for mitigating these effects has been tested and will be presented. Work has been done to characterize the interferometer performance of the Engineering Demonstration Unit, constructed by ABB, with a focus on gaining a better understanding of the modulation efficiency of the interferometer.

Olsen, Kevin; Walker, Kaley; Strong, Kimberly; Hipkin, Victoria; Toon, Geoff; Conway, Stephanie; Berube, Philippe; Veilleux, James

163

An algorithm for computing the mixed radix fast Fourier transform  

Microsoft Academic Search

This paper presents an algorithm for computing the fast Fourier transform, based on a method proposed by Cooley and Tukey. As in their algorithm, the dimensionnof the transform is factored (if possible), andn\\/pelementary transforms of dimensionpare computed for each factorpofn. An improved method of computing a transform step corresponding to an odd factor ofnis given; with this method, the number

R. Singleton

1969-01-01

164

Cryogenic Scan Mechanism for Fourier Transform Spectrometer  

NASA Technical Reports Server (NTRS)

A compact and lightweight mechanism has been developed to accurately move a Fourier transform spectrometer (FTS) scan mirror (a cube corner) in a near-linear fashion with near constant speed at cryogenic temperatures. This innovation includes a slide mechanism to restrict motion to one dimension, an actuator to drive the motion, and a linear velocity transducer (LVT) to measure the speed. The cube corner mirror is double-passed in one arm of the FTS; double-passing is required to compensate for optical beam shear resulting from tilting of the moving cube corner. The slide, actuator, and LVT are off-the-shelf components that are capable of cryogenic vacuum operation. The actuator drives the slide for the required travel of 2.5 cm. The LVT measures translation speed. A proportional feedback loop compares the LVT voltage with the set voltage (speed) to derive an error signal to drive the actuator and achieve near constant speed. When the end of the scan is reached, a personal computer reverses the set voltage. The actuator and LVT have no moving parts in contact, and have magnetic properties consistent with cryogenic operation. The unlubricated slide restricts motion to linear travel, using crossed roller bearings consistent with 100-million- stroke operation. The mechanism tilts several arc seconds during transport of the FTS mirror, which would compromise optical fringe efficiency when using a flat mirror. Consequently, a cube corner mirror is used, which converts a tilt into a shear. The sheared beam strikes (at normal incidence) a flat mirror at the end of the FTS arm with the moving mechanism, thereby returning upon itself and compensating for the shear

Brasunas, John C.; Francis, John L.

2011-01-01

165

A discrete Fourier transform for virtual memory machines  

NASA Technical Reports Server (NTRS)

An algebraic theory of the Discrete Fourier Transform is developed in great detail. Examination of the details of the theory leads to a computationally efficient fast Fourier transform for the use on computers with virtual memory. Such an algorithm is of great use on modern desktop machines. A FORTRAN coded version of the algorithm is given for the case when the sequence of numbers to be transformed is a power of two.

Galant, David C.

1992-01-01

166

Linear Response Theory 15.0.6 Fourier Transform  

E-print Network

Chapter 15 Linear Response Theory 15.0.6 Fourier Transform A function of time f(t) which is periodic with period T can be written as a Fourier series f(t) = n=- cneinot (15.1) where o = 2/T and the cn are complex Fourier coefficients which are given by cn = 1 T to+T to f(t)e-inot dt (15.2) We can

Palffy-Muhoray, Peter

167

Astronomical spectroscopy using an aliased, step-and-integrate, Fourier transform spectrometer  

E-print Network

Astronomical spectroscopy using an aliased, step-and-integrate, Fourier transform spectrometer. Keywords: Fourier transform spectroscopy, step-and-integrate, aliased, JCMT, submillimetre 1. INTRODUCTION, transmission. Fourier transform spectrometers (FTS), with their inherently broad spectral coverage

Naylor, David A.

168

A discrete Fourier transform associated with the affine Hecke algebra  

E-print Network

We introduce an explicit representation of the double affine Hecke algebra (of type $A_1$) at $q=1$ that gives rise to a periodic counterpart of a well-known Fourier transform associated with the affine Hecke algebra.

J. F. van Diejen; E. Emsiz

2012-09-14

169

Fourier transform techniques for the inference of cloud motion  

NASA Technical Reports Server (NTRS)

The development and evaluation are reported of phase shift techniques based on the Fourier transform for the estimation of cloud motion from geosynchronous meteorological satellite photographs. An alternative approach to cloud motion estimation, involving thresholding, was proposed and studied.

Lo, R. C.; Rosenfeld, A.

1974-01-01

170

Matrix probing, skeleton decompositions, and sparse Fourier transform  

E-print Network

In this thesis, we present three different randomized algorithms that help to solve matrices, compute low rank approximations and perform the Fast Fourier Transform. Matrix probing and its conditioning When a matrix A with ...

Chiu, Jiawei

2013-01-01

171

FT Digital Filtering and Simulating Fourier transform Apodization via Excel  

NSDL National Science Digital Library

This report presents an excel spreadsheet which simulates Fourier Transform apodization filtering on a noisy signal that contains either white or an environmental noise source. Users may download the report in PDF file format.

Overway, Ken

2008-02-04

172

Technique for the metrology calibration of a Fourier transform spectrometer  

SciTech Connect

A method is presented for using a Fourier transform spectrometer (FTS) to calibrate the metrology of a second FTS. This technique is particularly useful when the second FTS is inside a cryostat or otherwise inaccessible.

Spencer, Locke D.; Naylor, David A

2008-11-10

173

Fast computation of magnetostatic fields by nonuniform fast Fourier transforms  

NASA Astrophysics Data System (ADS)

The bottleneck of micromagnetic simulations is the computation of the long-ranged magnetostatic fields. This can be tackled on regular N-node grids with fast Fourier transforms in time N log N, whereas the geometrically more versatile finite element methods (FEMs) are bounded to N4/3 in the best case. We report the implementation of a nonuniform fast Fourier transform algorithm, which brings a N log N convergence to FEM, with no loss of accuracy in the results.

Kritsikis, Evaggelos; Toussaint, Jean-Christophe; Fruchart, Olivier; Szambolics, Helga; Buda-Prejbeanu, Liliana

2008-09-01

174

Dynamic measurement of deformation using Fourier transform digital holographic interferometry  

NASA Astrophysics Data System (ADS)

Digital holographic interferometry (DHI) is a well-established optical technique for measurement of nano-scale deformations. It has become more and more important due to the rapid development of applications in aerospace engineering and biomedicine. Traditionally, phase shift technique is used to quantitatively measure the deformations in DHI. However, it cannot be applied in dynamic measurement. Fourier transform phase extraction method, which can determine the phase distribution from only a single hologram, becomes a promising method to extract transient phases in DHI. This paper introduces a digital holographic interferometric system based on 2D Fourier transform phase extraction method, with which deformations of objects can be measured quickly. In the optical setup, the object beam strikes a CCD via a lens and aperture, and the reference beam is projected on the CCD through a single-mode fiber. A small inclination angle between the diverging reference beam and optical axial is introduced in order to physically separate the Fourier components in frequency domain. Phase maps are then obtained by the utilization of Fourier transform and windowed inverse Fourier transform. The capability of the Fourier transform DHI is discussed by theoretical discussion as well as experiments.

Gao, Xinya; Wu, Sijin; Yang, Lianxiang

2013-10-01

175

Canonical Transformations in Quantum Mechanics  

E-print Network

Quantum canonical transformations are defined algebraically outside of a Hilbert space context. This generalizes the quantum canonical transformations of Weyl and Dirac to include non-unitary transformations. The importance of non-unitary transformations for constructing solutions of the Schr\\"odinger equation is discussed. Three elementary canonical transformations are shown both to have quantum implementations as finite transformations and to generate, classically and infinitesimally, the full canonical algebra. A general canonical transformation can be realized quantum mechanically as a product of these transformations. Each transformation corresponds to a familiar tool used in solving differential equations, and the procedure of solving a differential equation is systematized by the use of the canonical transformations. Several examples are done to illustrate the use of the canonical transformations. [This is an extensively revised version of hep-th-9205080: the first third of the paper is new material; the notation has been simplified, and further discussion has been added to the remainder.

Arlen Anderson

1993-05-13

176

Fractional Fourier transform of Cantor sets: further numerical study  

Microsoft Academic Search

This paper is a further work of the authors' paper published previously (Liao T H and Gao Q 2005 Chin. Phys. Lett. 22 2316). The amplitudes of fractional Fourier transform of Cantor sets are analysed from the viewpoint of multifractal by wavelet transform maxima method (WTMM). An integral operation is carried out before the application of WTMM, such that the

Qiong Gao; Tian-He Liao; Yuan-Feng Cui

2008-01-01

177

Eigenvectors and functions of the discrete Fourier transform  

Microsoft Academic Search

A method is presented for computing an orthonormal set of eigenvectors for the discrete Fourier transform (DFT). The technique is based on a detailed analysis of the eigenstructure of a special matrix which commutes with the DFT. It is also shown how fractional powers of the DFT can be efficiently computed, and possible applications to multiplexing and transform coding are

BRADLEY W. DICKINSON; KENNETH STEIGLITZ

1982-01-01

178

Fourier-transform coherent anti-Stokes Raman scattering microscopy  

E-print Network

, spectrally resolved images of CARS modes over the laser bandwidth 1500 cm-1 . We demonstrate the methodFourier-transform coherent anti-Stokes Raman scattering microscopy Jennifer P. Ogilvie,* Emmanuel-transform-based implementation of coherent anti-Stokes Raman scattering (CARS) microscopy. The method employs a single

Boyer, Edmond

179

Polar Fourier transforms of radially sampled NMR data.  

PubMed

Radial sampling of the NMR time domain has recently been introduced to speed up data collection significantly. Here, we show that radially sampled data can be processed directly using Fourier transforms in polar coordinates. We present a comprehensive theoretical analysis of the discrete polar Fourier transform, and derive the consequences of its application to radially sampled data using linear response theory. With adequate sampling, the resulting spectrum using a polar Fourier transform is indistinguishable from conventionally processed spectra with Cartesian sampling. In the case of undersampling in azimuth--the condition that provides significant savings in measurement time-the correct spectrum is still produced, but with limited distortion of the baseline away from the peaks, taking the form of a summation of high-order Bessel functions. Finally, we describe an intrinsic connection between the polar Fourier transform and the filtered backprojection method that has recently been introduced to process projection-reconstruction NOESY data. Direct polar Fourier transformation holds great potential for producing quantitatively accurate spectra from radially sampled NMR data. PMID:16820311

Coggins, Brian E; Zhou, Pei

2006-09-01

180

Electro-Optical Imaging Fourier-Transform Spectrometer  

NASA Technical Reports Server (NTRS)

An electro-optical (E-O) imaging Fourier-transform spectrometer (IFTS), now under development, is a prototype of improved imaging spectrometers to be used for hyperspectral imaging, especially in the infrared spectral region. Unlike both imaging and non-imaging traditional Fourier-transform spectrometers, the E-O IFTS does not contain any moving parts. Elimination of the moving parts and the associated actuator mechanisms and supporting structures would increase reliability while enabling reductions in size and mass, relative to traditional Fourier-transform spectrometers that offer equivalent capabilities. Elimination of moving parts would also eliminate the vibrations caused by the motions of those parts. Figure 1 schematically depicts a traditional Fourier-transform spectrometer, wherein a critical time delay is varied by translating one the mirrors of a Michelson interferometer. The time-dependent optical output is a periodic representation of the input spectrum. Data characterizing the input spectrum are generated through fast-Fourier-transform (FFT) post-processing of the output in conjunction with the varying time delay.

Chao, Tien-Hsin; Zhou, Hanying

2006-01-01

181

Lecture 11 Fast Fourier Transform (FFT) Weinan E1,2  

E-print Network

Lecture 11 Fast Fourier Transform (FFT) Weinan E1,2 and Tiejun Li2 1 Department of Mathematics@pku.edu.cn No.1 Science Building, 1575 #12;Examples Fast Fourier Transform Applications Outline Examples Fast Fourier Transform Applications #12;Examples Fast Fourier Transform Applications Signal processing

Li, Tiejun

182

Perturbation in the Fractional Fourier Span due to Erroneous Transform Order and Window Function  

Microsoft Academic Search

Fractional Fourier Transform is a generalization of the classical Fourier Transform. The Fractional Fourier span in general depends on the amplitude and phase functions of the signal and varies with the transform order. However, with the development of the Fractional Fourier filter banks, it is advantageous in some cases to have different transform orders for different filter banks to achieve

Sukrit Shankar; Chetana Shanta Patsa; Jaydev Sharma

2008-01-01

183

Computing the Fast Fourier Transform on a vector computer  

NASA Technical Reports Server (NTRS)

Two algorithms are presented for performing a Fast Fourier Transform on a vector computer and are compared on the Control Data Corporation STAR-100. The relative merits of the two algorithms are shown to depend upon whether only a few or many independent transforms are desired. A theorem is proved which shows that a set of independent transforms can be computed by performing a partial transformation on a single vector. The results of this theorem also apply to nonvector machines and have reduced the average time per transform by a factor of two on the CDC 6600 computer.

Korn, D. G.; Lambiotte, J. J., Jr.

1979-01-01

184

Canonical Transformations in Quantum Mechanics  

E-print Network

Three elementary canonical transformations are shown both to have quantum implementations as finite transformations and to generate, classically and infinitesimally, the full canonical algebra. A general canonical transformation can, in principle, be realized quantum mechanically as a product of these transformations. It is found that the intertwining of two super-Hamiltonians is equivalent to there being a canonical transformation between them. A consequence is that the procedure for solving a differential equation can be viewed as a sequence of elementary canonical transformations trivializing the super-Hamiltonian associated to the equation. It is proposed that the quantum integrability of a system is equivalent to the existence of such a sequence.

Arlen Anderson

1992-05-22

185

Fixed-point error analysis of Winograd Fourier transform algorithms  

NASA Technical Reports Server (NTRS)

The quantization error introduced by the Winograd Fourier transform algorithm (WFTA) when implemented in fixed-point arithmetic is studied and compared with that of the fast Fourier transform (FFT). The effect of ordering the computational modules and the relative contributions of data quantization error and coefficient quantization error are determined. In addition, the quantization error introduced by the Good-Winograd (GW) algorithm, which uses Good's prime-factor decomposition for the discrete Fourier transform (DFT) together with Winograd's short length DFT algorithms, is studied. Error introduced by the WFTA is, in all cases, worse than that of the FFT. In general, the WFTA requires one or two more bits for data representation to give an error similar to that of the FFT. Error introduced by the GW algorithm is approximately the same as that of the FFT.

Patterson, R. W.; Mcclellan, J. H.

1978-01-01

186

q-Generalization of the inverse Fourier transform  

E-print Network

A wide class of physical distributions appears to follow the q-Gaussian form, which plays the role of attractor according to a Central Limit Theorem generalized in the presence of specific correlations between the relevant random variables. In the realm of this theorem, a q-generalized Fourier transform plays an important role. We introduce here a method which univocally determines a distribution from the knowledge of its q-Fourier transform and some supplementary information. This procedure involves a recently q-generalized Dirac delta and the class of functions on which it acts. The present method conveniently extends the inverse of the standard Fourier transform, and is therefore expected to be very useful in the study of many complex systems.

M. Jauregui; C. Tsallis

2010-10-29

187

Photonic fractional Fourier transformer with a single dispersive device.  

PubMed

In this work we used the temporal analog of spatial Fresnel diffraction to design a temporal fractional Fourier transformer with a single dispersive device, in this way avoiding the use of quadratic phase modulators. We demonstrate that a single dispersive passive device inherently provides the fractional Fourier transform of an incident optical pulse. The relationships linking the fractional Fourier transform order and scaling factor with the dispersion parameters are derived. We first provide some numerical results in order to prove the validity of our proposal, using a fiber Bragg grating as the dispersive device. Next, we experimentally demonstrate the feasibility of this proposal by using a spool of a standard optical fiber as the dispersive device. PMID:23571945

Cuadrado-Laborde, C; Carrascosa, A; Díez, A; Cruz, J L; Andres, M V

2013-04-01

188

Lensless Fourier-Transform Ghost Imaging with Classical Incoherent Light  

E-print Network

The Fourier-Transform ghost imaging of both amplitude-only and pure-phase objects was experimentally observed with classical incoherent light at Fresnel distance by a new lensless scheme. The experimental results are in good agreement with the standard Fourier-transform of the corresponding objects. This scheme provides a new route towards aberration-free diffraction-limited 3D images with classically incoherent thermal light, which have no resolution and depth-of-field limitations of lens-based tomographic systems.

Minghui Zhang; Qing Wei; Xia Shen; Yongfeng Liu; Honglin Liu; Jing Cheng; Shensheng Han

2006-05-22

189

Fractional Fourier transform in temporal ghost imaging with classical light  

SciTech Connect

We investigate temporal, second-order classical ghost imaging with long, incoherent, scalar plane-wave pulses. We prove that in rather general conditions, the intensity correlation function at the output of the setup is given by the fractional Fourier transform of the temporal object. In special cases, the correlation function is shown to reduce to the ordinary Fourier transform and the temporal image of the object. Effects influencing the visibility and the resolution are considered. This work extends certain known results on spatial ghost imaging into the time domain and could find applications in temporal tomography of pulses.

Setaelae, Tero [Department of Applied Physics, Aalto University, P.O. Box 13500, FI-00076 Aalto (Finland); Shirai, Tomohiro [Photonics Research Institute, National Institute of Advanced Industrial Science and Technology, 1-2-1 Namiki, Tsukuba 305-8564 (Japan); Friberg, Ari T. [Department of Applied Physics, Aalto University, P.O. Box 13500, FI-00076 Aalto (Finland); Department of Physics and Mathematics, University of Eastern Finland, P.O. Box 111, FI-80101 Joensuu (Finland)

2010-10-15

190

Lensless Fourier-transform ghost imaging with classical incoherent light  

SciTech Connect

The Fourier-transform ghost imaging of both amplitude-only and pure-phase objects was experimentally observed with classical incoherent light at Fresnel distance by a lensless scheme. The experimental results are in good agreement with the standard Fourier transform of the corresponding objects. This scheme provides a route toward aberration-free diffraction-limited three-dimensional images with classically incoherent thermal light (or neutrons), which have no resolution and depth-of-field limitations of lens-based tomographic systems.

Zhang, Minghui; Wei, Qing; Shen, Xia; Liu, Yongfeng; Liu, Honglin; Cheng, Jing; Han, Shensheng [Key Laboratory for Quantum Optics and Center for Cold Atom Physics, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800 (China)

2007-02-15

191

Lineshape determination using multiple pathlengths in Fourier transform interferometers  

NASA Astrophysics Data System (ADS)

In Fourier transform spectroscopy degradation in spectral resolution and the introduction of false spectral features (`feet') both result from the limited optical pathlength used by a real instrument. This work describes a quantitative relationship between the truncation length of an interferogram and the distortion of the computed halfwidth for the three most common spectral shapes: Gaussian, Lorentzian, and Voigt profiles. The technique can also be used to aid in the alignment and calibration of a Fourier transform interferometer by deriving a calculated truncated interferogram lineshape of a `known' spectral line to compare with the lineshape actually produced by the instrument.

Cook, William B.

1994-09-01

192

Extending Fourier transformations to Hamilton's quaternions and Clifford's geometric algebras  

NASA Astrophysics Data System (ADS)

We show how Fourier transformations can be extended to Hamilton's algebra of quaternions. This was initially motivated by applications in nuclear magnetic resonance and electric engineering. Followed by an ever wider range of applications in color image and signal processing. Hamilton's algebra of quaternions is only one example of the larger class of Clifford's geometric algebras, complete algebras encoding a vector space and all its subspace elements. We introduce how Fourier transformations are extended to Clifford algebras and applied in electromagnetism, and in the processing of images, color images, vector field and climate data.

Hitzer, Eckhard

2013-10-01

193

The Michelson Interferometer and Fourier Transform Spectroscopy A Michelson interferometer with a movable mirror in one arm is an essential element in Fourier Transform (FT)  

E-print Network

The Michelson Interferometer and Fourier Transform Spectroscopy A Michelson interferometer with a movable mirror in one arm is an essential element in Fourier Transform (FT) spectroscopy. A source by the following Fourier Transform. ( )( ) ( )cos 2B I d = To illustrate the FT method we will assume

Rioux, Frank

194

Fast algorithms for the discrete W transform and for the discrete Fourier transform  

Microsoft Academic Search

A systematic method of sparse matrix factorization is developed for all four versions of the discrete W transform, the discrete cosine transform, and the discrete sine transform, as well as for the discrete Fourier transform. The factorization leads to fast algorithms in which only real arithmetic is involved. A scheme for reducing multiplications and a convenient index system are introduced.

Zhongde Wang

1984-01-01

195

Recovering Missing Slices of the Discrete Fourier Transform using Ghosts  

E-print Network

The Discrete Fourier Transform (DFT) underpins the solution to many inverse problems commonly possessing missing or un-measured frequency information. This incomplete coverage of Fourier space always produces systematic artefacts called Ghosts. In this paper, a fast and exact method for de-convolving cyclic artefacts caused by missing slices of the DFT is presented. The slices discussed here originate from the exact partitioning of DFT space, under the projective Discrete Radon Transform, called the Discrete Fourier Slice Theorem. The method has a computational complexity of O(n log2 n) (where n = N^2) and is constructed from a new Finite Ghost theory. This theory is also shown to unify several aspects of work done on Ghosts over the past three decades. The paper concludes with a significant application to fast, exact, non-iterative image reconstruction from sets of discrete slices obtained for a limited range of projection angles.

Shekhar Chandra; Imants Svalbe; Jeanpierre Guedon; Andrew Kingston; Nicolas Normand

2010-12-30

196

Calibration of optical detectors using discrete Fourier transform techniques  

NASA Technical Reports Server (NTRS)

A method for determining the detector electrooptical transfer function (DEOTF) at different discrete frequencies simultaneously is presented. It involves simulation of the detector with a waveform of unknown frequency composition, such as a square wave or impulse function. The DEOTF is calculated as the ratio of the discrete Fourier transform of the detector output to the transform of the input waveform. This technique was successfully applied to Golay cell and bolometer detectors and can be used for other linear detector systems.

Hagopian, John G.; Eichhorn, William

1990-01-01

197

Visible-NIR imaging optics for a Fourier transform spectrometer  

NASA Astrophysics Data System (ADS)

We present details of optical design, opto-mechanical design and testing of a visible-NIR imaging optical system for a Fourier transform spectrometer dedicated to astronomical application at the Mont Mégantic Observatory (Observatoire du Mont Mégantic, OMM, located south Québec city, Canada). Design considerations as well as testing and experimental results are presented.

Thibault, Simon; Reecht, Jérôme; Lavigne, Jean-François; Desnoyers, Nichola

2004-10-01

198

An Adaptation of the Fast Fourier Transform for Parallel Processing  

Microsoft Academic Search

A modified version of the Fast Fourier Transform is developed and described. This version is well adapted for use in a special-purpose computer designed for the purpose. It is shown that only three operators are needed. One operator replaces successive pairs of data points by their sums and differences. The second operator performs a fixed permutation which is an ideal

Marshall C. Pease; Menlo Parh

1968-01-01

199

Signal estimation from modified short-time Fourier transform  

Microsoft Academic Search

In this paper, we present an algorithm to estimate a signal from its modified short-time Fourier transform (STFT). This algorithm is computationally simple and is obtained by minimizing the mean squared error between the STFT of the estimated signal and the modified STFT. Using this algorithm, we also develop an iterative algorithm to estimate a signal from its modified STFT

DANIEL W. GRIFFIN; JAE S. LIM

1984-01-01

200

SU(3) phase states and finite Fourier transform  

E-print Network

We describe the construction of SU(3) phase operators using Fourier-like transform on a hexagonal lattice. The advantages and disadvantages of this approach are contrasted with other results, in particular with the more traditional approach based on polar decomposition of operators.

Brandon Zanette; Hubert de Guise

2011-10-25

201

Redundancy, the Discrete Fourier Transform, and Impulse Noise Cancellation  

Microsoft Academic Search

The relationship between the discrete Fourier transform and error-control codes is examined. Under certain conditions we show that discrete-time sequences carry redundant information which then allow for the detection and correction of errors. An application of this technique to impulse noise cancellation for pulse amplitude modulation transmission is described.

J. Wolf

1983-01-01

202

The interpolated fast Fourier transform: a comparative study  

Microsoft Academic Search

The properties of five interpolating fast Fourier transform (IFFT) methods (IFFT) are studied with respect to their systematic errors and their noise sensitivity, for a monofrequency signal. It is shown that windows with small spectral side lobes do not always result in a better overall performance of the IFFT method and that time-domain estimators can be more efficient than the

J. Schoukens; Rik Pintelon; H. Van Hamme

1992-01-01

203

A guided tour of the fast Fourier transform  

Microsoft Academic Search

For some time the Fourier transform has served as a bridge between the time domain and the frequency domain. It is now possible to go back and forth between waveform and spectrum with enough speed and economy to create a whole new range of applications for this classic mathematical device. This article is intended as a primer on the fast

G. D. Bergland

1969-01-01

204

Rotation of 10 Be stars through Fourier transform analysis  

E-print Network

Here we determine the projected rotational velocity of 10 Be stars using Fourier Transform Method. Also, we discuss the gravity darkening and extend of deviation from solid body rotation for our sample of stars. We found that 7 of considered stars are affected by strong gravity darkening or/and solar differential rotation.

Natasa Gavrilovic

2006-02-28

205

Wavelength-scale stationary-wave integrated Fourier transform spectrometry  

E-print Network

1 Wavelength-scale stationary-wave integrated Fourier transform spectrometry Etienne le Coarer1 issued by either reflection (as the principle of colour photography by G. Lippmann) or counterpropagative an elegant way of reducing the volume of spectrometer to a few hundreds of cubic wavelengths

Boyer, Edmond

206

Rainbow Fourier transform Mikhail D. Alexandrov a,b,n  

E-print Network

Rainbow Fourier transform Mikhail D. Alexandrov a,b,n , Brian Cairns b , Michael I. Mishchenko b Rainbow Optical particle characterization Remote sensing a b s t r a c t We present a novel technique between 1351 and 1651 exhibit a sharply defined rainbow structure, the shape of which is determined mostly

207

Rainbow Fourier transform Mikhail D. Alexandrov a,b,n  

E-print Network

71 73 75 77 79 81 Rainbow Fourier transform Mikhail D. Alexandrov a,b,n , Brian Cairns b , Michael I, USAQ3 a r t i c l e i n f o Keywords: ElectromagneticQ4 scattering Polarization Mie theory Rainbow angle range between 1351 and 1651 exhibit a sharply defined rainbow structure, the shape of which

208

Initial Results from the USNO Dispersed Fourier Transform Spectrograph  

Microsoft Academic Search

We have designed and constructed a ``dispersed Fourier transform spectrometer'' (dFTS), consisting of a conventional FTS followed by a grating spectrometer. By combining these two devices, we negate a substantial fraction of the sensitivity disadvantage of a conventional FTS for high-resolution, broadband, optical spectroscopy, while preserving many of the advantages inherent to interferometric spectrometers. In addition, we have implemented a

Arsen R. Hajian; Bradford B. Behr; Andrew T. Cenko; Robert P. Olling; David Mozurkewich; J. Thomas Armstrong; Brian Pohl; Sevan Petrossian; Kevin H. Knuth; Robert B. Hindsley; Marc Murison; Michael Efroimsky; Ronald Dantowitz; Marek Kozubal; Douglas G. Currie; Tyler E. Nordgren; Christopher Tycner; Robert S. McMillan

2007-01-01

209

On the Parametrization of Algebraic Discrete Fourier Transforms  

E-print Network

Karlsruhe, Germany (nueckel|klappi)@ira.uka.de Abstract. Computing the Discrete Fourier Transform (DFT of the base#12;eld Fq and can be used to compute the spectrum of the DFT. We derive a com- plete project called IDEAS [2]. The main goal of IDEAS is the development of an intelligent environ- ment

Klappenecker, Andreas

210

Interferometric Fourier transform coherent anti-stokes Raman scattering  

E-print Network

, "Three-dimensional vibrational imaging by coherent anti-Stokes Raman scattering," Phys. Rev. Lett. 82. Caster, O. Nicolet, and S. R. Leone, "Chemical imaging by single pulse interferometric coherent antiInterferometric Fourier transform coherent anti- stokes Raman scattering Meng Cui Department

Boyer, Edmond

211

APPLICATION OF FOURIER TRANSFORM SPECTROSCOPY TO AIR POLLUTION PROBLEMS  

EPA Science Inventory

The nature of information that can be retrieved from spectra obtained with Fourier transform spectroscopy is discussed. Nonlinear, least-squares analysis of spectra is capable of retrieving information that is beyond the reach of conventional methods and has improved precision an...

212

Coherent electromagnetic field imaging through Fourier transform heterodyne  

Microsoft Academic Search

The authors present a detection process capable of directly imaging the transverse amplitude, phase, and if desired, Doppler shift of coherent electromagnetic fields. Based on coherent detection principles governing conventional heterodyned RADAR\\/LIDAR systems, Fourier Transform Heterodyne (FTH) incorporates transverse spatial encoding of the local oscillator for image capture. Appropriate selection of spatial encoding functions, or basis set, allows image retrieval

B. J. Cooke; B. E. Laubscher; N. L. Olivas; R. M. Goeller; M. Cafferty; S. D. Briles; A. E. Galbraith; A. C. Grubler

1998-01-01

213

Physics 343 Lecture # 5: Sun, Stars, and Planets; Fourier Transforms  

E-print Network

Physics 343 Lecture # 5: Sun, Stars, and Planets; Fourier Transforms #12; Schedule mydata.rad :2012:050:16:30:00 : freq 1418 1 : Sun : offset 20 0 :30 : Sun : npoint : offset 0 0 :60 ... this order records useless data should be combined as ": Sun n" overwrites offsets from pointing #12;February

Baker, Andrew J.

214

Convolutional Neural Network with embedded Fourier Transform for EEG classification  

Microsoft Academic Search

In BCI (brain - computer interface) systems, brain signals must be processed to identify distinct activities that convey different mental states. We propose a new technique for the classification of electroencephalographic (EEG) steady-state visual evoked potential (SSVEP) activity for non-invasive BCI. The proposed method is based on a convolutional neural network that includes a Fourier transform between hidden layers in

Hubert Cecotti; Axel Graeser

2008-01-01

215

The conformational analysis of push-pull enaminones using Fourier transform IR and NMR spectroscopy, and quantum chemical calculations. V. ?-Methyl-, fluorine-?-N,N-dimethylaminovinyl trifluoromethyl ketones  

NASA Astrophysics Data System (ADS)

IR Fourier spectra of two enaminoketones with general formula F3Csbnd COsbnd CRdbnd CHsbnd N(CH3)2, R = F (DMTFBN); R = CH3, (DMTMBN) were studied in various pure solvents. For comparison results of earlier investigated enaminoketone R = H (DMTBN) was also presented. On the basis of NMR and IR spectra it was shown that enaminoketones DMTBN, DMTFBN and DMTMBN presented in solutions as equilibrium of two conformers, (E-s-Z) ? (E-s-E) (for DMTFBN these conformers are denoted as (Z-s-Z) and (Z-s-E), respectively). DFT calculations were carried out to evaluate relative energy and dipole moment of each spatial form. It was shown that ‘closed-ring' complex formation between (E-s-Z) and (E-s-E) conformers of DMTBN accounts for discrepancies between DFT calculations of conformer relative energies and experimentally evaluated enthalpies of (E-s-Z) ? (E-s-E) equilibrium. In ?-substituted DMTFBN and DMTMBN, where formation of ‘closed-ring' complex was impossible we did not observe such discrepancies. For both (E-s-Z) and (E-s-E) conformers of the DMTBN and DMTMBN the main influence on the ?˜(Cdbnd O) vibrations has the solvent's hydrogen bond donor (HBD) acidity, whereas for the DMTFBN an influence of the solvent's polarity/polarizability dominated.

Vdovenko, Sergey I.; Gerus, Igor I.; Zhuk, Yuri I.; Kukhar, Valery P.; Röschenthaler, Gerd-Volker

2014-10-01

216

Fast Fourier Transform for Fitness Landscapes Dan Rockmorea, Peter Kosteleca, Wim Hordijkb, Peter F.  

E-print Network

Fast Fourier Transform for Fitness Landscapes Dan Rockmorea, Peter Kosteleca, Wim Hordijkb, Peter F of the Walsh/Fourier transforms are feasible for landscapes with up to 108 configurations using Fast Fourier as the generating set on Sn. Keywords. Spectral Analysis, Fast Fourier Transform, Walsh Functions, Cayley Graphs

Stadler, Peter F.

217

Discrete fourier transform (DFT) analysis for applications using iterative transform methods  

NASA Technical Reports Server (NTRS)

According to various embodiments, a method is provided for determining aberration data for an optical system. The method comprises collecting a data signal, and generating a pre-transformation algorithm. The data is pre-transformed by multiplying the data with the pre-transformation algorithm. A discrete Fourier transform of the pre-transformed data is performed in an iterative loop. The method further comprises back-transforming the data to generate aberration data.

Dean, Bruce H. (Inventor)

2012-01-01

218

A Unified Method of Finding Laplace Transforms, Fourier Transforms, and Fourier Series. [and] An Inversion Method for Laplace Transforms, Fourier Transforms, and Fourier Series. Integral Transforms and Series Expansions. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Units 324 and 325.  

ERIC Educational Resources Information Center

This document contains two units that examine integral transforms and series expansions. In the first module, the user is expected to learn how to use the unified method presented to obtain Laplace transforms, Fourier transforms, complex Fourier series, real Fourier series, and half-range sine series for given piecewise continuous functions. In…

Grimm, C. A.

219

The Extended Fourier Transform for 2D Spectral Estimation  

NASA Astrophysics Data System (ADS)

We present a linear algebraic method, named the e Xtended Fourier Transform (XFT), for spectral estimation from truncated time signals. The method is a hybrid of the discrete Fourier transform (DFT) and the regularized resolvent transform (RRT) (J. Chen et al., J. Magn. Reson.147, 129-137 (2000)). Namely, it estimates the remainder of a finite DFT by RRT. The RRT estimation corresponds to solution of an ill-conditioned problem, which requires regularization. The regularization depends on a parameter, q, that essentially controls the resolution. By varying q from 0 to ? one can "tune" the spectrum between a high-resolution spectral estimate and the finite DFT. The optimal value of q is chosen according to how well the data fits the form of a sum of complex sinusoids and, in particular, the signal-to-noise ratio. Both 1D and 2D XFT are presented with applications to experimental NMR signals.

Armstrong, Geoffrey S.; Mandelshtam, Vladimir A.

2001-11-01

220

Group Fourier transform and the phase space path integral for finite dimensional Lie groups  

E-print Network

We formulate a notion of group Fourier transform for a finite dimensional Lie group. The transform provides a unitary map from square integrable functions on the group to square integrable functions on a non-commutative dual space. We then derive the first order phase space path integral for quantum mechanics on the group by using a non-commutative dual space representation obtained through the transform. Possible advantages of the formalism include: (1) The transform provides an alternative to the spectral decomposition via representation theory of Lie groups and the use of special functions. (2) The non-commutative dual variables are physically more intuitive, since despite the non-commutativity they are analogous to the corresponding classical variables. The work is expected, among other possible applications, to allow for the metric representation of Lorentzian spin foam models in the context of quantum gravity.

Matti Raasakka

2011-11-28

221

The Fractional Fourier Transform and Applications David H. Bailey and Paul N. Swarztrauber  

E-print Network

The Fractional Fourier Transform and Applications David H. Bailey and Paul N. Swarztrauber October transform", which admits computation by an algorithm that has complexity proportional to the fast Fourier transform algorithm. Whereas the discrete Fourier transform (DFT) is based on integral roots of unity e;2 i

Bailey, David H.

222

Application of Fourier transforms for microwave radiometric inversions  

NASA Technical Reports Server (NTRS)

Existing microwave radiometer technology now provides a suitable method for remote determination of the ocean surface's absolute brightness temperature. To extract the brightness temperature of the water from the antenna temperature, an unstable Fredholm integral equation of the first kind is solved. Fourier transform techniques are used to invert the integral after it is placed into a cross correlation form. Application and verification of the methods to a two-dimensional modeling of a laboratory wave tank system are included. The instability of the ill-posed Fredholm equation is examined and a restoration procedure is included which smooths the resulting oscillations. With the recent availability and advances of fast Fourier transform (FFT) techniques, the method presented becomes very attractive in the evaluation of large quantities of data.

Holmes, J. J.; Balanis, C. A.; Truman, W. M.

1975-01-01

223

A simple scanning mirror mechanism for a Fourier transform spectrometer  

NASA Astrophysics Data System (ADS)

We present a simple scanning mirror mechanism for a Fourier transform spectrometer, consisting of a voice coil actuator, a ball-bearing slide, and a single cube corner mirror or retroreflector. The use of a single cube corner reduces significantly the sensitivity of the Fourier transform spectrometer to the tilt of its moving mirror, enabling the simple mechanism. With simple velocity feedback using a linear velocity transducer, we achieve a scan speed stability of 2%-5% (root-mean-square) for scan speeds from 40 to 440 ?m/s for a travel of 2.2 cm, corresponding to a spectral resolution of 0.06 cm-1. Fringe amplitude stability is about 5%. This scan mechanism was operated at standard temperature and pressure, but the relatively minute amount of lubricant in the ball-bearing slide may indicate possible operation under vacuum and/or cryogenic conditions.

Brasunas, John C.; Cushman, G. Mark

1998-04-01

224

Fourier transform digital holographic adaptive optics imaging system  

PubMed Central

A Fourier transform digital holographic adaptive optics imaging system and its basic principles are proposed. The CCD is put at the exact Fourier transform plane of the pupil of the eye lens. The spherical curvature introduced by the optics except the eye lens itself is eliminated. The CCD is also at image plane of the target. The point-spread function of the system is directly recorded, making it easier to determine the correct guide-star hologram. Also, the light signal will be stronger at the CCD, especially for phase-aberration sensing. Numerical propagation is avoided. The sensor aperture has nothing to do with the resolution and the possibility of using low coherence or incoherent illumination is opened. The system becomes more efficient and flexible. Although it is intended for ophthalmic use, it also shows potential application in microscopy. The robustness and feasibility of this compact system are demonstrated by simulations and experiments using scattering objects. PMID:23262541

Liu, Changgeng; Yu, Xiao; Kim, Myung K.

2013-01-01

225

5/12/11 8:54 AMFast Fourier Transform Page 1 of 17http://paulbourke.net/miscellaneous/dft/  

E-print Network

5/12/11 8:54 AMFast Fourier Transform Page 1 of 17http://paulbourke.net/miscellaneous/dft/ D F T (Discrete Fourier Transform) F F T (Fast Fourier Transform) Written by Paul Bourke June 1993 Introduction This document describes the Discrete Fourier Transform (DFT), that is, a Fourier Transform as applied

Masci, Frank

226

Time-to-frequency Fourier transformation with photon echoes.  

PubMed

We propose to use photon echoes in rare-earth-doped crystals to implement the Fourier-transform chirp algorithm. The process is considered for application to spectral analysis of fast radio-frequency signals. Compared with surface acoustic wave devices, the proposed scheme gives access to the larger bandwidths of rare-earth-doped crystals and greater flexibility. An experimental demonstration of the proposed process is reported. PMID:18049617

Ménager, L; Le Gouët, J L; Lorgeré, I

2001-09-15

227

Multicommutation Fourier transform infrared determination of benzene in gasoline  

Microsoft Academic Search

A fully mechanized method to determine benzene in motor gasolines has been developed based on the use of Fourier transform infrared spectroscopy (FT-IR) and multicommutation. The flow network comprised a set of three-way solenoid valves and was controlled by means of a microcomputer furnished with an electronic interface and running by a software written in QUICK BASIC 4.5. The flow

Eva Ródenas-Torralba; Josep Ventura-Gayete; Ángel Morales-Rubio; Salvador Garrigues; Miguel de la Guardia

2004-01-01

228

Fast Fourier transform analysis of rotor-bearing systems  

NASA Technical Reports Server (NTRS)

Nonlinear transient analysis of rotor-bearing systems is becoming increasingly important in the analysis of modern-day rotating machinery to model such phenomena as oil film whirl. This paper develops an analysis technique incorporating modal analysis and fast Fourier transform techniques to analyze rotors with residual shaft bow and realistic nonlinear bearings. The technique is demonstrated on single-mass and three-mass rotor examples. Comparisons of the theoretical results with experimental data give excellent agreement.

Choy, K. C.; Gunter, E. J.; Allaire, P. E.

1978-01-01

229

The determination of peroxide value by fourier transform infrared spectroscopy  

Microsoft Academic Search

A rapid method for the quantitative determination of peroxide value (PV) of vegetable oils by Fourier transform infrared (FTIR)\\u000a transmission spectroscopy is described. Calibration standards were prepared by the addition oft-butyl hydroperoxide to a series of vegetable oils, along with random amounts of oleic acid and water. Additional standards\\u000a were derived through the addition of mono- and diglyceride spectral contributions,

F. R. van de Voort; A. A. Ismail; J. Sedman; J. Dubois; T. Nicodemo

1994-01-01

230

An Orthogonally Multiplexed QAM System Using the Discrete Fourier Transform  

Microsoft Academic Search

An orthogonally multiplexed QAM (O-QAM) system is a multichannel system with a baud rate spacing between adjacent carrier frequencies; this property is desirable to digitally implement the system using the discrete Fourier transformation (DFT). This paper provides a novel digital signal processing method based on anN\\/2-point DFT processing in the O-QAM system. A complexity comparison between a digital O-QAM system

BOTARO HIROSAKI

1981-01-01

231

Off-Axis Elliptical Zone Plate For Nonsymmetric Fourier Transforming  

NASA Astrophysics Data System (ADS)

An off-axis elliptical zone plate (EZP) together with refractive optics has been used for obtaining the 2-D nonsymmetric Fourier transform (NFT) of a given object with parallel beam illumination. The NFT thus obtained is exact, excepting a linear phase factor due to the carrier spatial frequency used in the EZP recording. Experimental results show the ability of this system for separating quasi-unidimensional spectra of slightly different orientation.

Bara, S.; Gomez-Reino, C.

1989-01-01

232

Transpose-free Fast Fourier Transform for Turbulence Simulation  

E-print Network

Pseudo-spectral method is one of the most accurate techniques for simulating turbulent flows. Fast Fourier transform (FFT) is an integral part of this method. In this paper, we present a new procedure to compute FFT in which we save operations during interprocess communications by avoiding transpose of the array. As a result, our transpose-free FFT is 15\\% to 20\\% faster than FFTW.

Chatterjee, A G; Chaudhuri, M

2014-01-01

233

Measuring Binary Star Orbits with a Dispersed Fourier Transform Spectrograph  

Microsoft Academic Search

The Dispersed Fourier Transform Spectrograph (dFTS) concept combines a Michelson interferometer with a dispersive spectrograph to provide high-resolution optical spectra of stellar targets. An internal laser metrology system calibrates the wavelength scale, yielding radial velocity accuracy as small as 1.5 m\\/s without a superposed reference spectrum. We deployed our second-generation instrument, dFTS2, to the Steward Observatory 2.3-meter Bok Telescope from

Bradford B. Behr; A. R. Hajian; A. T. Cenko; R. S. McMillan; M. Murison; R. Hindsley; J. Meade

2010-01-01

234

Ultra-rapid-scanning Fourier transform infrared spectrometry  

Microsoft Academic Search

Several applications of Fourier transform infrared (FT-IR) spectrometry are discussed where both conventional rapid-scanning interferometers and step-scan interferometers are unable to provide the needed information. A new interferometer is described by which it is possible to acquire interferograms with 0.25 cm optical path difference (4 cm?1 spectral resolution) in less than 1 ms. The moving element of this interferometer is

Peter R. Griffiths; Blayne L. Hirsche; Christopher J. Manning

1999-01-01

235

Fourier transform raman spectroscopy of synthetic and biological calcium phosphates  

Microsoft Academic Search

Fourier-transform (FT) Raman spectroscopy was used to characterize the organic and mineral components of biological and synthetic calcium phosphate minerals. Raman spectroscopy provides information on biological minerals that is complimentary to more widely used infrared methodologies as some infrared-inactive vibrational modes are Raman-active. The application of FT-Raman technology has, for the first time, enabled the problems of high sample fluorescence

G. R. Sauer; W. B. Zunic; J. R. Durig; R. E. Wuthier

1994-01-01

236

Pulsed Nozzle Fourier Transform Microwave Spectrometer: Advances and Applications  

Microsoft Academic Search

The pulsed nozzle Fourier transform microwave (PNFTMW) spectrometer was developed by Balle and Flygare [A new method for observing the rotational spectra of weak molecular complexes: KrHCl. J. Chem. Phys. 1979, 71 (6), 2723–2724 and 1980, 72 (2), 922–932] in 1979. The design, fabrication, and operation of this spectrometer are complicated and it has largely remained a research laboratory tool

E. Arunan; Sagarika Dev; Pankaj K. Mandal

2004-01-01

237

Quantum Canonical Transformations: Physical Equivalence of Quantum Theories  

E-print Network

Two quantum theories are physically equivalent if they are related, not by a unitary transformation, but by an isometric transformation. The conditions under which a quantum canonical transformation is an isometric transformation are given.

Arlen Anderson

1993-02-15

238

Wavelength-encoded tomography based on optical temporal Fourier transform  

NASA Astrophysics Data System (ADS)

We propose and demonstrate a technique called wavelength-encoded tomography (WET) for non-invasive optical cross-sectional imaging, particularly beneficial in biological system. The WET utilizes time-lens to perform the optical Fourier transform, and the time-to-wavelength conversion generates a wavelength-encoded image of optical scattering from internal microstructures, analogous to the interferometery-based imaging such as optical coherence tomography. Optical Fourier transform, in principle, comes with twice as good axial resolution over the electrical Fourier transform, and will greatly simplify the digital signal processing after the data acquisition. As a proof-of-principle demonstration, a 150 -?m (ideally 36 ?m) resolution is achieved based on a 7.5-nm bandwidth swept-pump, using a conventional optical spectrum analyzer. This approach can potentially achieve up to 100-MHz or even higher frame rate with some proven ultrafast spectrum analyzer. We believe that this technique is innovative towards the next-generation ultrafast optical tomographic imaging application.

Zhang, Chi; Wong, Kenneth K. Y.

2014-09-01

239

Mass spectral peak distortion due to fourier transform signal processing.  

PubMed

Distortions of peaks can occur when one uses the standard method of signal processing of data from the Orbitrap and other FT-based methods of mass spectrometry. These distortions arise because the standard method of signal processing is not a linear process. If one adds two or more functions, such as time-dependent signals from a Fourier transform mass spectrometer and performs a linear operation on the sum, the result is the same as if the operation was performed on separate functions and the results added. If this relationship is not valid, the operation is non-linear and can produce unexpected and/or distorted results. Although the Fourier transform itself is a linear operator, the standard algorithm for processing spectra in Fourier transform-based methods include non-linear mathematical operators such that spectra processed by the standard algorithm may become distorted. The most serious consequence is that apparent abundances of the peaks in the spectrum may be incorrect. In light of these considerations, we performed theoretical modeling studies to illustrate several distortion effects that can be observed, including abundance distortions. In addition, we discuss experimental systems where these effects may manifest, including suggested systems for study that should demonstrate these peak distortions. Finally, we point to several examples in the literature where peak distortions may be rationalized by the phenomena presented here. PMID:25261219

Rockwood, Alan L; Erve, John C L

2014-12-01

240

AN APPROACH TO LOW-POWER, HIGH-PERFORMANCE, FAST FOURIER TRANSFORM PROCESSOR DESIGN  

E-print Network

AN APPROACH TO LOW-POWER, HIGH-PERFORMANCE, FAST FOURIER TRANSFORM PROCESSOR DESIGN a dissertation The Fast Fourier Transform (FFT) is one of the most widely used digital signal process- ing algorithms

Mohsenin, Tinoosh

241

Micro-Diffuse Reflectance And Matrix Isolation Fourier Transform Infrared Techniques For The Identification Of Tetrachlorodibenzodioxins  

NASA Astrophysics Data System (ADS)

Diffuse reflectance infrared Fourier transform (DRIFT) and matrix isolation gas chromatography Fourier transform infrared (MI/GC/FT-IR) spectra of the 22 tetrachloro dibenzodioxin (TCDD) isomers have been measured. The spectrum of each TCDD isomer is unique.

Gurka, Donald F.; Billets, Stephen; Brasch, Jimmie W.; Barnes, Russell H.; Riggle, Charles J.; Bourne, Sidney

1985-12-01

242

Improved digital filters for evaluating Fourier and Hankel transform integrals  

USGS Publications Warehouse

New algorithms are described for evaluating Fourier (cosine, sine) and Hankel (J0,J1) transform integrals by means of digital filters. The filters have been designed with extended lengths so that a variable convolution operation can be applied to a large class of integral transforms having the same system transfer function. A f' lagged-convolution method is also presented to significantly decrease the computation time when computing a series of like-transforms over a parameter set spaced the same as the filters. Accuracy of the new filters is comparable to Gaussian integration, provided moderate parameter ranges and well-behaved kernel functions are used. A collection of Fortran IV subprograms is included for both real and complex functions for each filter type. The algorithms have been successfully used in geophysical applications containing a wide variety of integral transforms

Anderson, Walter L.

1975-01-01

243

Clifford Fourier Transform for Color Image Thomas Batard, Michel Berthier and Christophe Saint-Jean  

E-print Network

Clifford Fourier Transform for Color Image Processing Thomas Batard, Michel Berthier and Christophe Saint-Jean Abstract The aim of this paper is to define a Clifford Fourier transform that is suit- able to generalize the classical approach of scalar signal processing with the Fourier transform to higher dimen

Paris-Sud XI, Université de

244

Radon and Fourier transforms for D-modules Andrea D'Agnolo  

E-print Network

Radon and Fourier transforms for D-modules Andrea D'Agnolo and Michael Eastwood Version: July 17, 2002 Contents 1 Radon and Fourier transforms for D-modules 3 1.1 Review on algebraic D-modules . . . . . . . . . . . . . . . . 3 1.2 Review on the Fourier-Laplace transform . . . . . . . . . . 5 1.3 Review on the Radon

D'Agnolo, Andrea

245

Fourier transform of the 3d NS equations The 3d NS equations are  

E-print Network

1 Fourier transform of the 3d NS equations The 3d NS equations are (1) vi t + vj vi xj = - p xi transforms (2) vi x( ) = ui k( )eikx k p x( ) = p k( )eikx k we obtain the Fourier transform of (1 easily add it in at the end. Our interest is in the advection and pressure terms. Introducing the Fourier

Salmon, Rick

246

An Accurate Discrete Fourier Transform for Image Processing Normand Beaudoin' and Steven S . Beauchernint  

E-print Network

An Accurate Discrete Fourier Transform for Image Processing Normand Beaudoin' and Steven S . Beauchernint Abstract The classical method of numerically computing the Fourier transform of digitizedfunctions in one or in d- dimensions is the so-called discrete Fourier transform (DFT),efficiently implemented

Beauchemin, Steven S.

247

Clifford Fourier Transform for Color Image Thomas Batard, Michel Berthier and Christophe Saint-Jean  

E-print Network

Clifford Fourier Transform for Color Image Processing Thomas Batard, Michel Berthier and Christophe Saint-Jean Abstract The aim of this paper is to define a Clifford Fourier transform that is suit- able the classical approach of scalar signal processing with the Fourier transform to higher dimen- sional signals

248

An update on the imaging Fourier transform spectrometer for Brad G. Gom and David A. Naylor*  

E-print Network

An update on the imaging Fourier transform spectrometer for SCUBA-2 Brad G. Gom and David A. Naylor and current design and of an imaging Fourier transform spectrometer (IFTS) for use with SCUBA-2, the second. Keywords: Imaging, Fourier, Transform, Spectrometer, SCUBA-2, Submillimetre 1. INTRODUCTION SCUBA-2

Naylor, David A.

249

Polar Fourier transforms of radially sampled NMR data Brian E. Coggins, Pei Zhou *  

E-print Network

Polar Fourier transforms of radially sampled NMR data Brian E. Coggins, Pei Zhou * Department directly using Fourier transforms in polar coordinates. We present a comprehensive theoretical analysis of the discrete polar Fourier transform, and derive the consequences of its application to radially sampled data

Richardson, David

250

An Incremental Algorithm for Signal Reconstruction from Short-Time Fourier Transform Magnitude  

E-print Network

An Incremental Algorithm for Signal Reconstruction from Short-Time Fourier Transform Magnitude Jake-time Fourier transform (STFT). In contrast to existing algorithms based on alternating projections, we offer-domain signal from only the magnitude of the short-time Fourier transform (STFT) is a common prob- lem in speech

Poggio, Tomaso

251

Computational Fluid Dynamics JOURNAL vol.?? no.? June 2006 (pp.) A Clifford Fourier Transform for  

E-print Network

Computational Fluid Dynamics JOURNAL vol.?? no.? June 2006 (pp.­) A Clifford Fourier Transform field analysis used the Clifford Fourier transform for efficient pattern recognition for vector field to rectilinear grids. We combine this approach with a fast Fourier transform to handle scalar data on arbitrary

Hamann, Bernd

252

Fourier transform microwave spectroscopy of ScS (X2 ) and YS (X2  

E-print Network

Fourier transform microwave spectroscopy of ScS (X2 R+ ) and YS (X2 R+ ) G.R. Adande, D.T. Halfen measured in the range 8­48 GHz using Fourier transform microwave (FTMW) spectroscopy. The radicals were wavelengths, as well as by Fourier transform infrared and optical double resonance methods [7

Ziurys, Lucy M.

253

Project Summary MRI: Development of a Chirped-Pulse, Fourier-Transform mm-Wave Pulsed  

E-print Network

Project Summary MRI: Development of a Chirped-Pulse, Fourier-Transform mm-Wave Pulsed Uniform technologies: chirped-pulse Fourier-transform mm-wave spectroscopy and pulsed uniform supersonic flows: The instrument will leverage the ultra-broadband Chirped-pulse Fourier-transform Microwave (CP

Baskaran, Mark

254

Heterodyne-assisted pulsed spectroscopy with a nearly Fourier-transform limited,  

E-print Network

Heterodyne-assisted pulsed spectroscopy with a nearly Fourier-transform limited, injection. The measured TPE linewidth approaches the ultimate limit imposed by the Fourier transform of the pulse light sources can be no better than the Fourier-transform (FT) limit associated with the FWHM of pulse

Kono, Mitsu

255

Two-Dimensional Fourier Transform Analysis of Helicopter Flyover Noise  

NASA Technical Reports Server (NTRS)

A method to separate main rotor and tail rotor noise from a helicopter in flight is explored. Being the sum of two periodic signals of disproportionate, or incommensurate frequencies, helicopter noise is neither periodic nor stationary. The single Fourier transform divides signal energy into frequency bins of equal size. Incommensurate frequencies are therefore not adequately represented by any one chosen data block size. A two-dimensional Fourier analysis method is used to separate main rotor and tail rotor noise. The two-dimensional spectral analysis method is first applied to simulated signals. This initial analysis gives an idea of the characteristics of the two-dimensional autocorrelations and spectra. Data from a helicopter flight test is analyzed in two dimensions. The test aircraft are a Boeing MD902 Explorer (no tail rotor) and a Sikorsky S-76 (4-bladed tail rotor). The results show that the main rotor and tail rotor signals can indeed be separated in the two-dimensional Fourier transform spectrum. The separation occurs along the diagonals associated with the frequencies of interest. These diagonals are individual spectra containing only information related to one particular frequency.

SantaMaria, Odilyn L.; Farassat, F.; Morris, Philip J.

1999-01-01

256

Two-Dimensional Fourier Transform Applied to Helicopter Flyover Noise  

NASA Technical Reports Server (NTRS)

A method to separate main rotor and tail rotor noise from a helicopter in flight is explored. Being the sum of two periodic signals of disproportionate, or incommensurate frequencies, helicopter noise is neither periodic nor stationary, but possibly harmonizable. The single Fourier transform divides signal energy into frequency bins of equal size. Incommensurate frequencies are therefore not adequately represented by any one chosen data block size. A two-dimensional Fourier analysis method is used to show helicopter noise as harmonizable. The two-dimensional spectral analysis method is first applied to simulated signals. This initial analysis gives an idea of the characteristics of the two-dimensional autocorrelations and spectra. Data from a helicopter flight test is analyzed in two dimensions. The test aircraft are a Boeing MD902 Explorer (no tail rotor) and a Sikorsky S-76 (4-bladed tail rotor). The results show that the main rotor and tail rotor signals can indeed be separated in the two-dimensional Fourier transform spectrum. The separation occurs along the diagonals associated with the frequencies of interest. These diagonals are individual spectra containing only information related to one particular frequency.

Santa Maria, Odilyn L.

1999-01-01

257

Conformal Transformations and Quantum Gravity  

E-print Network

Recently\\cite{BQG}, it was shown that quantum effects of matter could be identified with the conformal degree of freedom of the space-time metric. Accordingly, one can introduce quantum effects either by making a scale transformation (i.e. changing the metric), or by making a conformal transformation (i.e. changing all physical quantities). These two ways are investigated and compared. Also, it is argued that, the ultimate formulation of such a quantum gravity theory should be in the framework of the scalar-tensor theories.

Fatimah Shojai; Ali Shojai; Mehdi Golshani

1999-03-13

258

Numerical Simulations of the Fourier-Transformed Vlasov-Maxwell System in Higher Dimensions—Theory and Applications  

NASA Astrophysics Data System (ADS)

We present a review of recent developments of simulations of the Vlasov-Maxwell system of equations using a Fourier transform method in velocity space. In this method, the distribution functions for electrons and ions are Fourier transformed in velocity space, and the resulting set of equations are solved numerically. In the original Vlasov equation, phase mixing may lead to an oscillatory behavior and sharp gradients of the distribution function in velocity space, which is problematic in simulations where it can lead to unphysical electric fields and instabilities and to the recurrence effect where parts of the initial condition recur in the simulation. The particle distribution function is in general smoother in the Fourier transformed velocity space, which is desirable for the numerical approximations. By designing outflow boundary conditions in the Fourier transformed velocity space, the highest oscillating terms are allowed to propagate out through the boundary and are removed from the calculations, thereby strongly reducing the numerical recurrence effect. The outflow boundary conditions in higher dimensions including electromagnetic effects are discussed. The Fourier transform method is also suitable to solve the Fourier transformed Wigner equation, which is the quantum mechanical analogue of the Vlasov equation for classical particles.

Eliasson, Bengt

2010-09-01

259

Fast Fourier transform based direct integration algorithm for the linear canonical transform  

NASA Astrophysics Data System (ADS)

The linear canonical transform(LCT) is a parameterized linear integral transform, which is the general case of many well-known transforms such as the Fourier transform(FT), the fractional Fourier transform(FRT) and the Fresnel transform(FST). These integral transforms are of great importance in wave propagation problems because they are the solutions of the wave equation under a variety of circumstances. In optics, the LCT can be used to model paraxial free space propagation and other quadratic phase systems such as lens and graded-index media. A number of algorithms have been presented to fast compute the LCT. When they are used to compute the LCT, the sampling period in the transform domain is dependent on that in the signal domain. This drawback limits their applicability in some cases such as color digital holography. In this paper, a Fast-Fourier-Transform-based Direct Integration algorithm(FFT-DI) for the LCT is presented. The FFT-DI is a fast computational method of the Direct Integration(DI) for the LCT. It removes the dependency of the sampling period in the transform domain on that in the signal domain. Simulations and experimental results are presented to validate this idea.

Wang, Dayong; Liu, Changgeng; Wang, Yunxin; Zhao, Jie

2010-07-01

260

Fast Fourier transform based direct integration algorithm for the linear canonical transform  

NASA Astrophysics Data System (ADS)

The linear canonical transform(LCT) is a parameterized linear integral transform, which is the general case of many well-known transforms such as the Fourier transform(FT), the fractional Fourier transform(FRT) and the Fresnel transform(FST). These integral transforms are of great importance in wave propagation problems because they are the solutions of the wave equation under a variety of circumstances. In optics, the LCT can be used to model paraxial free space propagation and other quadratic phase systems such as lens and graded-index media. A number of algorithms have been presented to fast compute the LCT. When they are used to compute the LCT, the sampling period in the transform domain is dependent on that in the signal domain. This drawback limits their applicability in some cases such as color digital holography. In this paper, a Fast-Fourier-Transform-based Direct Integration algorithm(FFT-DI) for the LCT is presented. The FFT-DI is a fast computational method of the Direct Integration(DI) for the LCT. It removes the dependency of the sampling period in the transform domain on that in the signal domain. Simulations and experimental results are presented to validate this idea.

Wang, Dayong; Liu, Changgeng; Wang, Yunxin; Zhao, Jie

2011-03-01

261

Radon and Fourier transforms for Dmodules Andrea D'Agnolo and Michael Eastwood  

E-print Network

Radon and Fourier transforms for D­modules Andrea D'Agnolo and Michael Eastwood Contents Introduction 2 Acknowledgements 2 1. Radon and Fourier transforms for D­modules 3 1.1. Review on algebraic D­modules 3 1.2. Review on the Fourier­Laplace transform 5 1.3. Review on the Radon transform(s) 6 1.4. Review

262

Quantum Optical Version of Classical Optical Transformations and Beyond  

E-print Network

By the newly developed technique of integration within an ordered product (IWOP) of operators, we explore quantum optical version of classical optical transformations such as optical Fresnel transform, Hankel transform, fractional Fourier transform, Wigner transform, wavelet transform and Fresnel-Hadmard combinatorial transform etc. In this way one may gain benefit for developing classical optics theory from the research in quantum optics, or vice-versa. We can not only find some new quantum mechanical unitary operators which correspond to the known optical transformations, deriving a new theorem for calculating quantum tomogram of density operators, but also can reveal some new classical optical transformations. We derive GFO's normal product form and its canonical coherent state representation and find that GFO is the loyal representation of symplectic group multiplication rule. We show that GFT is just the transformation matrix element of GFO in the coordinate representation such that two successive GFTs is still a GFT. The ABCD rule of the Gaussian beam propagation is directly demonstrated in the context of quantum optics. Especially, the introduction of quantum mechanical entangled state representations opens up a new area to finding new classical optical transformations. The complex wavelet transform and the condition of mother wavelet are studied in the context of quantum optics too. Throughout our discussions, the coherent state, the entangled state representation of the two-mode squeezing operators and the IWOP technique are fully used. All these confirms Dirac's assertion: " ... for a quantum dynamic system that has a classical analogue, unitary transformation in the quantum theory is the analogue of contact transformation in the classical theory".

Hong-yi Fan; Li-yun Hu

2010-10-03

263

Fast Fourier Transform Notes 18.310, Fall 2005, Prof. Peter Shor  

E-print Network

Fast Fourier Transform Notes 18.310, Fall 2005, Prof. Peter Shor 1 Introduction: Fourier Series the integral aj = 1 L L x=0 y(x)e-2ijx/L (2) 2 The Fourier transform Given a function f(x) defined for all real, as follows f(x) = eikx g(k)dk Here g(x) is called the Fourier transform of f(x), and f(x) is the inverse

Shor, Peter W.

264

Particle field holography data reduction by Fourier transform analysis  

NASA Astrophysics Data System (ADS)

The size distribution of a particle field hologram is obtained with a Fourier transformation of the Fraunhofer diffraction pattern of the reconstructed hologram. Off-axis absorption holograms of particle fields with known characteristics were obtained and analyzed with a commercially available instrument. The mean particle size of the reconstructed hologram was measured with an error of + or - 5 percent, while the distribution broadening was estimated within + or - 15 percent. Small sections of a pulsed laser hologram of a synthetic fuel spray were analyzed with this method thus yielding a spatially resolved size distribution. The method yields fast and accurate automated analysis of particle field holograms.

Hess, C. F.; Trolinger, J. D.; Wilmot, T. R.

1985-01-01

265

Fourier-transform Raman spectroscopic study of human hair  

NASA Astrophysics Data System (ADS)

Fourier-transform Raman microscopic spectra of normal, untreated and bleached hair fibres are presented. Vibrational assignments are made and differences are ascribed to the production of cysteic acid from cysteine. Changes in conformation associated with the disulphide bond in the keratotic component are noted from the ?(CSSC) vibrational modes at wave numbers near 500 cm -1. Raman spectra of hair root ends have also been investigated with a diminution in cysteine content being observed. Application of the technique to the biomedical investigation of healthy and diseased hair is proposed.

Akhtar, W.; Edwards, H. G. M.; Farwell, D. W.; Nutbrown, M.

1997-07-01

266

Transfer Function Identification Using Orthogonal Fourier Transform Modeling Functions  

NASA Technical Reports Server (NTRS)

A method for transfer function identification, including both model structure determination and parameter estimation, was developed and demonstrated. The approach uses orthogonal modeling functions generated from frequency domain data obtained by Fourier transformation of time series data. The method was applied to simulation data to identify continuous-time transfer function models and unsteady aerodynamic models. Model fit error, estimated model parameters, and the associated uncertainties were used to show the effectiveness of the method for identifying accurate transfer function models from noisy data.

Morelli, Eugene A.

2013-01-01

267

SCUBA-2 Fourier transform spectrometer (FTS-2) commissioning results  

NASA Astrophysics Data System (ADS)

We present the latest commissioning results and instrument performance for the SCUBA-2 imaging Fourier Transform Spectrometer (FTS-2) installed at the James Clerk Maxwell Telescope (JCMT). This ancillary instrument provides intermediate spectral resolution (R ~10 to 5000) across both the 450 and 850 ?m atmospheric transmission windows with a FOV of ~5 arcmin2. The superconducting TES sensors and SQUID readout of SCUBA-2 present unique challenges for operation of an FTS; the sensitivity requirements demand high detector linearity and stability in addition to control of systematic atmospheric and optical spillover effects. We discuss the challenges encountered during commissioning and ongoing efforts to mitigate their effects.

Gom, Brad G.; Naylor, David A.; Friberg, Per; Bell, Graham S.; Bintley, Daniel; Abdelazim, Sherif; Sherwood, Matt

2014-07-01

268

High-frequency fourier transform ion cyclotron resonance mass spectrometry.  

PubMed

The experimental Fourier transform ion cyclotron resonance (FT/ICR) frequency range has been extended to 107 MHz. We report the observation of FT/ICR signals from electron-ionized species of mass-to-charge ratio 8, 7, 6, 5, 4, 3, 2, and 1 ? per elementary charge. We show that moderately high charge states of atomic ions (e.g., N(3+)) are easily generated and detected. Several applications for high-frequency FT/ICR mass spectrometry are proposed and discussed. PMID:24234797

Schweikhard, L; Alber, G M; Marshall, A G

1993-02-01

269

Synthetic quadrature phase detector/demodulator for Fourier transform spectrometers.  

PubMed

A method is developed to demodulate (velocity correct) Fourier transform spectrometer data that are taken with an analog to digital converter that digitizes equally spaced in time. This method makes it possible to use simple low-cost, high-resolution audio digitizers to record high-quality data without the need for an event timer or quadrature laser hardware and makes it possible to use a metrology laser of any wavelength. The reduced parts count and simple implementation make it an attractive alternative in space-based applications when compared to previous methods such as the Brault algorithm. PMID:19104542

Campbell, Joel

2008-12-20

270

Fourier Transform Infrared Spectroscopy of Trifluoroiodomethane ICP Discharge  

NASA Astrophysics Data System (ADS)

Trifluoroiodomethane (CF3I) is an experimental gas that currently is being considered for semiconductor etching. We will report the breakdown characteristics of CF3I in an ICP plasma. In this study, the gas chemistry was examined through the use of Fourier transform infrared (FTIR) spectroscopy. This allowed us to identify the fraction of CF3I remaining in the discharge as well as some of the daughter species produced. Our results indicate that the major multi-atomic species found in the system include Tetrafluoromethane (CF4) and Trifluoromethyl (CF3). Mass balance examination also suggests the creation of atomic and molecular Iodide.

Fagioli, Cassius; Urrabazo, David; Goeckner, Matthew

2012-10-01

271

Fourier Transform Infrared Spectroscopy for Process Monitoring and Control  

E-print Network

FOURIER TRANSFORM INFRARED SPECl'ROSCOPY FOR PROCESS MONITORING AND CONTROL Peter R. Solomon Martin D. Carangelo Robert M. Carangelo President Software Engineer Vice-President On-Line Technologies, Inc. On-Line Technologies, Inc. On...O 1:; 'a Q) 5.0 e .... ~ 2.5 ~~ 0.0 :.;;. \\ (i R~ (565K) it '-' 6500 4500 2500 500 Wavenumbers (em-I) Fipre 2. The spectra for acetylene, CO 2 , and butane in He at 555 K are shown in (A) (1 transmittance); (B) radiance; and (C...

Solomon, P. R.; Carangelo, M. D.; Carangelo, R. M.

272

Ordered fast fourier transforms on a massively parallel hypercube multiprocessor  

NASA Technical Reports Server (NTRS)

Design alternatives for ordered Fast Fourier Transformation (FFT) algorithms were examined on massively parallel hypercube multiprocessors such as the Connection Machine. Particular emphasis is placed on reducing communication which is known to dominate the overall computing time. To this end, the order and computational phases of the FFT were combined, and the sequence to processor maps that reduce communication were used. The class of ordered transforms is expanded to include any FFT in which the order of the transform is the same as that of the input sequence. Two such orderings are examined, namely, standard-order and A-order which can be implemented with equal ease on the Connection Machine where orderings are determined by geometries and priorities. If the sequence has N = 2 exp r elements and the hypercube has P = 2 exp d processors, then a standard-order FFT can be implemented with d + r/2 + 1 parallel transmissions. An A-order sequence can be transformed with 2d - r/2 parallel transmissions which is r - d + 1 fewer than the standard order. A parallel method for computing the trigonometric coefficients is presented that does not use trigonometric functions or interprocessor communication. A performance of 0.9 GFLOPS was obtained for an A-order transform on the Connection Machine.

Tong, Charles; Swarztrauber, Paul N.

1989-01-01

273

A new hybrid algorithm for computing a fast discrete Fourier transform  

NASA Technical Reports Server (NTRS)

For certain long transform lengths, Winograd's algorithm for computing the discrete Fourier transform is extended considerably. This is accomplished by performing the cyclic convolution, required by Winograd's method, with the Mersenne-prime number theoretic transform. This new algorithm requires fewer multiplications than either the standard fast Fourier transform or Winograd's more conventional algorithm.

Reed, I. S.; Truong, T. K.

1978-01-01

274

Fractional Fourier transform of Cantor sets: further numerical study  

NASA Astrophysics Data System (ADS)

This paper is a further work of the authors' paper published previously (Liao T H and Gao Q 2005 Chin. Phys. Lett. 22 2316). The amplitudes of fractional Fourier transform of Cantor sets are analysed from the viewpoint of multifractal by wavelet transform maxima method (WTMM). An integral operation is carried out before the application of WTMM, such that the function obtained can be considered as the perturbed devil staircase. Also, wavelets with large number of vanishing moments are used, which makes the complete singularity spectrum more accessible. The validity of multifractal formalism is guaranteed by restricting parameter q to a proper range, so that the phenomenon of multifractal phase transition can be explained reasonably. Particularly, the method of determining the range of parameter q in the above paper is developed to be more operational and rigorous.

Gao, Qiong; Liao, Tian-He; Cui, Yuan-Feng

2008-06-01

275

S-duality as a beta-deformed Fourier transform  

E-print Network

An attempt is made to formulate Gaiotto's S-duality relations in an explicit quantitative form. Formally the problem is that of evaluation of the Racah coefficients for the Virasoro algebra, and we approach it with the help of the matrix model representation of the AGT-related conformal blocks and Nekrasov functions. In the Seiberg-Witten limit, this S-duality reduces to the Legendre transformation. In the simplest case, its lifting to the level of Nekrasov functions is just the Fourier transform, while corrections are related to the beta-deformation. We calculate them with the help of the matrix model approach and observe that they vanish for beta=1. Explicit evaluation of the same corrections from the U_q(sl(2)) infinite-dimensional representation formulas due to B.Ponsot and J.Teshner remains an open problem.

D. Galakhov; A. Mironov; A. Morozov

2012-05-22

276

Fourier Transform for Fermionic Systems and the Spectral Tensor Network  

NASA Astrophysics Data System (ADS)

Leveraging the decomposability of the fast Fourier transform, I propose a new class of tensor network that is efficiently contractible and able to represent many-body systems with local entanglement that is greater than the area law. Translationally invariant systems of free fermions in arbitrary dimensions as well as 1D systems solved by the Jordan-Wigner transformation are shown to be exactly represented in this class. Further, it is proposed that these tensor networks be used as generic structures to variationally describe more complicated systems, such as interacting fermions. This class shares some similarities with the Evenbly-Vidal branching multiscale entanglement renormalization ansatz, but with some important differences and greatly reduced computational demands.

Ferris, Andrew J.

2014-07-01

277

Fourier transform for fermionic systems and the spectral tensor network.  

PubMed

Leveraging the decomposability of the fast Fourier transform, I propose a new class of tensor network that is efficiently contractible and able to represent many-body systems with local entanglement that is greater than the area law. Translationally invariant systems of free fermions in arbitrary dimensions as well as 1D systems solved by the Jordan-Wigner transformation are shown to be exactly represented in this class. Further, it is proposed that these tensor networks be used as generic structures to variationally describe more complicated systems, such as interacting fermions. This class shares some similarities with the Evenbly-Vidal branching multiscale entanglement renormalization ansatz, but with some important differences and greatly reduced computational demands. PMID:25032911

Ferris, Andrew J

2014-07-01

278

Data Transmission by Frequency-Division Multiplexing Using the Discrete Fourier Transform  

Microsoft Academic Search

The Fourier transform data communication system is a realization of frequency-division multiplexing (FDM) in which discrete Fourier transforms are computed as part of the modulation and demodulation processes. In addition to eliminating the bunks of subcarrier oscillators and coherent demodulators usually required in FDM systems, a completely digital implementation can be built around a special-purpose computer performing the fast Fourier

S. B. WEINSTEIN; PAUL M. EBERT

1971-01-01

279

Progress report of a static Fourier transform spectrometer breadboard  

NASA Astrophysics Data System (ADS)

MOLI instrument - for MOtionLess Interferometer - takes advantage of the new concept of static Fourier transform spectrometer. It is a high-resolution spectrometer working over a narrow bandwidth, which is adapted to a wide range of atmospheric sounding missions and compatible with micro-satellite platform. The core of this instrument is an echelette cube. Mirrors on the classical design are replaced by stepped mirrors - integrated into that interference cube - thus suppressing any moving part. The steps' directions being set over a perpendicular axis, the overlap of both stepped mirrors creates a cluster of so-called "echelettes", each one corresponding to a different optical path difference (OPD). Hence the Fourier transform of the incoming radiance is directly imaged on a CCD array in a single acquisition. The frequency domain of the measurements is selected by an interferential filter disposed on the incoming optical path. A rotating wheel equipped with several filters allows the successive measurement of spectra around some bands of interest, i.e. O2, CO2 and CO absorption bands.

Rosak, A.; Tintó, F.

2004-06-01

280

Ultrafast and versatile spectroscopy by temporal Fourier transform  

NASA Astrophysics Data System (ADS)

One of the most remarkable and useful properties of a spatially converging lens system is its inherent ability to perform the Fourier transform; the same applies for the time-lens system. At the back focal plane of the time-lens, the spectral information can be instantaneously obtained in the time axis. By implementing temporal Fourier transform for spectroscopy applications, this time-lens-based architecture can provide orders of magnitude improvement over the state-of-art spatial-dispersion-based spectroscopy in terms of the frame rate. On the other hand, in addition to the single-lens structure, the multi-lens structures (e.g. telescope or wide-angle scope) will provide very versatile operating conditions. Leveraging the merit of instantaneous response, as well as the flexible lens structure, here we present a 100-MHz frame rate spectroscopy system - the parametric spectro-temporal analyzer (PASTA), which achieves 17 times zoom in/out ratio for different observation ranges.

Zhang, Chi; Wei, Xiaoming; Marhic, Michel E.; Wong, Kenneth K. Y.

2014-06-01

281

Imaging Fourier transform spectrometer (IFTS): parametric sensitivity analysis  

NASA Astrophysics Data System (ADS)

Imaging Fourier transform spectrometers (IFTS) allow for very high spectral resolution hyperspectral imaging while using moderate size 2D focal plane arrays in a staring mode. This is not the case for slit scanning dispersive imaging spectrometers where spectral sampling is related to the focal plane pixel count along the spectral dimension of the 2D focal plane used in such an instrument. This can become a major issue in the longwave infrared (LWIR) where the operability and yield of highly sensitivity arrays (i.e.HgCdTe) of large dimension are generally poor. However using an IFTS introduces its own unique set of issues and tradeoffs. In this paper we develop simplified equations for describing the sensitivity of an IFTS, including the effects of data windowing. These equations provide useful insights into the optical, focal plane and operational design trade space that must be considered when examining IFTS concepts aimed at a specific sensitivity and spectral resolution application. The approach is illustrated by computing the LWIR noise-equivalent spectral radiance (NESR) corresponding to the NASA Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS) concept assuming a proven and reasonable noise-equivalent irradiance (NEI) capability for the focal plane.

Keller, Robert A.; Lomheim, Terrence S.

2005-06-01

282

The Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS): noise performance  

NASA Astrophysics Data System (ADS)

The NASA New Millennium Program (NMP) Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS) instrument was designed to demonstrate new and emerging technologies and provide immense improvements in satellite based remote sensing of the atmosphere from a geostationary orbit [1]. Combining a Fourier Transform Spectrometer (FTS) and Large Area Focal Plane Arrays, GIFTS measures incident infrared radiance with an extraordinary combination of spectral, temporal, and spatial resolution and coverage. Thermal vacuum testing of the GIFTS Engineering Development Unit (EDU) was performed at the Space Dynamics Laboratory and completed in May 2006 [2,3]. The GIFTS noise performance measured during EDU thermal vacuum testing indicates that threshold performance has been realized, and that goal performance (or better) has been achieved over much of both the Longwave Infrared (LWIR) and Short/Midwave Infrared (SMWIR) detector bands. An organizational structure for the division of the noise sources and effects for the GIFTS instrument is presented. To comprehensively characterize and predict the effects of measurement noise on expected instrument performance, the noise sources are categorically divided and a method of combining the independent effects is defined. Within this architecture, the total noise is principally decomposed into spectrally correlated noise and random (spectrally uncorrelated) noise. The characterization of the spectrally correlated noise sources specified within the structure is presented in detail.

Taylor, Joe K.; Revercomb, Henry E.; Tobin, David C.; Best, Fred A.; Knuteson, Robert O.; Elwell, John D.; Cantwell, Gregory W.; Scott, Deron K.; Bingham, Gail E.; Smith, William L.; Zhou, Daniel K.; Reisse, Robert A.

2006-12-01

283

Ultrafast and versatile spectroscopy by temporal Fourier transform  

PubMed Central

One of the most remarkable and useful properties of a spatially converging lens system is its inherent ability to perform the Fourier transform; the same applies for the time-lens system. At the back focal plane of the time-lens, the spectral information can be instantaneously obtained in the time axis. By implementing temporal Fourier transform for spectroscopy applications, this time-lens-based architecture can provide orders of magnitude improvement over the state-of-art spatial-dispersion-based spectroscopy in terms of the frame rate. On the other hand, in addition to the single-lens structure, the multi-lens structures (e.g. telescope or wide-angle scope) will provide very versatile operating conditions. Leveraging the merit of instantaneous response, as well as the flexible lens structure, here we present a 100-MHz frame rate spectroscopy system – the parametric spectro-temporal analyzer (PASTA), which achieves 17 times zoom in/out ratio for different observation ranges. PMID:24939667

Zhang, Chi; Wei, Xiaoming; Marhic, Michel E.; Wong, Kenneth K. Y.

2014-01-01

284

Multi-component gas analyzer based on Fourier transform spectrometer  

NASA Astrophysics Data System (ADS)

A multi-component Fourier Transform InfraRed (FTIR) gas analyzer with a low spectral resolution (8cm-1) is described in this paper. The hardware of this analyzer is consisting of a rugged Fourier Transform Spectrometer (FTS), an uncooled pyroelectric Deuterated L-Alanine TriGlycine Sulfate (DLATGS) detector, a glass body long-path gas cell and relevant sampling devices. The transplantable software and algorithms include the building of spectral library from the free sources such as EPA, NIST, HITRAN etc, identification of spectrum components and a modified classical least square regression with automatic baseline compensation. In order to validate this system, we implemented a continuous on-line experiment using the 55 ?mol.mol-1 methane and 28 ?mol.mol-1 nitrous oxide standard mixtures. The experimental results show this low resolution analyzer has accuracy and robust analysis abilities. The description in this paper is helpful to facilitate the development of a FTIR multi-component gas analyzer.

Ren, Li-Bing; Wei, Hao-Yun; Li, Yan

2010-08-01

285

Atmospheric Evaluation Using Various Open Path Fourier Transform Infrared  

NASA Astrophysics Data System (ADS)

This dissertation is comprised of three different Fourier transform infrared (FT-IR) monitoring configurations that utilize active and passive open path Fourier transform infrared (OP-FT-IR) spectrometry. The configurations include: active monitoring using a SiC source (chapters 2 and 3); passive monitoring using the ambient background and sample emission and absorption (chapters 4 and 7); and a monitoring configuration that is a hybrid of these two utilizing on -site structures at above ambient temperatures often found at industrial sites as sources of IR radiation (chapters 5 and 6). Chapter 1 gives an introduction to the dissertation. Chapter 2 is an introduction to OP-FT-IR monitoring and is broken into four sections: IR, FT-IR, OP-FT-IR, and laboratory calibrations. This chapter includes an extensive suggested reading section including OP-FT-near-IR spectrometry. Chapter 3 describes some active OP-FT-IR spectrometry done with the EPA at a coal gasification Superfund site in Fairfield, Iowa. Chapter 4 is an introduction to passive FT-IR spectrometry. Chapters 5 and 6 explore the technique using on-site structures at above ambient temperatures at an agricultural chemical plant as sources for OP-FT-IR monitoring. Chapter 7 describes the analysis of passive FT-IR interferograms obtained in the laboratory for the detection of benzene.

Tucker, Melissa Dawn

286

On integral and finite Fourier transforms of continuous q-Hermite polynomials  

SciTech Connect

We give an overview of the remarkably simple transformation properties of the continuous q-Hermite polynomials H{sub n}(x vertical bar q) of Rogers with respect to the classical Fourier integral transform. The behavior of the q-Hermite polynomials under the finite Fourier transform and an explicit form of the q-extended eigenfunctions of the finite Fourier transform, defined in terms of these polynomials, are also discussed.

Atakishiyeva, M. K. [Universidad Autonoma del Estado de Morelos, Facultad de Ciencias (Mexico); Atakishiyev, N. M., E-mail: natig_atakishiyev@hotmail.co [Universidad Nacional Autonoma de Mexico, Instituto de Matematicas, Unidad Cuernavaca (Mexico)

2009-05-15

287

Schemes for quantum key distribution with higher-order alphabets using single-photon fractional Fourier optics  

NASA Astrophysics Data System (ADS)

We propose generalized quantum key distribution schemes using spatially encoded d -dimensional qudits based on fractional Fourier transform operations. We determine the necessary conditions on the orders of the transforms which ensure a shared secret random key string and briefly discuss the transmission rate and a possible encoding procedure. We also show that the fractional Fourier transform can be used to analyze more general eavesdropping strategies, including an intermediate-basis attack. The error rate and information gain for the intercept-resend and intermediate-basis attacks are briefly analyzed for a particular example. Effects of atmospheric turbulence in a free-space transmission are considered.

Walborn, S. P.; Lemelle, D. S.; Tasca, D. S.; Souto Ribeiro, P. H.

2008-06-01

288

Numerical Inversion of Laplace Transforms by Relating Them to the Finite Fourier Cosine Transform  

Microsoft Academic Search

In this paper the problem of readily determining the inverse Laplace transform numerically by a method which meets the efficiency requirements of automatic digital computation is discussed. Because the result inverse function is given as a Fourier cosine series, the procedure requires only about ten FORTRAN statements. Furthermore, it does not require the use of involved algorithms for the generation

Harvey Dubner; Joseph Abate

1968-01-01

289

SUPER-RESOLUTION FROM SHORT-TIME FOURIER TRANSFORM MEASUREMENTS Celine Aubel, David Stotz, and Helmut Bolcskei  

E-print Network

SUPER-RESOLUTION FROM SHORT-TIME FOURIER TRANSFORM MEASUREMENTS C´eline Aubel, David Stotz often has access to windowed Fourier transform measurements, i.e., short-time Fourier transform (STFT-factor penalty. Contributions: In practical applications one often has ac- cess to windowed Fourier transform, i

Bölcskei, Helmut

290

A test for second order stationarity of a time series based on the Discrete Fourier Transform (Technical Report)  

E-print Network

A test for second order stationarity of a time series based on the Discrete Fourier Transform Fourier transform at the canonical frequencies. It is well known that the discrete Fourier transform. Keywords and phrases Discrete Fourier Transform, linear time series, local stationarity, Portmanteau test

Subba Rao, Suhasini

291

Quantum optics of spatial transformation media  

E-print Network

Transformation media are at the heart of invisibility devices, perfect lenses and artificial black holes. In this paper, we consider their quantum theory. We show how transformation media map quantum electromagnetism in physical space to QED in empty flat space.

Ulf Leonhardt; Thomas G. Philbin

2007-07-25

292

Initial Results from the USNO Dispersed Fourier Transform Spectrograph  

NASA Astrophysics Data System (ADS)

We have designed and constructed a ``dispersed Fourier transform spectrometer'' (dFTS), consisting of a conventional FTS followed by a grating spectrometer. By combining these two devices, we negate a substantial fraction of the sensitivity disadvantage of a conventional FTS for high-resolution, broadband, optical spectroscopy, while preserving many of the advantages inherent to interferometric spectrometers. In addition, we have implemented a simple and inexpensive laser metrology system, which enables very precise calibration of the interferometer wavelength scale. The fusion of interferometric and dispersive technologies with a laser metrology system yields an instrument well suited to stellar spectroscopy, velocimetry, and extrasolar planet detection, which is competitive with existing high-resolution, high-accuracy stellar spectrometers. In this paper we describe the design of our prototype dFTS, explain the algorithm we use to efficiently reconstruct a broadband spectrum from a sequence of narrowband interferograms, and present initial observations and resulting velocimetry of stellar targets.

Hajian, Arsen R.; Behr, Bradford B.; Cenko, Andrew T.; Olling, Robert P.; Mozurkewich, David; Armstrong, J. Thomas; Pohl, Brian; Petrossian, Sevan; Knuth, Kevin H.; Hindsley, Robert B.; Murison, Marc; Efroimsky, Michael; Dantowitz, Ronald; Kozubal, Marek; Currie, Douglas G.; Nordgren, Tyler E.; Tycner, Christopher; McMillan, Robert S.

2007-05-01

293

Wavenumber scanning-based Fourier transform white-light interferometry.  

PubMed

Fourier transform white-light interferometry recovers the optical path difference of an interferometer by measuring the phase change caused by scanning wavelength. However, the optical spectrum, obtained by wavelength scanning method (?-method), contains a chirp in period. The chirp would induce deviation and decrease the measurement accuracy. An improved method, the wavenumber scanning method (k-method), is proposed and experimentally demonstrated, in which there is no chirp in the optical spectrum. The measurement results using the k-method and the ?-method are compared experimentally. The experimental results show that the standard deviation of the measurement results decreases from 0.015 to 0.004 ?m, when an extrinsic Fabry-Perot interferometer with a cavity length of 387 ?m is interrogated. PMID:22859041

Wang, Zhen; Jiang, Yi

2012-08-01

294

Solar radiometry at millimeter wavelengths. [Fast Fourier Transformation solutions  

NASA Technical Reports Server (NTRS)

In the area of resolution enhancement, the use of Fast Fourier Transform programs was investigated for possible application to millimeter wavelength maps of the sun. A difficulty arises with the La Posta maps in that they are limited to 35 arc-minutes square while the smeared out solar image is larger than that. A list of possible cometary emission lines near 13 millimeters is presented. Although preparation of the list was inspired by the appearance of Comet Kohoutek, the results are applicable to any future comet. The brightness temperature of the sun at 8.6 millimeters was measured using the moon as a calibration source. The result does not confirm a deep absorption feature as apparently observed by earlier workers.

Henze, W.

1974-01-01

295

Calibration of the Geostationary Imaging Fourier Transform Spectrometer (GIFTS)  

NASA Astrophysics Data System (ADS)

The NASA New Millennium Program's Geostationary Imaging Fourier Transform Spectrometer (GIFTS) requires highly accurate radiometric and spectral calibration in order to carry out its mission to provide water vapor, wind, temperature, and trace gas profiling from geostationary orbit. A calibration concept has bene developed for the GIFTS Phase A instrument design. The in-flight calibration is performed using views of two on-board blackbody sources along with cold space. A radiometric calibration uncertainty analysis has been developed and used to show that the expected performance for GIFTS exceeds its top level requirement to measure brightness temperature to better than 1 K. For the Phase A GIFTS design, the spectral calibration is established by the highly stable diode laser used as the reference for interferogram sampling, and verified with comparisons to atmospheric calculations.

Best, Fred A.; Revercomb, Henry E.; Bingham, Gail E.; Knuteson, Robert O.; Tobin, David C.; LaPorte, Daniel D.; Smith, William L.

2001-02-01

296

Calibration of the Geostationary Imaging Fourier Transform Spectrometer (GIFTS)  

NASA Technical Reports Server (NTRS)

The NASA New Millennium Program's Geostationary Imaging Fourier Transform Spectrometer (GIFTS) requires highly accurate radiometric and spectral calibration in order to carry out its mission to provide water vapor, wind, temperature, and trace gas profiling from geostationary orbit. A calibration concept has been developed for the GIFTS Phase A instrument design. The in-flight calibration is performed using views of two on-board blackbody sources along with cold space. A radiometric calibration uncertainty analysis has been developed and used to show that the expected performance for GIFTS exceeds its top level requirement to measure brightness temperature to better than 1 K. For the Phase A GIFTS design, the spectral calibration is established by the highly stable diode laser used as the reference for interferogram sampling, and verified with comparisons to atmospheric calculations.

Best, F. A.; Revercomb, H. E.; Bingham, G. E.; Knuteson, R. O.; Tobin, D. C.; LaPorte, D. D.; Smith, W. L.

2001-01-01

297

How to tickle spins with a fourier transform NMR spectrometer.  

PubMed

In the long bygone days of continuous-wave nuclear magnetic resonance (NMR) spectroscopy, a selected transition within a multiplet of a high-resolution spectrum could be irradiated by a highly selective continuous-wave (CW) radio-frequency (rf) field with a very weak amplitude ?(2)/(2?)?J. This causes splittings of connected transitions, allowing one to map the connectivities of all transitions within the energy-level diagram of the spin system. Such "tickling" experiments stimulated the invention of two-dimensional spectroscopy, but seem to have been forgotten for nearly 50 years. We show that tickling can readily be achieved in homonuclear systems with Fourier transform spectrometers by applying short pulses in the intervals between the sampling points. Extensions to heteronuclear systems are even more straightforward since they can be carried out using very weak CW rf fields. PMID:23281148

Segawa, Takuya F; Carnevale, Diego; Bodenhausen, Geoffrey

2013-02-01

298

Decay of the Fourier transform of surfaces with vanishing curvature  

E-print Network

We prove $L^p$-bounds on the Fourier transform of measures $\\mu$ supported on two dimensional surfaces. Our method allows to consider surfaces whose Gauss curvature vanishes on a one-dimensional submanifold. Under a certain non-degeneracy condition, we prove that $\\wh\\mu\\in L^{4+\\beta}$, $\\beta>0$, and we give a logarithmically divergent bound on the $L^4$-norm. We use this latter bound to estimate almost singular integrals involving the dispersion relation, $e(p)= \\sum_1^3 [1-\\cos p_j]$, of the discrete Laplace operator on the cubic lattice. We briefly explain our motivation for this bound originating in the theory of random Schr\\"odinger operators.

Laszlo Erdos; Manfred Salmhofer

2006-04-18

299

Quark-antiquark static energy from a restricted Fourier transform  

E-print Network

We provide a fully analytical determination of the perturbative quark-antiquark static energy in position space as defined by a restricted Fourier transformation from momentum to position space. Such a determination is complicated by the fact that the static energy genuinely decomposes into a strictly perturbative part (made up of contributions $\\sim\\alpha_s^n$, with $n\\in\\mathbb{N}$) which is conventionally evaluated in momentum space, and a so-called ultrasoft part (including terms $\\sim\\alpha_s^{n+m}\\ln^m\\alpha_s$, with $n\\geq3$ and $m\\in\\mathbb{N}$) which, conversely, is naturally evaluated in position space. Our approach facilitates the explicit determination of the static energy in position space at the accuracy with which the perturbative potential in momentum space is known, i.e., presently up to order $\\alpha_s^4$.

Felix Karbstein

2013-11-28

300

Initial Results from the USNO Dispersed Fourier Transform Spectrograph  

E-print Network

We have designed and constructed a ``dispersed Fourier Transform Spectrometer'' (dFTS), consisting of a conventional FTS followed by a grating spectrometer. By combining these two devices, we negate a substantial fraction of the sensitivity disadvantage of a conventional FTS for high resolution, broadband, optical spectroscopy, while preserving many of the advantages inherent to interferometric spectrometers. In addition, we have implemented a simple and inexpensive laser metrology system, which enables very precise calibration of the interferometer wavelength scale. The fusion of interferometric and dispersive technologies with a laser metrology system yields an instrument well-suited to stellar spectroscopy, velocimetry, and extrasolar planet detection, which is competitive with existing high-resolution, high accuracy stellar spectrometers. In this paper, we describe the design of our prototype dFTS, explain the algorithm we use to efficiently reconstruct a broadband spectrum from a sequence of narrowband interferograms, and present initial observations and resulting velocimetry of stellar targets.

Arsen R. Hajian; Bradford B. Behr; Andrew T. Cenko; Robert P. Olling; David Mozurkewich; J. Thomas Armstrong; Brian Pohl; Sevan Petrossian; Kevin H. Knuth; Robert B. Hindsley; Marc Murison; Michael Efroimsky; Ronald Dantowitz; Marek Kozubal; Douglas G. Currie; Tyler E. Nordgren; Christopher Tycner; Robert S. McMillan

2006-11-15

301

Analysis of far-infrared emission Fourier transform spectra  

NASA Technical Reports Server (NTRS)

An analysis method that uses the nonlinear least-squares fit technique has been developed for emission spectra obtained with a Fourier transform spectrometer. This method is used for the analysis of submillimeter-region atmospheric emission spectra obtained with a balloon-borne FT spectrometer that was carried out as a correlative measurement for the Limb IR Monitor of the Stratosphere (LIMS) satellite experiment. The retrieved mixing ratios of H2O and O3 in the stratosphere from four spectral intervals have standard deviations of about 10 percent, and the average values agree to within 10 percent of corresponding results from the LIMS satellite experiment which used a broadband emission radiometer in the IR region.

Park, J. H.; Carli, B.

1986-01-01

302

Identification of Amanita mushrooms by fourier transform infrared spectroscopy  

NASA Astrophysics Data System (ADS)

Amanita is one of cosmopolitan genera of basidiomycetes. This genus contains some of the most poisonous toadstools, as well as several species of the most favorite edible mushrooms. In this paper, Fourier transform infrared spectroscopy was used for obtaining vibrational spectra of the fruiting bodies of wild growing Amanita mushrooms. The results show that the mushrooms exhibit characteristic spectra, whose strong absorption bands appear at about 1655, 1076, and 1040 cm -1. The vibrational spectra indicate that the main compositions of the Amanita mushrooms are proteins and polysaccharides. The observed spectral differences might be used to discriminate different species of Amanita. It is showed that FTIR spectroscopic method is a valuable tool for rapid and nondestructive identification of Amanita mushrooms.

Zhao, Dezhang; Liu, Gang; Song, Dingshan; Liu, Jian-hong; Zhou, Yilan; Ou, Jiaming; Sun, Shizhong

2006-09-01

303

A direct digital synthesis chirped pulse Fourier transform microwave spectrometer  

NASA Astrophysics Data System (ADS)

Chirped pulse Fourier transform microwave (CP-FTMW) spectrometers have become the instrument of choice for acquiring rotational spectra, due to their high sensitivity, fast acquisition rate, and large bandwidth. Here we present the design and capabilities of a recently constructed CP-FTMW spectrometer using direct digital synthesis (DDS) as a new method for chirped pulse generation, through both a suite of extensive microwave characterizations and deep averaging of the 10-14 GHz spectrum of jet-cooled acetone. The use of DDS is more suited for in situ applications of CP-FTMW spectroscopy, as it reduces the size, weight, and power consumption of the chirp generation segment of the spectrometer all by more than an order of magnitude, while matching the performance of traditional designs. The performance of the instrument was further improved by the use of a high speed digitizer with dedicated signal averaging electronics, which facilitates a data acquisition rate of 2.1 kHz.

Finneran, Ian A.; Holland, Daniel B.; Carroll, P. Brandon; Blake, Geoffrey A.

2013-08-01

304

Observing Extended Sources with the \\Herschel SPIRE Fourier Transform Spectrometer  

E-print Network

The Spectral and Photometric Imaging Receiver (SPIRE) on the European Space Agency's Herschel Space Observatory utilizes a pioneering design for its imaging spectrometer in the form of a Fourier Transform Spectrometer (FTS). The standard FTS data reduction and calibration schemes are aimed at objects with either a spatial extent much larger than the beam size or a source that can be approximated as a point source within the beam. However, when sources are of intermediate spatial extent, neither of these calibrations schemes is appropriate and both the spatial response of the instrument and the source's light profile must be taken into account and the coupling between them explicitly derived. To that end, we derive the necessary corrections using an observed spectrum of a fully extended source with the beam profile and the source's light profile taken into account. We apply the derived correction to several observations of planets and compare the corrected spectra with their spectral models to study the beam c...

Wu, Ronin; Etxaluze, Mireya; Makiwa, Gibion; Naylor, David A; Salji, Carl; Swinyard, Bruce M; Ferlet, Marc; van der Wiel, Matthijs H D; Smith, Anthony J; Fulton, Trevor; Griffin, Matt J; Baluteau, Jean-Paul; Benielli, Dominique; Glenn, Jason; Hopwood, Rosalind; Imhof, Peter; Lim, Tanya; Lu, Nanyao; Panuzzo, Pasquale; Pearson, Chris; Sidher, Sunil; Valtchanov, Ivan

2013-01-01

305

Data processing in Fourier transform ion cyclotron resonance mass spectrometry.  

PubMed

The Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometer intricately couples advanced physics, instrumentation, and electronics with chemical and particularly biochemical research. However, general understanding of the data processing methodologies used lags instrumentation, and most data processing algorithms we are familiar with in FT-ICR are not well studied; thus, professional skill and training in FT-ICR operation and data analysis is still the key to achieve high performance in FT-ICR. This review article is focused on FT-ICR data processing, and explains the procedures step-by-step for users with the goal of maximizing spectral features, such as mass accuracy, resolving power, dynamic range, and detection limits. PMID:24403247

Qi, Yulin; O'Connor, Peter B

2014-01-01

306

Seismic data denoising based on the fractional Fourier transformation  

NASA Astrophysics Data System (ADS)

Seismic data may suffer from too severe noise contamination to carry out further processing and interpretation procedure. In the paper, a new scheme was proposed based on the fractional Fourier transform (FrFT) in time frequency domain to mitigate noise. The scheme consists of two steps. In the first step, the seismic signal is filtered with the ordinary Butterworth filter in the frequency domain. The residual noises after frequency filtering are with the same frequencies with the filtered seismic signals. In order to mitigate the residual noises further, the FrFT filter is applied in the second step. The results from the simulated seismic signals and the measurements data verify the validity of the proposed scheme in both frequency and time-frequency domains.

Zhai, Ming-Yue

2014-10-01

307

Fourier-transform absorption spectroscopy in reciprocating engines.  

PubMed

We have adapted our in-cylinder Fourier-transform spectroscopy technique to measure absorption spectra in a reciprocating engine. Previously, we had used the technique for emission spectroscopy; the upgrade to absorption spectroscopy mode is important because it allows for more quantitative analysis of gas properties than is possible with emission spectroscopy. Here, we discuss fuel, H(2)O, and CO(2) spectra measured in an engine using a spark-plug-based probe for optical access and use the water portion of the spectra to determine in-cylinder gas temperature. The temperature results show that heat transfer effects can significantly bias thermometry when fiber-coupled engine probes are used. PMID:20820214

Rein, Keith D; Sanders, Scott T

2010-09-01

308

A Fourier transform Raman spectrometer with visible laser excitation  

E-print Network

We present the development and performance of a Fourier transformation (FT) based Raman spectrometer working with visible laser (532 nm) excitation. It is generally thought that FT-Raman spectrometers are not viable in the visible range where shot-noise limits the detector performance and therein they are outperformed by grating based, dispersive ones. We show that contrary to this common belief, the recent advances of high-performance interference filters makes the FT-Raman design a valid alternative to dispersive Raman spectrometers for samples which do not luminesce. We critically compare the performance of our spectrometer to two dispersive ones: a home-built single channel and a state-of-the-art CCD based instruments. We demonstrate a similar or even better sensitivity than the CCD based dispersive spectrometer particularly when the laser power density is considered. The instrument possesses all the known advantages of the FT principle of spectral accuracy, high throughput, and economic design. We also d...

Dzsaber, S; Bernáth, B; Gyüre, B; Fehér, T; Kramberger, C; Pichler, T; Simon, F

2014-01-01

309

High throughput full Stokes Fourier transform imaging spectropolarimetry.  

PubMed

A complete full Stokes imaging spectropolarimeter is proposed. Four separate polarized spectra are fed into the Sagnac Fourier transform spectrometer without slit using different angle combinations of the polarized elements. The four polarized spectra are separated without spatial aliasing. And the system has a good performance to resist the instrument noise due to its high light throughput. The mathematical model for the approach is derived and an optimization of the retardance is discussed. For acquiring the four spectra simultaneously, an improved robust polarization modulator using aperture division is outlined. Then the system is discussed in detail including the imaging principle and spectral resolution. Lastly, two proven experiments are carried out and the experimental results in visible light are outlined. PMID:24514802

Meng, Xin; Li, Jianxin; Xu, Tingting; Liu, Defang; Zhu, Rihong

2013-12-30

310

Generalized formulation of an encryption system based on a joint transform correlator and fractional Fourier transform  

NASA Astrophysics Data System (ADS)

We propose a generalization of the encryption system based on double random phase encoding (DRPE) and a joint transform correlator (JTC), from the Fourier domain to the fractional Fourier domain (FrFD) by using the fractional Fourier operators, such as the fractional Fourier transform (FrFT), fractional traslation, fractional convolution and fractional correlation. Image encryption systems based on a JTC architecture in the FrFD usually produce low quality decrypted images. In this work, we present two approaches to improve the quality of the decrypted images, which are based on nonlinear processing applied to the encrypted function (that contains the joint fractional power spectrum, JFPS) and the nonzero-order JTC in the FrFD. When the two approaches are combined, the quality of the decrypted image is higher. In addition to the advantages introduced by the implementation of the DRPE using a JTC, we demonstrate that the proposed encryption system in the FrFD preserves the shift-invariance property of the JTC-based encryption system in the Fourier domain, with respect to the lateral displacement of both the key random mask in the decryption process and the retrieval of the primary image. The feasibility of this encryption system is verified and analyzed by computer simulations.

Vilardy, Juan M.; Torres, Yezid; Millán, María S.; Pérez-Cabré, Elisabet

2014-12-01

311

Discrete Fourier transforms when the number of data samples is prime  

Microsoft Academic Search

The discrete Fourier transform of a sequence of N points, where N is a prime number, is shown to be essentially a circular correlation. This can be recognized by rearranging the members of the sequence and the transform according to a rule involving a primitive root of N. This observation permits the discrete Fourier transform to be computed by means

C. M. Rader

1968-01-01

312

Fourier domain target transformation analysis in the thermal infrared  

NASA Technical Reports Server (NTRS)

Remote sensing uses of principal component analysis (PCA) of multispectral images include band selection and optimal color selection for display of information content. PCA has also been used for quantitative determination of mineral types and abundances given end member spectra. The preliminary results of the investigation of target transformation PCA (TTPCA) in the fourier domain to both identify end member spectra in an unknown spectrum, and to then calculate the relative concentrations of these selected end members are presented. Identification of endmember spectra in an unknown sample has previously been performed through bandmatching, expert systems, and binary classifiers. Both bandmatching and expert system techniques require the analyst to select bands or combinations of bands unique to each endmember. Thermal infrared mineral spectra have broad spectral features which vary subtly with composition. This makes identification of unique features difficult. Alternatively, whole spectra can be used in the classification process, in which case there is not need for an expert to identify unique spectra. Use of binary classifiers on whole spectra to identify endmember components has met with some success. These techniques can be used, along with a least squares fit approach on the endmembers identified, to derive compositional information. An alternative to the approach outlined above usese target transformation in conjunction with PCA to both identify and quantify the composition of unknown spectra. Preprocessing of the library and unknown spectra into the fourier domain, and using only a specific number of the components, allows for significant data volume reduction while maintaining a linear relationship in a Beer's Law sense. The approach taken here is to iteratively calculate concentrations, reducing the number of endmember components until only non-negative concentrations remain.

Anderson, D. L.

1993-01-01

313

Imaging sensor for the Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS)  

NASA Astrophysics Data System (ADS)

Accurate high resolution temperature sounding through our atmosphere is paramount to improving our weather forecasting, monitoring, and analysis capability. From the vantagepoint of earth Orbit, remote temperature sounding is becoming a reality and its accuracy is bolstered by recent advances in infrared hyper-spectral sensor capability. One promising approach takes advantage of a two-dimensional, imaging Fourier transform spectrometer to obtain a data cube with the field of view along one plane and multiple IR spectra (one for every FPA pixel) along the orthogonal axis. The spatial resolution is limited only by the pixel pitch in the imaging focal plane and the optics used to collect the data. The maximum optical path difference in the Michelson FTS defines the spectral resolution and dictates the number of path-length interferogram samples (FPA frames required per cube. This paper discusses the unique challenges placed on the focal plane by the Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS) approach and how advanced focal plane technology is applied to satisfy these challenges. Two focal planes are required to provide spectral coverage from 4.4 to 6.1um and 8.85-14.6um. Currently, the GIFT"s LWIR focal plane is the longest wavelength two-dimensional PV HgCdTe array of this size (128 square on 60 um centers) planned for space deployment. The paper presents performance data of Liquid Phase Epitaxy (LPE) fabricated HgCdTe detectors and design details of the advanced readout integrated circuit necessary to meet the demanding requirements of the imaging sensor for the GIFTS instrument.

Stobie, James A.; Hairston, Allen W.; Tobin, Stephen P.; Huppi, Ronald J.; Huppi, Ray

2002-12-01

314

Quantization maps, algebra representation, and non-commutative Fourier transform for Lie groups  

SciTech Connect

The phase space given by the cotangent bundle of a Lie group appears in the context of several models for physical systems. A representation for the quantum system in terms of non-commutative functions on the (dual) Lie algebra, and a generalized notion of (non-commutative) Fourier transform, different from standard harmonic analysis, has been recently developed, and found several applications, especially in the quantum gravity literature. We show that this algebra representation can be defined on the sole basis of a quantization map of the classical Poisson algebra, and identify the conditions for its existence. In particular, the corresponding non-commutative star-product carried by this representation is obtained directly from the quantization map via deformation quantization. We then clarify under which conditions a unitary intertwiner between such algebra representation and the usual group representation can be constructed giving rise to the non-commutative plane waves and consequently, the non-commutative Fourier transform. The compact groups U(1) and SU(2) are considered for different choices of quantization maps, such as the symmetric and the Duflo map, and we exhibit the corresponding star-products, algebra representations, and non-commutative plane waves.

Guedes, Carlos; Oriti, Daniele [Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, 14476 Potsdam (Germany)] [Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, 14476 Potsdam (Germany); Raasakka, Matti [Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, 14476 Potsdam (Germany) [Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, 14476 Potsdam (Germany); LIPN, Institut Galilée, Université Paris-Nord, 99, av. Clement, 93430 Villetaneuse (France)

2013-08-15

315

Polarization-modulated Fourier transform infrared spectroscopy of a polylactic acid film.  

E-print Network

??Fourier-Transform Infrarotspektroskopie (FTIR) ist ein etabliertes Messverfahren in der industriellen Prozessanalyse, bei der derzeit noch weitestgehend auf die Messung der Änderung der Polarisation des Lichtes,… (more)

Kilgus, Jakob

2013-01-01

316

Vector power multiple-parameter fractional Fourier transform of image encryption algorithm  

NASA Astrophysics Data System (ADS)

In this paper, we propose a multiple-parameter fractional Fourier transform with its transform order being a real vector, based on which a high-security image encryption scheme is also given. This novel fractional Fourier transform has removed the restriction on the dimension of transform order and highly enhances the security of image encryption scheme proposed in this paper without increasing the computational complexity and hardware cost. The numerical results verify the efficacy and security of this image encryption method. The vector power multi-parameter fractional Fourier transform is a generalized form of the classical fractional Fourier transform with all the previous fractional Fourier transform as its special cases and has theoretical significance in information processing and information security.

Ran, Qiwen; Zhao, Tieyu; Yuan, Lin; Wang, Jian; Xu, Lei

2014-11-01

317

IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 48, NO. 5, MAY 2000 1329 The Discrete Fractional Fourier Transform  

E-print Network

Fourier Transform Ã?ag~atay Candan, Student Member, IEEE, M. Alper Kutay, Member, IEEE, and Haldun M. Ozaktas Abstract--We propose and consolidate a definition of the discrete fractional Fourier transform that generalizes the discrete Fourier transform (DFT) in the same sense that the continuous fractional Fourier

Candan, Cagatay

318

Advantages of Karhunen Loève transform over fast Fourier transform for planetary radar and space debris detection  

NASA Astrophysics Data System (ADS)

The present article describes that the range of any radiotelescope (and radar in general) may be increased by virtue of software, if one replaces the fast Fourier transform by the Karhunen Loève transform. The range increases with the inverse of the fourth root of the signal-to-noise ratio when this ratio decreases. Thus, the range on any radiotelescope (and radar) may be increased without changing the hardware at all, but by changing the software only. This improvement in the range of the radiotelescope is currently implemented at the 32-m antenna located at Medicina, near Bologna, in Italy, for both SETI and general radioastronomy.

Maccone, Claudio

2007-04-01

319

A new hybrid algorithm for computing a fast discrete Fourier transform  

NASA Technical Reports Server (NTRS)

In this paper for certain long transform lengths, Winograd's algorithm for computing the discrete Fourier transform (DFT) is extended considerably. This is accomplished by performing the cyclic convolution, required by Winograd's method, with the Mersenne prime number-theoretic transform developed originally by Rader. This new algorithm requires fewer multiplications than either the standard fast Fourier transform (FFT) or Winograd's more conventional algorithm. However, more additions are required.

Reed, I. S.; Truong, T. K.

1979-01-01

320

An Introduction to Fast Fourier Transforms through the Study of Oscillating Reactions.  

ERIC Educational Resources Information Center

Discusses an experiment designed to introduce students to the basic principles of the fast Fourier transform and Fourier smoothing through transformation of time-dependent optical absorption data from an oscillating reaction. Uses the Belousov-Zhabotinskii reaction. Describes the experimental setup and data analysis techniques.

Eastman, M. P.; And Others

1986-01-01

321

Analysis of Carbon Monoxide and Propane Concentrations in Moped Exhaust Emission using Fourier Transform Infrared Spectroscopy  

Microsoft Academic Search

The method of Fourier transform infrared spectroscopy has been used to determine the concentration of carbon monoxide and propane in exhaust emission from a Piaggio Ciao moped. Emissions from vary- ing ways of driving have been collected and examined using a Perkin- Elmer 1725X Fourier transform infrared spectrometer. The obtained spectra have then been compared to spectra from calibration gases.

Lisa Carlsson; Martin Engstrom; Ulrika Kumlien; Ami Ljungstrom; Sara Nordenhall

322

THE FOURIER-SERIES METHOD FOR INVERTING TRANSFORMS OF PROBABILITY DISTRIBUTIONS  

E-print Network

of the method. This Fourier analysis applies to the inversion problem because the Fourier coefficients are just.g., to calculate moments and to determine the asymptotic behavior of tail probabilities. However, the transforms the Laplace-Stieltjes transform (LST) of this cdf as W^ (s) = 0 e- st dW(t) = 1 - [1 - G^ (s)]/s 1

Whitt, Ward

323

Velocity and Acceleration Measurement from the Spatio-Temporal Fourier Transform of Low Light Level Images  

Microsoft Academic Search

The spatio-temporal Fourier transform is usually applied to determine the velocity of an object from a series of standard light intensity frames. In this paper the technique has been extended to determine the object acceleration. The techniques for velocity and acceleration determination based on the spatio-temporal Fourier transform have been applied to experimental low light level images. Under these conditions,

Manuel P. Cagigal; Pedro M. Prieto

1995-01-01

324

Fourier transform microwave spectrum of the propane-water complex: A prototypical water-hydrophobe system  

E-print Network

Fourier transform microwave spectrum of the propane-water complex: A prototypical water) The Fourier transform microwave spectrum of the propane-water complex (C3H,-H,O) has been observed and analyzed. This spectrum includes transitions assigned to propane complexed with both the ortho and para

Cohen, Ronald C.

325

Superconducting bolometer for far-infrared Fourier transform spectroscopy  

NASA Astrophysics Data System (ADS)

A voltage-biased superconducting bolometer with a heat sink temperature of 4.2 K has been developed for Fourier transform spectroscopy in the far infrared. This device is based on a Nb transition edge sensor with Tc=8.1 K. It will operate for absorbed infrared power up to 3×10-6 W and has an absorber area of 7 mm2. The response is inherently linear and the noise equivalent power (NEP)=1.2×10-13 W Hz-1/2 is dominated by thermal fluctuation noise. This NEP is at least a factor 10 better than that expected for a conventional 4.2 K semiconductor bolometer which is optimized for 1% saturation at the same infrared power. The optical response time ?=1.2 ms is dominated by the internal thermalization time. A smaller version of this bolometer could be useful for diffraction-limited spectroscopy of small samples throughout the infrared. Estimates suggest that values of detectivity D*>1011 cm Hz+1/2 W-1 and time constants approaching 270 ?s could be achieved.

Skidmore, J. T.; Gildemeister, J.; Lee, A. T.; Myers, M. J.; Richards, P. L.

2003-01-01

326

Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS): Imaging and Tracking Capability  

NASA Technical Reports Server (NTRS)

The geosynchronous-imaging Fourier transform spectrometer (GIFTS) engineering demonstration unit (EDU) is an imaging infrared spectrometer designed for atmospheric soundings. It measures the infrared spectrum in two spectral bands (14.6 to 8.8 microns, 6.0 to 4.4 microns) using two 128 128 detector arrays with a spectral resolution of 0.57/cm with a scan duration of approx. 11 seconds. From a geosynchronous orbit, the instrument will have the capability of taking successive measurements of such data to scan desired regions of the globe, from which atmospheric status, cloud parameters, wind field profiles, and other derived products can be retrieved. The GIFTS EDU provides a flexible and accurate testbed for the new challenges of the emerging hyperspectral era. The EDU ground-based measurement experiment, held in Logan, Utah during September 2006, demonstrated its extensive capabilities and potential for geosynchronous and other applications (e.g., Earth observing environmental measurements). This paper addresses the experiment objectives and overall performance of the sensor system with a focus on the GIFTS EDU imaging capability and proof of the GIFTS measurement concept.

Zhou, D. K.; Larar, A. M.; Liu, Xu; Reisse, R. A.; Smith, W. L.; Revercomb, H. E.; Bingham, G. E.; Zollinger, L. J.; Tansock, J. J.; Huppi, Ronald J.

2007-01-01

327

Fourier transform infrared phase shift cavity ring down spectrometer  

NASA Astrophysics Data System (ADS)

OPTRA has developed a Fourier transform infrared phase shift cavity ring down spectrometer (FTIR-PS-CRDS) system under a U.S. EPA SBIR contract. This system uses the inherent wavelength-dependent modulation imposed by the FTIR on a broadband thermal source for the phase shift measurement. This spectrally-dependent phase shift is proportional to the spectrally-dependent ring down time. The spectral dependence of both of these values is introduced by the losses of the cavity including those due to the molecular absorption of the sample. OPTRA's approach allows broadband detection of chemicals across the feature-rich fingerprint region of the long-wave infrared. This represents a broadband and spectral range enhancement to conventional CRDS which is typically done at a single wavelength in the near IR; at the same time the approach is a sensitivity enhancement to traditional FTIR, owing to the long effective path of the resonant cavity. In previous papers1,2, OPTRA has presented a breadboard system aimed at demonstrating the feasibility of the approach and a prototype design implementing performance enhancements based on the results of breadboard testing. In this final paper in the series, we will present test results illustrating the realized performance of the fully assembled and integrated breadboard, thereby demonstrating the utility of the approach.

Schundler, Elizabeth; Mansur, David J.; Vaillancourt, Robert; Benedict-Gill, Ryan; Newbry, Scott P.; Engel, James R.; Dupuis, Julia Rentz

2014-05-01

328

Liquid chromatography/fourier transform ir spectrometry interface flow cell  

SciTech Connect

This patent describes a Fourier transform infrared spectrometer. A sample material is isolated by liquid chromatography and directed through an elongated tube of small inner diameter for irradiation by an infrared beam in obtaining an infrared spectrum of the sample material representing the composition thereof. A sample flow cell comprises: a generally cylindrical crystal having a longitudinal axis and a generally circular cross-section. The crystal is transparent to infrared radiation and is positioned in line with the infrared beam. Its longitudinal axis is aligned generally perpendicular to the infrared beam, whereby the infrared beam is incident upon the crystal and is focused generally on the crystal's longitudinal axis and is transmitted therethrough so as to exit therefrom; and a small diameter, linear bore having a circular cross-section positioned within the crystal along the longitudinal axis and extending the length thereof and oriented generally perpendicular to the direction of propagation of the infrared beam therein. The bore is coupled to the elongated tube for receiving and directing the sample material in the path of the infrared beam. The exiting infrared beam includes the infrared spectrum of the sample material.

Johnson, C.C.; Taylor, L.T.

1986-10-21

329

Fourier transform infrared Hadamard tomography of sooting flames  

SciTech Connect

An experimental technique is described that combines tomography, Hadamard signal encodement, and a patented Fourier transform infrared (FT-IR) emission/transmission (E/T) technique to perform simultaneous spatially resolved gas species and soot measurements during combustion. Tomographic analysis of line-of-sight FT-IR data allows spatially resolved measurements to be made. Hadamard encodement of the tomographic sections increases the overall signal throughput, improving the signal to noise (S/N) ratio for each measurement. The Hadamard technique leads to a major simplification in the tomographic apparatus in that the scanning apparatus that would normally be required is eliminated, and focusing of the infrared light is much easier. An experiment demonstrating Hadamard data processing as applied to FT-IR tomography is described. Deconvolution of the encoded data is shown to be accurate and gives the predicted improvement in S/N ratio. The FT-IR Hadamard tomography is performed to measure soot in a fuel-rich diffusion flame. Spatially resolved concentration measurements agree well with previous data, and clearly show striking three-dimensional features that could not normally be measured by simple line-of-sight techniques.

Bates, S.C.; Carangelo, R.; Knight, K.; Serio, M. (Advanced Fuel Research, 87 Church Street, East Hartford, Connecticut 06108 (United States))

1993-05-01

330

An all-fibre-optic Fourier transform spectrometer  

NASA Astrophysics Data System (ADS)

A novel fibre-optic Fourier transform spectrometer was constructed. The optical retardation between the arms of a Mach - Zehnder-type interferometer made of single-mode optical fibre is modulated by variation of the fibre temperature. Spectra of a multimode laser diode and a broad-band light source were recorded. Frequency shifts within the observed spectra can be explained with the frequency dispersion of the coefficient of the dependence of the refractive index on temperature, 0957-0233/7/11/011/img5. An oversampling scheme utilizing a phase-locked loop circuit was successfully tested. This allows for the acquisition of spectra with shorter wavelength components than the wavelength of the reference laser if a fibre with sufficiently low cut-off wavelength is employed. Thus, the accessible wavelength region may be extended to the near UV using a conventional silica fibre. Coherent averaging of multiple interferograms was successfully applied to enhance the signal-to-noise ratio of interferograms.

Stelzle, Martin; Tuchtenhagen, Jürgen; Rabolt, John F.

1996-11-01

331

Spin glass field theory with replica Fourier transforms  

NASA Astrophysics Data System (ADS)

We develop a field theory for spin glasses using replica Fourier transforms (RFT). We present the formalism for the case of replica symmetry and the case of replica symmetry breaking on an ultrametric tree, with the number of replicas n and the number of replica symmetry breaking steps R generic integers. We show how the RFT applied to the two-replica fields allows one to construct a new basis which block-diagonalizes the four-replica mass-matrix, into the replicon, anomalous and longitudinal modes. The eigenvalues are given in terms of the mass RFT and the propagators in the RFT space are obtained by inversion of the block-diagonal matrix. The formalism allows one to express any i-replica vertex in the new RFT basis and hence enables one to perform a standard perturbation expansion. We apply the formalism to calculate the contribution of the Gaussian fluctuations around the Parisi solution for the free-energy of an Ising spin glass.

Pimentel, I. R.; De Dominicis, C.

2014-11-01

332

Calibration of the Herschel SPIRE Fourier Transform Spectrometer  

E-print Network

The Herschel SPIRE instrument consists of an imaging photometric camera and an imaging Fourier Transform Spectrometer (FTS), both operating over a frequency range of 450-1550 GHz. In this paper, we briefly review the FTS design, operation, and data reduction, and describe in detail the approach taken to relative calibration (removal of instrument signatures) and absolute calibration against standard astronomical sources. The calibration scheme assumes a spatially extended source and uses the Herschel telescope as primary calibrator. Conversion from extended to point-source calibration is carried out using observations of the planet Uranus. The model of the telescope emission is shown to be accurate to within 6% and repeatable to better than 0.06% and, by comparison with models of Mars and Neptune, the Uranus model is shown to be accurate to within 3%. Multiple observations of a number of point-like sources show that the repeatability of the calibration is better than 1%, if the effects of the satellite absolu...

Swinyard, B M; Hopwood, R; Valtchanov, I; Lu, N; Fulton, T; Benielli, D; Imhof, P; Marchili, N; Baluteau, J -P; Bendo, G J; Ferlet, M; Griffin, M J; Lim, T L; Makiwa, G; Naylor, D A; Orton, G S; Papageorgiou, A; Pearson, C P; Schulz, B; Sidher, S D; Spencer, L D; van der Wiel, M H D; Wu, R

2014-01-01

333

Fourier Transform Power Spectra Analysis of Dwarf Irregular Galaxies  

NASA Astrophysics Data System (ADS)

The LITTLE THINGS survey has obtained deep HI emission line maps with the data from VLA B, C and D array configurations for a representative sample of nearby dwarf irregular galaxies, and supplemented this with images from the FUV to the NIR. We present the fourier transform power spectra of the HI maps, FUV and NIR images for a subsample of nearly face-on (minor-to-major axis ratio > 0.8) LITTLE THINGS galaxies in order to examine structures within the galaxies' gas and stellar disks.The radial variations of the power spectra will be compared with global properties. We will also compare the relationship between the gas, star formation and stellar mass on different physical scales and at different radii, and discuss the possibility of using breaks in power-law power spectra to constrain the disk thickness. The LITTLE THINGS team is grateful to the National Science Foundation for funding through grants AST-0707563, AST-0707426, AST-0707468, and AST-0707835 to DAH, BGE, CES, and LMY. HZ was partly supported by NSF of China through grants \\#10425313, \\#10833006 and \\#10621303 to Professor Yu Gao.

Zhang, Hongxin; Hunter, D. A.; LITTLE THINGS Team

2012-01-01

334

Fourier transform infrared spectroscopic analysis of cell differentiation  

NASA Astrophysics Data System (ADS)

Stem cells and its differentiations have got a lot of attentions in regenerative medicine. The process of differentiations, the formation of tissues, has become better understood by the study using a lot of cell types progressively. These studies of cells and tissue dynamics at molecular levels are carried out through various approaches like histochemical methods, application of molecular biology and immunology. However, in case of using regenerative sources (cells, tissues and biomaterials etc.) clinically, they are measured and quality-controlled by non-invasive methods from the view point of safety. Recently, the use of Fourier Transform Infrared spectroscopy (FT-IR) has been used to monitor biochemical changes in cells, and has gained considerable importance. The objective of this study is to establish the infrared spectroscopy of cell differentiation as a quality control of cell sources for regenerative medicine. In the present study, as a basic study, we examined the adipose differentiation kinetics of preadipocyte (3T3-L1) and the osteoblast differentiation kinetics of bone marrow mesenchymal stem cells (Kusa-A1) to analyze the infrared absorption spectra. As a result, we achieved to analyze the adipose differentiation kinetics using the infrared absorption peak at 1739 cm-1 derived from ester bonds of triglyceride and osteoblast differentiation kinetics using the infrared absorption peak at 1030 cm-1 derived from phosphate groups of calcium phosphate.

Ishii, Katsunori; Kimura, Akinori; Kushibiki, Toshihiro; Awazu, Kunio

2007-02-01

335

Liquid chromatography/Fourier transform IR spectrometry interface flow cell  

DOEpatents

A zero dead volume (ZDV) microbore high performance liquid chromatography (..mu.. HPLC)/Fourier transform infrared (FTIR) interface flow cell includes an IR transparent crystal having a small diameter bore therein through which a sample liquid is passed. The interface flow cell further includes a metal holder in combination with a pair of inner, compressible seals for directly coupling the thus configured spectrometric flow cell to the outlet of a ..mu.. HPLC column end fitting to minimize the transfer volume of the effluents exiting the ..mu.. HPLC column which exhibit excellent flow characteristics due to the essentially unencumbered, open-flow design. The IR beam passes transverse to the sample flow through the circular bore within the IR transparent crystal, which is preferably comprised of potassium bromide (KBr) or calcium fluoride (CaF/sub 2/), so as to minimize interference patterns and vignetting encountered in conventional parallel-plate IR cells. The long IR beam pathlength and lensing effect of the circular cross-section of the sample volume in combination with the refractive index differences between the solvent and the transparent crystal serve to focus the IR beam in enhancing sample detection sensitivity by an order of magnitude.

Johnson, C.C.; Taylor, L.T.

1985-01-04

336

Fourier-transform method for accurate analysis of Moessbauer spectra  

SciTech Connect

We report a simple analytic form for the convolution integral in transmission Moessbauer spectroscopy allowing accurate representation of the line shape even for very thick absorbers (t = 10), and permitting easy fitting to the true line-shape function. This representation permits the accurate determination of all Moessbauer-effect (ME) parameters, including position, width, cross section, and interference. This analytic method can be applied to deconvolute accurately information contained in either source or absorber, and an explicit analytic form for the emission and absorption Fourier transforms is given. We show that from the asymptotics of the line shape, it is possible to determine all line-shape parameters, and that line-shape asymptotics can circumvent short-ranged hyperfine or instrumental broadening contributions to the observed spectrum. A formula for the correction to the line shape caused by source self-absorption is given, and it is shown that when there is significant source resonance self-absorption a ''good'' fit to data, judged by a chi-squared analysis, can yield completely wrong ME line-shape parameters. We find an equation for the dependence of the area under the absorption curve and the resonance peak height, and give its explicit dependence on the interference parameter and source broadening parameters. Although these effects have been neglected in earlier work, their contribution may be of order 10% in many cases of interest.

Mullen, J.G.; Djedid, A.; Schupp, G.; Cowan, D.; Cao, Y.; Crow, M.L.; Yelon, W.B.

1988-03-01

337

Single beam Fourier transform digital holographic quantitative phase microscopy  

NASA Astrophysics Data System (ADS)

Quantitative phase contrast microscopy reveals thickness or height information of a biological or technical micro-object under investigation. The information obtained from this process provides a means to study their dynamics. Digital holographic (DH) microscopy is one of the most used, state of the art single-shot quantitative techniques for three dimensional imaging of living cells. Conventional off axis DH microscopy directly provides phase contrast images of the objects. However, this process requires two separate beams and their ratio adjustment for high contrast interference fringes. Also the use of two separate beams may make the system more vulnerable to vibrations. Single beam techniques can overcome these hurdles while remaining compact as well. Here, we describe the development of a single beam DH microscope providing whole field imaging of micro-objects. A hologram of the magnified object projected on to a diffuser co-located with a pinhole is recorded with the use of a commercially available diode laser and an arrayed sensor. A Fourier transform of the recorded hologram directly yields the complex amplitude at the image plane. The method proposed was investigated using various phase objects. It was also used to image the dynamics of human red blood cells in which sub-micrometer level thickness variation were measurable.

Anand, A.; Faridian, A.; Chhaniwal, V. K.; Mahajan, S.; Trivedi, V.; Dubey, S. K.; Pedrini, G.; Osten, W.; Javidi, B.

2014-03-01

338

Remote detection of organics using Fourier transform infrared spectroscopy  

SciTech Connect

Fourier transform infrared (FTIR) spectroscopy is an ideal technique for remote detection of organic emissions. There is an atmospheric window in the 1200 to 800 cm{sup {minus}1} region, which corresponds to the fingerprint'' region for organic molecules. Virtually all organic molecules have a unique absorption/emission pattern in the fingerprint region. A remote-passive FTIR relies on ambient emission of infrared energy from organics to obtain spectra. The instrumentation consists of inlet optics, and interferometer, a mercury cadmium telluride (MCT) detector, and an on-board computer. The transportable unit measures 40 cm by 50 cm and has been used to collect data while mounted on a helicopter or ground vehicle. Through the use of this FTIR combined with least squares software, it is possible to analyze qualitatively and quantitatively for organic vapors from either the air or ground. The data presented will include quantitative releases of common organics present in incinerator stacks, hazardous wastes, and illegal laboratories. Data will be presented for pure compounds, mixtures, and target analytes in the presence of interfering compounds. The sensitivity, reproducibility, and the potential of the technique will be discussed. 1 ref., 8 figs., 6 tabs.

Demirgian, J.C.; Spurgash, S.M.

1990-01-01

339

Exploring two-dimensional electron gases with two-dimensional Fourier transform spectroscopy  

NASA Astrophysics Data System (ADS)

The dephasing of the Fermi edge singularity excitations in two modulation doped single quantum wells of 12 nm and 18 nm thickness and in-well carrier concentration of ˜4 × 1011 cm-2 was carefully measured using spectrally resolved four-wave mixing (FWM) and two-dimensional Fourier transform (2DFT) spectroscopy. Although the absorption at the Fermi edge is broad at this doping level, the spectrally resolved FWM shows narrow resonances. Two peaks are observed separated by the heavy hole/light hole energy splitting. Temperature dependent "rephasing" (S1) 2DFT spectra show a rapid linear increase of the homogeneous linewidth with temperature. The dephasing rate increases faster with temperature in the narrower 12 nm quantum well, likely due to an increased carrier-phonon scattering rate. The S1 2DFT spectra were measured using co-linear, cross-linear, and co-circular polarizations. Distinct 2DFT lineshapes were observed for co-linear and cross-linear polarizations, suggesting the existence of polarization dependent contributions. The "two-quantum coherence" (S3) 2DFT spectra for the 12 nm quantum well show a single peak for both co-linear and co-circular polarizations.

Paul, J.; Dey, P.; Tokumoto, T.; Reno, J. L.; Hilton, D. J.; Karaiskaj, D.

2014-10-01

340

Exploring two-dimensional electron gases with two-dimensional Fourier transform spectroscopy.  

PubMed

The dephasing of the Fermi edge singularity excitations in two modulation doped single quantum wells of 12 nm and 18 nm thickness and in-well carrier concentration of ?4 × 10(11) cm(-2) was carefully measured using spectrally resolved four-wave mixing (FWM) and two-dimensional Fourier transform (2DFT) spectroscopy. Although the absorption at the Fermi edge is broad at this doping level, the spectrally resolved FWM shows narrow resonances. Two peaks are observed separated by the heavy hole/light hole energy splitting. Temperature dependent "rephasing" (S1) 2DFT spectra show a rapid linear increase of the homogeneous linewidth with temperature. The dephasing rate increases faster with temperature in the narrower 12 nm quantum well, likely due to an increased carrier-phonon scattering rate. The S1 2DFT spectra were measured using co-linear, cross-linear, and co-circular polarizations. Distinct 2DFT lineshapes were observed for co-linear and cross-linear polarizations, suggesting the existence of polarization dependent contributions. The "two-quantum coherence" (S3) 2DFT spectra for the 12 nm quantum well show a single peak for both co-linear and co-circular polarizations. PMID:25296819

Paul, J; Dey, P; Tokumoto, T; Reno, J L; Hilton, D J; Karaiskaj, D

2014-10-01

341

Quantum Canonical Transformations and Integrability: Beyond Unitary Transformations  

E-print Network

Quantum canonical transformations are defined in analogy to classical canonical transformations as changes of the phase space variables which preserve the Dirac bracket structure. In themselves, they are neither unitary nor non-unitary. A definition of quantum integrability in terms of canonical transformations is proposed which includes systems which have fewer commuting integrals of motion than degrees of freedom. The important role of non-unitary transformations in integrability is discussed.

Arlen Anderson

1993-02-15

342

Geostationary Imaging Fourier Transform Spectrometer (GIFTS): science applications  

NASA Astrophysics Data System (ADS)

A revolutionary satellite weather forecasting instrument, called the "GIFTS" which stands for the "Geostationary Imaging Fourier Transform Spectrometer", was recently completed and successfully tested in a space chamber at the Utah State University's Space Dynamics Laboratory. The GIFTS was originally proposed by the NASA Langley Research Center, the University of Wisconsin, and the Utah State University and selected for flight demonstration as NASA's New Millennium Program (NMP) Earth Observing-3 (EO-3) mission, which was unfortunately cancelled in 2004. GIFTS is like a digital 3-d movie camera that, when mounted on a geostationary satellite, would provide from space a revolutionary four-dimensional view of the Earth's atmosphere. GIFTS will measure the distribution, change, and movement of atmospheric moisture, temperature, and certain pollutant gases, such as carbon monoxide and ozone. The observation of the convergence of invisible water vapor, and the change of atmospheric temperature, provides meteorologists with the observations needed to predict where, and when, severe thunderstorms, and possibly tornados, would occur, before they are visible on radar or in satellite cloud imagery. The ability of GIFTS to observe the motion of moisture and clouds at different altitudes enables atmospheric winds to be observed over vast, and otherwise data sparse, oceanic regions of the globe. These wind observations would provide the means to greatly improve the forecast of where tropical storms and hurricanes will move and where and when they will come ashore (i.e., their landfall position and time). GIFTS, if flown into geostationary orbit, would provide about 80,000 vertical profiles per minute, each one like a low vertical resolution (1-2km) weather balloon sounding, but with a spacing of 4 km. GIFTS is a revolutionary atmospheric sensing tool. A glimpse of the science measurement capabilities of GIFTS is provided through airborne measurements with the NPOESS Airborne Sounding Testbed - Interferometer (NAST-I).

Smith, W. L.; Revercomb, H. E.; Zhou, D. K.; Bingham, G. E.; Feltz, W. F.; Huang, H. L.; Knuteson, R. O.; Larar, A. M.; Liu, X.; Reisse, R.; Tobin, D. C.

2006-12-01

343

Libyan Desert Glass: New field and Fourier transform infrared data  

NASA Astrophysics Data System (ADS)

Results are presented of new geological observations and laboratory analyses on Libyan Desert Glass (LDG), a unique kind of impact glass found in Egypt, probably 28.5-29.4 million years in age. A new LDG occurrence has been discovered some 50 km southward of the main LDG occurrences in the Great Sand Sea. From Fourier transform infrared (FTIR) analysis, the molecular structure of LDG is refined and significant differences are shown between LDG specimens and other pure silica glasses (fulgurite, industrial fused quartz, and amorphous biogenic silica) that are related to differences in their structures. The slight variations observed here for the mean Si-O-Si angle between the different glasses are attributed to their thermal histories. With regard to the other glasses analyzed, the LDG infrared spectral parameters point to a higher ratio of discontinuities and defects in the tetrahedral (SiO4) network. The quantitative mineralogical constitutions of sandstones and quartzites from the LDG geological setting were analyzed by FTIR. Cretaceous sandstones have a specific composition (about 90 wt% quartz, 10% dickite), clearly different from the Paleozoic ones (about 90 wt% quartz, but ?7% kaolinite). It is shown that the reddish silts bearing the LDG are constituted mainly of microquartz enriched with dickite, whose particle size distribution is characteristic of fluvio-lacustrine deposits, probably Oligocene to Miocene in age. The target rocks, most probably quartz sand, resulted from the weathering (loss of the cementing microquartz) of the Cretaceous sandstones from the Gilf Khebir Plateau with deposition in a high-energy environment.

Fröhlich, F.; Poupeau, G.; Badou, A.; Le Bourdonnec, F. X.; Sacquin, Y.; Dubernet, S.; Bardintzeff, J. M.; Véran, M.; Smith, D. C.; Diemer, E.

2013-12-01

344

Dual Comb Fourier Transform Spectroscopy in the Green Region  

NASA Astrophysics Data System (ADS)

Laser combs in combination with other advancing tools of laser science, nonlinear optics, photonics, and electronic signal processing have the potential to vastly enhance the range and capabilities of molecular laser spectroscopy. The high versatility of frequency comb sources can indeed harness new techniques for ultra-rapid and ultra-sensitive recording of complex molecular spectra. The recent proof-of-principle demonstrations of dual comb Fourier transform spectroscopy have mostly been carried out in the near-infrared region, around 1.0 and 1.5 ?m. The mode-locked ytterbium- or erbium-doped fiber femtosecond laser systems emitting in this range indeed require few adjustment thanks to their guided light and permit reliable unattended operation. With expanded wavelength coverage and continued improvements in speed and sensitivity, dual comb spectroscopy should find use as a novel, time-domain spectroscopic analytical tool. As far as molecular spectroscopy is concerned, the mid-infrared and visible-ultraviolet wavelength regions show both the potential for specificity and sensitivity for tracing molecules. In particular, the visible-ultraviolet region complements the mid-infrared molecular fingerprint range, as it provides access to many electronic transitions, in particular belonging to reactive species. In this contribution, we report on our progress in the implementation of dual comb spectroscopy in the 520 nm green region. We present preliminary results on a powerful new sensitive ultra-rapid tool for linear rovibronic absorption spectroscopy, based on frequency-doubled ytterbium-doped fiber lasers and we discuss its intriguing prospects for spectroscopy of short lived transient species.

Knize, R. J.; Bernhardt, B.; Picqué, N.; Hänsch, T. W.

2010-06-01

345

Complexation of chitosan with acetic acid according to Fourier transform Raman spectroscopy data  

NASA Astrophysics Data System (ADS)

The results of the interaction between the protonated chitosan (CHI) macromolecule and the acetate ion in dilute acetic acid solutions were studied by Fourier transform Raman spectroscopy and quantum-chemical modeling. The complexation of CHI with the acetate ion showed itself as the 934 cm-1 band in the Raman spectrum, which suggests the formation of [CHI+ · CH3COO-] type ion pairs. It was concluded that a comparative analysis of the integrated intensities of the Raman bands in the range 880-940 cm-1 makes it possible to judge about the relative content of hydrated acetate ions, CHI macromolecules of the [CHI+ · CH3COO-] complex, and acetic acid molecules not involved in CHI protonation.

Mikhailov, G. P.; Tuchkov, S. V.; Lazarev, V. V.; Kulish, E. I.

2014-06-01

346

Far-field radiation patterns of aperture antennas by the Winograd Fourier transform algorithm  

NASA Technical Reports Server (NTRS)

A more time-efficient algorithm for computing the discrete Fourier transform, the Winograd Fourier transform (WFT), is described. The WFT algorithm is compared with other transform algorithms. Results indicate that the WFT algorithm in antenna analysis appears to be a very successful application. Significant savings in cpu time will improve the computer turn around time and circumvent the need to resort to weekend runs.

Heisler, R.

1978-01-01

347

A Synthetic Quadrature Phase Detector/Demodulator for Fourier Transform Transform Spectrometers  

NASA Technical Reports Server (NTRS)

A method is developed to demodulate (velocity correct) Fourier transform spectrometer (FTS) data that is taken with an analog to digital converter that digitizes equally spaced in time. This method makes it possible to use simple low cost, high resolution audio digitizers to record high quality data without the need for an event timer or quadrature laser hardware, and makes it possible to use a metrology laser of any wavelength. The reduced parts count and simplicity implementation makes it an attractive alternative in space based applications when compared to previous methods such as the Brault algorithm.

Campbell, Joel

2008-01-01

348

The Fourier-series method for inverting transforms of probability distributions  

Microsoft Academic Search

This paper reviews the Fourier-series method for calculating cumulative distribution functions (cdf's) and probability mass functions (pmf's) by numerically inverting characteristic functions, Laplace transforms and generating functions. Some variants of the Fourier-series method are remarkably easy to use, requiring programs of less than fifty lines. The Fourier-series method can be interpreted as numerically integrating a standard inversion integral by means

Joseph Abate; Ward Whitt

1992-01-01

349

10508 Biochemistry 1995,34, 10508-10518 Temperature-Induced Changes in Protein Structures Studied by Fourier Transform  

E-print Network

by Fourier Transform Infrared Spectroscopy and Global Analysis? I. H. M. van Stokkum,*,s H. Linsdell,# J. M@ ABSTRACT: Fourier transform infrared (FTIR) spectroscopy has been used to study temperature)l. A technique widely used nowadays to study protein structureis Fourier transform infrared (FTIR

van Stokkum, Ivo

350

Application of a Fourier transform based filtering technique to improve signal-to-noise ratio in modulation spectroscopy experiments  

E-print Network

Application of a Fourier transform based filtering technique to improve signal-to-noise ratio of a fast Fourier transform FFT based simplified filtering procedure to improve S/N ratio, thereby enabling) is the Fourier transform of the above data. The frequency scale has been normalized with respect to the Nyquist

Ghosh, Sandip

351

Fast Fourier Transform for Fitness Landscapes Dan Rockmore a , Peter Kostelec a , Wim Hordijk b , Peter F.  

E-print Network

Fast Fourier Transform for Fitness Landscapes Dan Rockmore a , Peter Kostelec a , Wim Hordijk b that explicit computations of the Walsh/Fourier transforms are feasible for landscapes with up to 10 8 configurations using Fast Fourier Transform techniques. We find that the cost function of a linear sum assignment

Stadler, Peter F.

352

Fast Fourier Transform on FPGA: Design Choices and Evaluation Peter A. Milder, Franz Franchetti, James C. Hoe, and Markus Pschel  

E-print Network

Fast Fourier Transform on FPGA: Design Choices and Evaluation Peter A. Milder, Franz Franchetti University Pittsburgh, PA, U.S.A. {pam, franzf, jhoe, pueschel}@ece.cmu.edu The discrete Fourier transform algorithms for computing the DFT, called fast Fourier transforms (FFTs), exhibit concurrency and regularity

Franchetti, Franz

353

A shortcut to inverse Fourier transforms: Approximate reconstruction of transient heating curves from sparse frequency domain data  

E-print Network

A shortcut to inverse Fourier transforms: Approximate reconstruction of transient heating curves 12 February 2010 Available online 19 March 2010 Keywords: Heating curve Fourier transform Transient, such as the transient heating curve, can be derived through inverse Fourier transform (IFT). However, IFT is known

354

IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 21, NO. 19, OCTOBER 1, 2009 1375 Fourier Transform Ultrashort Optical Pulse Shaping  

E-print Network

, and Jianping Yao, Senior Member, IEEE Abstract--Fourier transform ultrashort optical pulse shaping using response of the entire pulse shaping system is equal to the Fourier transform of the square of the grating. INTRODUCTION F OURIER synthesis, also known as Fourier transform pulse shaping, is one of the most commonly

Yao, Jianping

355

An asymptotically hierarchy-consistent, iterative sequence transformation for convergence acceleration of Fourier series  

Microsoft Academic Search

We derive the I transformation, an iterative sequence transformation that is useful for the convergence acceleration of certain\\u000a Fourier series. The derivation is based on the concept of hierarchical consistency in the asymptotic regime. We show that\\u000a this sequence transformation is a special case of the J transformation. Thus, many properties of the I transformation can\\u000a be deduced from the

Herbert H. H. Homeier; Theoretische Chemie

1998-01-01

356

Optimal warping function design for discrete time-warped Fourier transforms  

Microsoft Academic Search

We have recently introduced the class of generalized scale transforms and its subclass of warped Fourier transforms. Members in each class are defined by continuous time warping functions. While the two transforms admit a mathematically elegant analysis of warp-shift invariant systems it is still unclear how to design warping functions that deliver optimal representations for a given class of signals

Robert M. Nickel; William J. Williams

2000-01-01

357

Momentum-space Lippmann-Schwinger-Equation, Fourier-transform with Gauss-Expansion-Method  

E-print Network

In these notes we construct the momentum-space potentials from configuration-space using for the Fourier-transformation the Gaussian-Expansion-Method (GEM). This has the advantage that the Fourier-Bessel integrals can be performed analytically, avoiding possible problems with the oscillations in the Bessel functions for large r, in particular for $p_f \

Rijken, Th A

2014-01-01

358

Momentum-space Lippmann-Schwinger-Equation, Fourier-transform with Gauss-Expansion-Method  

E-print Network

In these notes we construct the momentum-space potentials from configuration-space using for the Fourier-transformation the Gaussian-Expansion-Method (GEM). This has the advantage that the Fourier-Bessel integrals can be performed analytically, avoiding possible problems with the oscillations in the Bessel functions for large r, in particular for $p_f \

Th. A. Rijken

2014-09-19

359

Polarized fourier transform infrared microscopy as a tool for structural analysis of adsorbates in molecular sieves  

SciTech Connect

This report tries to determine whether polarized fourier transform infrared microscopy could be useful in the analysis of the adsorbate structure in zeolites. Measurements on p-xylene loaded single crystals of silicalite I were performed.

Schueth, F. [Gutenberg-Universitaet, Mainz (Germany)

1992-09-17

360

Fourier Transform Infrared Spectroscopy: Part II. Advantages of FT-IR.  

ERIC Educational Resources Information Center

This is Part II in a series on Fourier transform infrared spectroscopy (FT-IR). Described are various advantages of FT-IR spectroscopy including energy advantages, wavenumber accuracy, constant resolution, polarization effects, and stepping at grating changes. (RH)

Perkins, W. D.

1987-01-01

361

A High Resolution Fourier-Transform Spectrometer for the Measurement of Atmospheric Column Abundances  

NASA Technical Reports Server (NTRS)

A compact, high resolution Fourier-transform spectrometer for atmospheric near ultraviolet spectroscopy has been installed at the Jet Propulsion Laboratory's Table Mountain Facility (34.4N, 117.7 W, elevation 2290m).

Cageao, R.; Sander, S.; Blavier, J.; Jiang, Y.; Nemtchinov, V.

2000-01-01

362

The Fourier Transform in Chemistry. Part 1. Nuclear Magnetic Resonance: Introduction.  

ERIC Educational Resources Information Center

Using fourier transformation methods in nuclear magnetic resonance has made possible increased sensitivity in chemical analysis. This article describes these methods as they relate to magnetization, the RF magnetic field, nuclear relaxation, the RF pulse, and free induction decay. (CW)

King, Roy W.; Williams, Kathryn R.

1989-01-01

363

Fourier Transforms of Finite Chirps Peter G. Casazza and Matthew Fickus  

E-print Network

is altered whenever the wave is emanating from or reflecting off a moving body. As such, chirps have-Fourier transform is introduced. Chirplets have been used in image processing for over a decade [5]. For that matter

Casazza, Pete

364

Instrument Line Shape Modeling and Correction for Off-Axis Detectors in Fourier Transform Spectrometry  

NASA Technical Reports Server (NTRS)

Spectra measured by off-axis detectors in a high-resolution Fourier transform spectrometer (FTS) are characterized by frequency scaling, asymmetry and broadening of their line shape, and self-apodization in the corresponding interferogram.

Bowman, K.; Worden, H.; Beer, R.

1999-01-01

365

QUANTITATIVE FOURIER TRANSFORM INFRARED SPECTROSCOPIC INVESTIGATION OF HUMIC SUBSTANCE FUNCTIONAL GROUP COMPOSITION  

EPA Science Inventory

Infrared (IR) spectroscopy has been widely used for the structural investigation of humic substances. Although Fourier Transform Infrared (FTIR) instrumentation has been available for sometime, relatively little work with these instruments has been reported for humic substances,...

366

MATRIX MATERIALS FOR DIFFUSE REFLECTANCE FOURIER TRANSFORM INFRARED SPECTROMETRY OF SUBSTANCES IN POLAR SOLVENTS  

EPA Science Inventory

Calcium floride, magnesium fluoride, sulfur, silver bromide, silver chloride, and five different particle sizes of diamond powder were studied for use as matrix materials for diffuse reflectance Fourier transform infrared spectrometry. Potassium chloride was used as a reference b...

367

HIGH SENSITIVITY FOURIER TRANSFORM NMR. INTERMOLECULAR INTERACTIONS BETWEEN ENVIRONMENTAL TOXIC SUBSTANCES AND BIOLOGICAL MACROMOLECULES  

EPA Science Inventory

This project explored the feasibility of developing new techniques for evaluation of the effects of environmental toxic materials on complex biopolymer systems using high sensitivity Fourier transform nuclear magnetic resonance (nmr) spectroscopy. Commercial instrumentation avail...

368

Forecasting performance of denoising signal by Wavelet and Fourier Transforms using SARIMA model  

NASA Astrophysics Data System (ADS)

The goal of this research is to determine the forecasting performance of denoising signal. Monthly rainfall and monthly number of raindays with duration of 20 years (1990-2009) from Bayan Lepas station are utilized as the case study. The Fast Fourier Transform (FFT) and Wavelet Transform (WT) are used in this research to find the denoise signal. The denoise data obtained by Fast Fourier Transform and Wavelet Transform are being analyze by seasonal ARIMA model. The best fitted model is determined by the minimum value of MSE. The result indicates that Wavelet Transform is an effective method in denoising the monthly rainfall and number of rain days signals compared to Fast Fourier Transform.

Ismail, Mohd Tahir; Mamat, Siti Salwana; Hamzah, Firdaus Mohamad; Karim, Samsul Ariffin Abdul

2014-07-01

369

FAST FOURIER TRANSFORMS: A TUTORIAL REVIEW AND A STATE OF THE ART  

Microsoft Academic Search

The publication of the Cooley-Tukey fast Fourier transform (FIT) algorithm in 1965 has opened a new area in digital signal processing by reducing the order of complexity of some crucial computational tasks like Fourier transform and convolution from N 2 to N log2 N, where N is the problem size. The development of the major algorithms (Cooley-Tukey and split-radix FFT,

P. DUHAMEL; M. VETTERLI

1990-01-01

370

A remark on Littlewood-Paley theory for the distorted Fourier transform  

E-print Network

We show that the usual Mikhlin multiplier theorem relative to the distorted Fourier transform holds in the range (3/2,3) at least for radial functions and potentials. The restricted range is due to the fact that the Schroedinger operator which gives rise to the distorted Fourier transform may have a zero energy resonance. Consequently, the Littlewood-Paley theorem is shown also only for the range (3/2,3).

Wilhelm Schlag

2005-08-29

371

Analysis and application of Fourier transform spectroscopy in atmospheric remote sensing  

NASA Technical Reports Server (NTRS)

An analysis method for Fourier transform spectroscopy is summarized with applications to various types of distortion in atmospheric absorption spectra. This analysis method includes the fast Fourier transform method for simulating the interferometric spectrum and the nonlinear least-squares method for retrieving the information from a measured spectrum. It is shown that spectral distortions can be simulated quite well and that the correct information can be retrieved from a distorted spectrum by this analysis technique.

Park, J. H.

1984-01-01

372

Implementation of a 2-D Fast Fourier Transform on an FPGA-Based Custom Computing Machine  

Microsoft Academic Search

The two dimensional fast Fourier transform (2-D FFT) is an indispensable operation in many digital signal processing applications but yet is deemed computationally expensive when performed on a conventional general purpose processors. This paper presents the implementation and performance figures for the Fourier transform on a FPGA-based custom computer. The computation of a 2-D FFT requires O(N2log2N) floating point arithmetic

Nabeel Shirazi; Peter M. Athanas; A. Lynn Abbott

1995-01-01

373

Note: Phase sensitive detection of photoluminescence with Fourier transform spectroscopy.  

PubMed

Although known for more than twenty years, there is limited information in the literature regarding the experimental parameters of lock-in based phase sensitive emission detection in conjunction with Fourier spectrometers. For this technique - also known as double modulation spectroscopy - we present a guideline for parameter optimization by measuring the photoluminescence of InSb:Te at cryogenic temperatures. PMID:22300001

Ullrich, B; Brown, G J

2012-01-01

374

High Accuracy Evaluation of the Finite Fourier Transform Using Sampled Data  

NASA Technical Reports Server (NTRS)

Many system identification and signal processing procedures can be done advantageously in the frequency domain. A required preliminary step for this approach is the transformation of sampled time domain data into the frequency domain. The analytical tool used for this transformation is the finite Fourier transform. Inaccuracy in the transformation can degrade system identification and signal processing results. This work presents a method for evaluating the finite Fourier transform using cubic interpolation of sampled time domain data for high accuracy, and the chirp Zeta-transform for arbitrary frequency resolution. The accuracy of the technique is demonstrated in example cases where the transformation can be evaluated analytically. Arbitrary frequency resolution is shown to be important for capturing details of the data in the frequency domain. The technique is demonstrated using flight test data from a longitudinal maneuver of the F-18 High Alpha Research Vehicle.

Morelli, Eugene A.

1997-01-01

375

Fourier transform infrared emission spectra of MgH and MgD A. Shayesteh and D. R. T. Appadoo  

E-print Network

Fourier transform infrared emission spectra of MgH and MgD A. Shayesteh and D. R. T. Appadoo, Ontario, N2L 3G1, Canada Received 9 February 2004; accepted 8 March 2004 High resolution Fourier transform the emission spectrum of the A 2 X 2 transition of MgH using a magnesium hollow cathode discharge and a Fourier

Le Roy, Robert J.

376

Characterization of distribution power quality events with Fourier and wavelet transforms  

Microsoft Academic Search

It is the objective of this paper to present unique features that characterize power quality events and methodologies to extract them from recorded voltage and\\/or current waveforms using Fourier and wavelet transforms. Examples of unique features include peak amplitudes, RMS, frequency, and statistics of wavelet transform coefficients. These features are derived from well documented theories, power engineers' heuristics gained through

Surya Santoso; W. Mack Grady; Edward J. Powers; Jeff Lamoree; Siddharth C. Bhatt

2000-01-01

377

A Graphical Presentation to Teach the Concept of the Fourier Transform  

ERIC Educational Resources Information Center

A study was conducted to visualize the reason why the Fourier transform technique is useful to detect the originating frequencies of a complicated superposition of waves. The findings reveal that students respond well when instructors adapt pictorial presentation to show how the time-domain function is transformed into the frequency domain.

Besalu, E.

2006-01-01

378

The Fourier-Stieltjes transform of Minkowski's ?(x) function and an affirmative answer to Salem's problem  

E-print Network

By using structural and asymptotic properties of the Kontorovich-Lebedev transform associated with Minkowski's question mark function, we give an affirmative answer to the question posed by R. Salem (Trans. Amer. Math. Soc., 53 (3), (1943), p. 439) whether its Fourier-Stieltjes transform vanishes at infinity.

Yakubovich, Semyon

2011-01-01

379

A Novel Technique for the Metrology Calibration of a Fourier Transform  

E-print Network

A Novel Technique for the Metrology Calibration of a Fourier Transform Spectrometer Locke D transform spectrom- eter (FTS) to calibrate the metrology of a second FTS. This technique is particularly to verify the performance of the metrology system. The FTS of the Herschel/SPIRE spectrometer is one

Naylor, David A.

380

Super-high-efficiency approximate calculation of series sum and discrete Fourier transform  

E-print Network

We present a super-high-efficiency approximate computing scheme for series sum and discrete Fourier transform. The summation of a series sum or a discrete Fourier transform is approximated by summing over part of the terms multiplied by corresponding weights. The calculation is valid for the function under the transform being piecewise smooth in the continuum variable. The scheme reduces significantly the requirement for computer memory storage and enhances the numerical computation efficiency without losing accuracy. By comparing with the known results of examples, we show the accuracy and the efficiency of the scheme. The efficiency can be higher than $10^6$ for the examples.

Xin-Zhong Yan

2013-11-18

381

Special functions from quantum canonical transformations  

E-print Network

Quantum canonical transformations are used to derive the integral representations and Kummer solutions of the confluent hypergeometric and hypergeometric equations. Integral representations of the solutions of the non-periodic three body Toda equation are also found. The derivation of these representations motivate the form of a two-dimensional generalized hypergeometric equation which contains the non-periodic Toda equation as a special case and whose solutions may be obtained by quantum canonical transformation.

Arlen Anderson

1993-10-26

382

Fourier-transform Ghost Imaging for pure phase object based on Compressive Sampling algorithm  

E-print Network

A special algorithm for the Fourier-transform Ghost Imaging (GI) scheme is discussed based on the Compressive Sampling (CS) theory. Though developed mostly in real space, CS algorithm could also be used for the Fourier spectrum reconstruction of pure phase object by setting a proper sensing matrix. This could find its application in diffraction imaging of X-ray, neutron and electron with higher efficiency and resolution. Simulation and experiment results are also presented to prove the feasibility.

Hui Wang; Shensheng Han

2009-11-20

383

Scaled diffraction calculation between tilted planes using nonuniform fast Fourier transform.  

PubMed

A method of diffraction calculation between tilted planes with variable sampling rates is proposed. The proposed method is based on the Fourier spectrum rotation from a tilted plane to a parallel plane. The nonuniform fast Fourier transformation (NUFFT) is used to calculate the nonuniform sampled Fourier spectrum on the tilted plane with variable sampling rates, which overcomes the sampling restriction of FFT in the conventional method. Both of the computer simulation and the optical experiment shows the feasibility of our method in calculating the hologram of polygon-based object with scalable size, which can be considered as an important application in the holographic three-dimensional display. PMID:25090546

Chang, Chenliang; Xia, Jun; Wu, Jun; Lei, Wei; Xie, Yi; Kang, Mingwu; Zhang, Qiuzhi

2014-07-14

384

1422 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 51, NO. 5, MAY 2003 A New Numerical Fourier Transform in d-Dimensions  

E-print Network

of numerically computing Fourier transforms of digitized functions in one or in -dimen- sions is the so-called discrete Fourier transform (DFT) efficiently implemented as fast Fourier transform (FFT) algorithms. In many cases, the DFT is not an adequate approximation to the continuous Fourier transform, and because

Beauchemin, Steven S.

385

PHYS 385 Lecture 3 -Fourier transforms 3 -1 2003 by David Boal, Simon Fraser University. All rights reserved; further copying or resale is strictly prohibited.  

E-print Network

PHYS 385 Lecture 3 - Fourier transforms 3 - 1 ©2003 by David Boal, Simon Fraser University. All rights reserved; further copying or resale is strictly prohibited. Lecture 3 - Fourier transforms What's important: · discrete Fourier transforms · continuous Fourier transforms Text: Gasiorowicz, App. A The two

Boal, David

386

Application and sensitivity investigation of Fourier transforms for microwave radiometric inversions  

NASA Technical Reports Server (NTRS)

Existing microwave radiometer technology now provides a suitable method for remote determination of the ocean surface's absolute brightness temperature. To extract the brightness temperature of the water from the antenna temperature equation, an unstable Fredholm integral equation of the first kind was solved. Fast Fourier Transform techniques were used to invert the integral after it is placed into a cross-correlation form. Application and verification of the methods to a two-dimensional modeling of a laboratory wave tank system were included. The instability of the Fredholm equation was then demonstrated and a restoration procedure was included which smooths the resulting oscillations. With the recent availability and advances of Fast Fourier Transform techniques, the method presented becomes very attractive in the evaluation of large quantities of data. Actual radiometric measurements of sea water are inverted using the restoration method, incorporating the advantages of the Fast Fourier Transform algorithm for computations.

Holmes, J. J.; Balanis, C. A.

1974-01-01

387

[Research on key technologies of all fiber optic Fourier transform spectrometer].  

PubMed

A noval all fiber optic Fourier transform spectrometer based on single mode fiber Mach-Zehnder interferometer is reported. The authors designed a piezoelectric optical phase modulator with two centimeter scan scale, which was used to replace the moving mirror of traditonal Fourier transform spectrometer. The 1 310 nm DFB laser was used as reference light source to make equal interval sampling of test light source's interferogram, and to eliminate errors of nonlinear modulation. Through making the inverse Fourier transform to test light source's interferogram, the authors obtained the spectrum of test source. The spectrum of ASE broadband light source was measured by FFTS system, and the experiment result agrees with that tested by grating spectrometer. Finally, the authors utilized fiber grating as sample to measure the resolution of FFTS system, and the spectral resolution is 0.78 cm(-1). PMID:19798938

Wang, An; Zhu, Ling; Zhang, Long; Liu, Yong; Zhu, Zhen; Li, Zhi-Gang; Wu, Jian-Dong; Fan, Yan-Ping

2009-07-01

388

The su(2)_? Hahn oscillator and a discrete Hahn-Fourier transform  

E-print Network

We define the quadratic algebra su(2)_{\\alpha} which is a one-parameter deformation of the Lie algebra su(2) extended by a parity operator. The odd-dimensional representations of su(2) (with representation label j, a positive integer) can be extended to representations of su(2)_{\\alpha}. We investigate a model of the finite one-dimensional harmonic oscillator based upon this algebra su(2)_{\\alpha}. It turns out that in this model the spectrum of the position and momentum operator can be computed explicitly, and that the corresponding (discrete) wavefunctions can be determined in terms of Hahn polynomials. The operation mapping position wavefunctions into momentum wavefunctions is studied, and this so-called discrete Hahn-Fourier transform is computed explicitly. The matrix of this discrete Hahn-Fourier transform has many interesting properties, similar to those of the traditional discrete Fourier transform.

E. I. Jafarov; N. I. Stoilova; J. Van der Jeugt

2011-06-06

389

Optical image processing for synthetic-aperture imaging ladar based on two-dimensional Fourier transform.  

PubMed

A two-dimensional (2D) Fourier transform algorithm for the image reconstruction of synthetic-aperture imaging ladar (SAIL) collected data is suggested. This algorithm consists of quadratic phase compensation in azimuth direction and 2D fast Fourier transform. Based on this algorithm and the parallel 2D Fourier transform capability of spherical lens, an optical principle scheme that processes the SAIL data is proposed. The basic principle, design equations, and necessary analysis are presented. To verify this principle scheme, an experimental optical SAIL processor setup is constructed. The imaging results of SAIL data obtained by our SAIL demonstrator are presented. The optical processor is compact, lightweight, and consumes low power. This optical processor can also provide inherent parallel and speed-of-light computing capability, and thus has potential applications in on-board and satellite-borne SAIL systems. PMID:24663462

Sun, Zhiwei; Hou, Peipei; Zhi, Ya'nan; Sun, Jianfeng; Zhou, Yu; Xu, Qian; Lu, Zhiyong; Liu, Liren

2014-03-20

390

Transformation in mandibular imaging with sweep imaging with fourier transform magnetic resonance imaging  

PubMed Central

Objective Current imaging techniques are often sub-optimal for the detection of mandibular invasion by squamous cell carcinoma. The aim of this study was to determine the feasibility of a magnetic resonance imaging (MRI) based technique known as Sweep Imaging with Fourier Transform (SWIFT) to visualize the structural changes of intra-mandibular anatomy during invasion. Design Descriptive case study Setting Tertiary academic institution Method Two specimens from patients with oral carcinoma who underwent segmental mandibulectomy were imaged using a 9.4 Tesla Varian MRI system. The SWIFT images were correlated with histological sections. Results The SWIFT technique with in vitro specimens produced images with sufficient resolution (156–273) and contrast to allow accurate depiction of tumor invasion of cortical and medullary bone. Both specimens had histopathological evidence of mandibular invasion with tumor. A high degree of correlation was found between MR images and histopathologic findings. Conclusion SWIFT MRI offers three-dimensional assessment of cortical and medullary bone in fine detail with excellent qualitative agreement with histopathology. MR imaging with the SWIFT technique demonstrates great potential to identify mandibular invasion by oral carcinoma. PMID:21930980

Kendi, Ayse Tuba Karagulle; Khariwala, Samir S.; Zhang, Jinjin; Idiyatullin, Djaudat S.; Corum, Curtis A.; Michaeli, Shalom; Pambuccian, Stefan E.; Garwood, Michael; Yueh, Bevan

2012-01-01

391

C. R. WORTHINGTON 783 Fourier transform of t(r) is T(R) and, using Cartesian  

E-print Network

C. R. WORTHINGTON 783 Fourier transform of t(r) is T(R) and, using Cartesian coordinates, T(X, Y, Z can write, after omitting the weight factors, the Fourier transform T(X, Y) as T(X, Y) = sinc ¢rAX sinc 7ryoY, (29) and T(/), Z = l~c, is given by T(1) -- sinc 7rzol/c. (30) The Fourier transform T(X, Y

Rossmann, Michael G.

392

Automated charge state determination of complex isotope-resolved mass spectra by peak-target Fourier transform  

Microsoft Academic Search

This study describes a new algorithm for charge state determination of complex isotope-resolved mass spectra. This algorithm\\u000a is based on peak-target Fourier transform (PTFT) of isotope packets. It is modified from the widely used Fourier transform\\u000a method because Fourier transform may give ambiguous charge state assignment for low signal-to-noise ratio (S\\/N) or overlapping\\u000a isotopic clusters. The PTFT algorithm applies a

Li Chen; Yee Leng Yap

2008-01-01

393

Simple example of track finding by Fourier transform and possibilities for vector or optical processors  

SciTech Connect

Simple examples of finding tracks by Fourier transform with filter or correlation function are presented. Possibilities for using this method in more complicated real situations and the processing times which might be achieved are discussed. The method imitates the simplest examples in the literature on optical pattern recognition and optical processing. The possible benefits of the method are in speed of processing in the optical Fourier transform wherein an entire picture is processed simultaneously. The speed of a computer vector processor may be competitive with present electro-optical devices. 2 refs., 6 figs.

Underwood, D.

1986-09-05

394

Use of the fractional Fourier transform in {pi}/2 converters of laser modes  

SciTech Connect

The possibility of using the fractional Fourier transform (FrFT) in optical schemes for astigmatic {pi}/2 converters of Hermite-Gaussian modes to donut Laguerre-Gaussian modes is considered. Several schemes of converters based on the FrFT of the half-integer and irrational orders are presented. The lowest FrFT order than can be used in astigmatic mode converters is found. The properties of converters based on the fractional and ordinary Fourier transforms are compared. (laser beams)

Malyutin, A A [A.M. Prokhorov General Physics Institute, Russian Academy of Sciences, Moscow (Russian Federation)

2004-02-28

395

The Los Alamos Fourier-transform spectrometer: Applications to molecular spectroscopy  

SciTech Connect

We outline design considerations and operating characteristics of the Los Alamos Fourier-transform spectrometer, a state-of-the-art instrument operating from 200 nm to 20 ..mu..m with a resolution of 0.0026 cm/sup /minus/1/ and very high wave number and intensity accuracy. Recent work in molecular spectroscopy carried out with this instrument will be discussed, including N/sub 2//sup +/ spectra obtained in inductively-coupled plasmas; high-temperature spectra of diatomic molecules of astrophysical interest; high-resolution rovibrational fine structure; and Fourier-transform Raman spectroscopy of species in expansion-cooled gases. 8 refs., 5 figs., 4 tabs.

Palmer, B.A.; McDowell, R.S.

1989-01-01

396

Quantum simulation of noncausal kinematic transformations.  

PubMed

We propose the implementation of Galileo group symmetry operations or, in general, linear coordinate transformations in a quantum simulator. With an appropriate encoding, unitary gates applied to our quantum system give rise to Galilean boosts or spatial and time parity operations in the simulated dynamics. This framework provides us with a flexible toolbox that enhances the versatility of quantum simulation theory, allowing the direct access to dynamical quantities that would otherwise require full tomography. Furthermore, this method enables the study of noncausal kinematics and phenomena beyond special relativity in a quantum controllable system. PMID:24033011

Alvarez-Rodriguez, U; Casanova, J; Lamata, L; Solano, E

2013-08-30

397

Quantum Algorithms Using the Curvelet Transform  

E-print Network

The curvelet transform is a directional wavelet transform over R^n, which is used to analyze functions that have singularities along smooth surfaces (Candes and Donoho, 2002). I demonstrate how this can lead to new quantum algorithms. I give an efficient implementation of a quantum curvelet transform, together with two applications: a single-shot measurement procedure for approximately finding the center of a ball in R^n, given a quantum-sample over the ball; and, a quantum algorithm for finding the center of a radial function over R^n, given oracle access to the function. I conjecture that these algorithms succeed with constant probability, using one quantum-sample and O(1) oracle queries, respectively, independent of the dimension n -- this can be interpreted as a quantum speed-up. To support this conjecture, I prove rigorous bounds on the distribution of probability mass for the continuous curvelet transform. This shows that the above algorithms work in an idealized "continuous" model.

Yi-Kai Liu

2008-10-28

398

A comparison of noise removal by the Fourier and the Haar transformations  

NASA Astrophysics Data System (ADS)

This paper compared noise removal using the Fourier series and the Haar wavelet transformations. The results showed that noise from the measured data can be filtered by neglecting high-order terms of Fourier coefficients. It also showed that signal denoising can be achieved by Haar wavelet transformation by filtering the noise before inverting the transformed data back to time domain. A further comparison using a set of data with variation 6.3mV from five measurements of a sample showed that the variations after denoising can be reduced to 3.8mV by the Fourier series and to 2.3mV by 3-level Haar wavelet. Both methods can filter noise in signal and keep the predicted curve consistent with the measured data. The signal becomes smooth if denoised by the Fourier series but the variation of signal, however, can be reduced more if denoised by the Haar wavelet. Moreover, from the computation complexity viewpoint, signal denoising by Haar wavelet is much better than that by Fourier series.

Kuo, Chang-Hsin; Tsai, Jhy-Cherng; Chen, Yi-Ji

2011-12-01

399

Addendum to 'A new hybrid algorithm for computing a fast discrete Fourier transform'  

NASA Technical Reports Server (NTRS)

The reported investigation represents a continuation of a study conducted by Reed and Truong (1979), who proposed a hybrid algorithm for computing the discrete Fourier transform (DFT). The proposed technique employs a Winograd-type algorithm in conjunction with the Mersenne prime-number theoretic transform to perform a DFT. The implementation of the technique involves a considerable number of additions. The new investigation shows an approach which can reduce the number of additions significantly. It is proposed to use Winograd's algorithm for computing the Mersenne prime-number theoretic transform in the transform portion of the hybrid algorithm.

Reed, I. S.; Truong, T. K.; Benjauthrit, B.

1981-01-01

400

Progress Towards Chirped-Pulse Fourier Transform Thz Spectroscopy  

NASA Astrophysics Data System (ADS)

New opportunities are provided by the development of higher power THz frequency multiplier sources, the development of a broadband Chirped-Pulse FTMW spectroscopy technique at microwave and mm Wave frequencies, and recently demonstrated heterodyne hot electron bolometer detection technology in the THz frequency region with near quantum noise-limited performance and high spectral resolution. Combining these three technologies and extending the chirped-pulse technique to 0.85 THz enables a host of new applications. NIST is currently pursing applications as a point sensor for greenhouse gases, volatile organic compounds, and potentially human breath. The generation and detection of phase stable chirped pulses at 850 GHz will be demonstrated. A description of the experimental setup and preliminary data will be presented for nitrous oxide. G.G. Brown, B.C. Dian, K.O. Douglass, S.M. Geyer, S. Shipman and B.H. Pate, Rev.Sci.Instrum. 79 (2008) 053103. E. Gerecht, D. Gu, L. You, K.S. Yngvesson, IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES. 56, (2008) 1083.

Douglass, Kevin O.; Plusquellic, David F.; Gerecht, Eyal

2010-06-01

401

Introduction to Quantum Simulation  

NASA Technical Reports Server (NTRS)

This viewgraph presentation addresses the problem of efficiently simulating the evolution of a quantum system. The contents include: 1) Quantum Simulation; 2) Extracting Answers from Quantum Simulations; 3) Quantum Fourier Transform; 4) Eigenvalue Estimation; 5) Fermionic Simulations.

Williams, Colin P.

2005-01-01

402

Limited-Angle 3-D Reconstructions Using Fourier Transform Iterations and Radon Transform Iterations.  

National Technical Information Service (NTIS)

The principles of limited-angle reconstruction of space-limited objects using the concepts of allowed cone and missing cone in Fourier space are discussed. The distortion of a point source resulting from setting the Fourier components in the missing cone ...

K. C. Tam, V. Perez-Mendez

1979-01-01

403

On Fourier integral transforms for $q$-Fibonacci and $q$-Lucas polynomials  

E-print Network

We study in detail two families of $q$-Fibonacci polynomials and $q$-Lucas polynomials, which are defined by non-conventional three-term recurrences. They were recently introduced by Cigler and have been then employed by Cigler and Zeng to construct novel $q$-extensions of classical Hermite polynomials. We show that both of these $q$-polynomial families exhibit simple transformation properties with respect to the classical Fourier integral transform.

Atakishiyev, Natig; Levi, Decio; Ragnisco, Orlando

2011-01-01

404

Probability density function of the single eigenvalue outside the semicircle using the exact Fourier transform  

SciTech Connect

It is shown that the probability density function far outside the semicircle is closely related to the form factor of N one-dimensional nucleons. The exact Fourier transform of the probability density function for the Gaussian unitary ensemble is given. Using this transform it is shown that the probability density function P(x) far outside the semicircle is a Gaussian function multiplied by powers of X.

Ullah, N.

1985-09-01

405

Characterization of biomass burning: Fourier transform infrared analysis of wood and vegetation combustion products  

Microsoft Academic Search

The Fourier transform infrared examination of the combustion products of a selection of forest materials has been undertaken in order to guide future detection of biomass burning using satellite remote sensing. Combustion of conifer Pinus strobus (white pine) and deciduous Prunus serotina (cherry), Acer rubrum (red maple), Friglans nigra (walnut), Fraxinus americana (ash), Betula papyrifera (birch), Querus alba (white oak)

Diomaris Padilla

2008-01-01

406

Investigation of infrared Fourier-Transform spectroscopy for oral cancer detection  

E-print Network

A system was developed using a Fourier Transform-n spectrometer to investigate spectral differences between malignant, benign and healthy oral tissue in the near-infrared range (2.0-2.5 microns). A hamster model for oral squamous cell carcinoma...

Cooney, Kevin Michael

2012-06-07

407

Fourier transform infrared spectroscopic study of thermal degradation of sugar cane bagasse  

Microsoft Academic Search

Thermal degradation of sugar cane bagasse has been studied between 200 and 800 °C under a nitrogen gas flow. Different experimental parameters of the pyrolysis have been investigated, including holding temperature, time duration of pyrolysis, and heating rate. The solid residues obtained were then analyzed by classical elemental analysis and Fourier transform infrared (FTIR) spectroscopy.The most important structure modifications appeared

Ketty Bilba; Alex Ouensanga

1996-01-01

408

Optical thin film synthesis program based on the use of Fourier transforms  

E-print Network

Optical thin film synthesis program based on the use of Fourier transforms J. A. Dobrowolski and D the essential equations necessaryfor the implementation of Sossi's formulation of the FT thin film synthesis There exist two basic approaches to the synthesis of optical multilayer systems with irregular spectral

Lowe, David

409

Determination of diosmin in pharmaceutical formulations using Fourier transform infrared spectrophotometry  

PubMed Central

A Fourier transform infrared (FT-IR) spectrometric method was developed for the rapid, direct measurement of diosmin in different pharmaceutical drugs. Conventional KBr-spectra were compared for best determination of active substance in commercial preparations. The Beer–Lambert law and two chemometric approaches, partial least squares (PLS) and principal component regression (PCR+) methods, were tried in data processing. PMID:23960715

Bunaciu, Andrei A.; Udristioiu, Gabriela Elena; Ruta, Lavinia L.; Fleschin, Serban; Aboul-Enein, Hassan Y.

2009-01-01

410

Determination of diosmin in pharmaceutical formulations using Fourier transform infrared spectrophotometry.  

PubMed

A Fourier transform infrared (FT-IR) spectrometric method was developed for the rapid, direct measurement of diosmin in different pharmaceutical drugs. Conventional KBr-spectra were compared for best determination of active substance in commercial preparations. The Beer-Lambert law and two chemometric approaches, partial least squares (PLS) and principal component regression (PCR+) methods, were tried in data processing. PMID:23960715

Bunaciu, Andrei A; Udristioiu, Gabriela Elena; Ru??, Lavinia L; Fleschin, Serban; Aboul-Enein, Hassan Y

2009-10-01

411

Alpha-rooting method of color image enhancement by discrete quaternion Fourier transform  

NASA Astrophysics Data System (ADS)

This paper presents a novel method for color image enhancement based on the discrete quaternion Fourier transform. We choose the quaternion Fourier transform, because it well-suited for color image processing applications, it processes all 3 color components (R,G,B) simultaneously, it capture the inherent correlation between the components, it does not generate color artifacts or blending , finally it does not need an additional color restoration process. Also we introduce a new CEME measure to evaluate the quality of the enhanced color images. Preliminary results show that the ?-rooting based on the quaternion Fourier transform enhancement method out-performs other enhancement methods such as the Fourier transform based ?-rooting algorithm and the Multi scale Retinex. On top, the new method not only provides true color fidelity for poor quality images but also averages the color components to gray value for balancing colors. It can be used to enhance edge information and sharp features in images, as well as for enhancing even low contrast images. The proposed algorithms are simple to apply and design, which makes them very practical in image enhancement.

Grigoryan, Artyom M.; Agaian, Sos S.

2014-02-01

412

Gaseous emanation detection algorithm using a Fourier transform interferometer operating in differential mode  

Microsoft Academic Search

Enactment of the Clean Air Act Amendments of 1990 has resulted in an increased ambient air monitoring needs for industry, some of which may be met efficiently using open- path optical remote sensing (ORS) techniques. Among the most promising of these techniques, we note the Fourier transform spectrometry (FTS). This technique is well suited for the detection of organic and

Richard L. Lachance; Jean-Marc Theriault; Claude Lafond; Andre Villemaire

1998-01-01

413

Topics in Chemical Instrumentation: Fourier Transform-Infrared Spectroscopy: Part I. Instrumentation.  

ERIC Educational Resources Information Center

Discusses: (1) the design of the Fourier Transform-Infrared Spectroscopy (FT-IR) spectrometer; (2) the computation of the spectrum from the interferogram; and (3) the use of apodization. (Part II will discuss advantages of FT-IR over dispersive techniques and show applications of FT-IR to difficult spectroscopic measurements.) (JN)

Perkins, W. D.

1986-01-01

414

Phase correction in piezoelectric photoacoustic Fourier transform infrared spectroscopy of mica  

Microsoft Academic Search

Piezoelectric photoacoustic IR spectra of mica are obtained using a Fourier transform IR spectrometer and lead zirconate titanate (PZT) as a detector. The spectra exhibit negative intensities and transmission like bands, instead of more conventional absorption bands generally observed with a gas- microphone cell. Correct spectra of mica\\/PZT are calculated only when the interferogram phase is constrained to the first

S. L. Zhang; Kirk H. Michaelian; James A. Burt

1997-01-01

415

Fourier-transform spectroscopy of O3 in the 3-micron region  

NASA Technical Reports Server (NTRS)

Fourier transform spectra of ozone have been recorded in the 2-5-micron region at a resolution of 0.01/cm. Absorption lines belonging to numerous vibration-rotation transitions have been observed in these spectra, and a detailed analysis of the band system centered at 3.6 microns has been completed.

Smith, M. A. H.; Rinsland, C. P.; Malathy Devi, V.; Flaud, J.-M.; Camy-Peyret, C.

1989-01-01

416

The Fractional Fourier Transform and Applications David H. Bailey and Paul N. Swarztrauber  

E-print Network

22, 1990 Abstract This paper describes the ``fractional Fourier transform'', which admits computation­integer periodicities, performing high­resolution trigonometric interpolation, detecting lines in noisy images also be applied in other situations that do not admit efficient solution using standard FFTs

Bernstein, Daniel

417

USE OF A FOURIER TRANSFORM SPECTROMETER AS A REMOTE SENSOR AT SUPERFUND SITES  

EPA Science Inventory

A Fourier transform infrared remote sensor (FTIR-RS) was used to measure chemical emissions at the Shaver's Park Superfund site in northwestern Georgia. he system was bistatic with a source/receiver at one end of a 250 path and a retroreflector at the other end. he source/receive...

418

Application of Synchrotron Radiation-Based Fourier Transform Infrared Spectromicroscopy to the Investigation of Bacterial  

E-print Network

of the bacteria on the aluminum slide within a 100 X 150 �m area, with 10 �m step widths in both the X and YApplication of Synchrotron Radiation-Based Fourier Transform Infrared Spectromicroscopy of TCE-cometabolizing bacteria exhibit preferential attachment to specific mineral phases within

419

Computation of Configuration-Space Obstacles Using the Fast Fourier Transform  

Microsoft Academic Search

A method is proposed for computing the configuration-space map of obstacles. The map is used in motion-planning algorithms. The method derives from the observation that, when the robot is a rigid object that can only translate, the configuration space is a convolution of the workspace and the robot. It makes use of the fast Fourier transform (FFT) algorithm to compute

Lydia E. Kavraki

1993-01-01

420

The reconstruction of a multidimensional sequence from the phase or magnitude of its Fourier transform  

Microsoft Academic Search

This paper addresses two fundamental issues involved in the reconstruction of a multidimensional sequence from either the phase or magnitude of its Fourier transform. The first issue relates to the uniqueness of a multidimensional sequence in terms of its phase or magnitude. Although phase or magnitude information alone is not sufficient, in general, to uniquely specify a sequence, a large

M. Hayes

1982-01-01

421

Green's function of a finite chain and the discrete Fourier transform  

E-print Network

A new expression for the Green's function of a finite one-dimensional lattice with nearest neighbor interaction is derived via discrete Fourier transform. Solution of the Heisenberg spin chain with periodic and open boundary conditions is considered as an example. Comparison to Bethe ansatz clarifies the relation between the two approaches.

S. Cojocaru

2007-04-22

422

MAFFT: a novel method for rapid multiple sequence alignment based on fast Fourier transform  

Microsoft Academic Search

A multiple sequence alignment program, MAFFT, has been developed. The CPU time is drastically reduced as compared with existing methods. MAFFT includes two novel techniques. (i) Homo- logous regions are rapidly identified by the fast Fourier transform (FFT), in which an amino acid sequence is converted to a sequence composed of volume and polarity values of each amino acid resi-

Kazutaka Katoh; Kazuharu Misawa; Kei-ichi Kum; Takashi Miyata

2002-01-01

423

On the use of windows for harmonic analysis with the discrete Fourier transform  

Microsoft Academic Search

This paper makes available a concise review of data windows and their affect on the detection of harmonic signals in the presence of broad-band noise, and in the presence of nearby strong harmonic interference. We also call attention to a number of common errors in the application of windows when used with the fast Fourier transform. This paper includes a

FREDRIC J. HARRIS

1978-01-01

424

The generation of correlated Rayleigh random variates by inverse discrete Fourier transform  

Microsoft Academic Search

A number of different algorithms are used for the generation of correlated Rayleigh random variates. This paper presents an analysis of the statistical properties of methods based on the inverse discrete Fourier transform (IDFT). A modification of the algorithm of Smith (1975) is presented, the new method requiring exactly one-half the number of IDPT operations and roughly two-thirds the computer

David J. Young; Norman C. Beaulieu

2000-01-01

425

Fast Fourier transform method of computing difference equations and simulating filters  

Microsoft Academic Search

Two methods for using the fast Fourier transform to reduce the number of arithmetic operations and, therefore the time required for computing discrete, preformulated, and finite convolutions are listed and justified. Under the idealistic assumption that the impulse response of a preformulated difference equation terminates, a theorem is proved that these two methods can be modified to compute such difference

H. Helms

1967-01-01

426

TEXTILE TECHNOLOGY Preliminary FourierTransform Infrared Spectroscopy Analysis of Cotton Trash  

Microsoft Academic Search

Ongoing research efforts at the United States Department of Agriculture (USDA) consist of developing methods for the identification of cot - ton trash. Botanical cotton trash (eg. leaf, stem, hull, bark) has been reported to be problematic in the processing efficiency and quality of cotton throughout ginning and textile processing. Fourier transform infrared (FTIR) spectroscopic methods are being utilized to

Angela Allen; Jonn Foulk; Gary Gamble

2007-01-01

427

A Holographic Optical Element for Non-symmetric Fourier Transform Systems  

Microsoft Academic Search

Up to now, the non-symmetric Fourier transform (NFT) of an object has been made using conventional refractive optics such as cylindrical and\\/or spherical lenses. In this paper, we propose the use of a holographic optical element in conjunction with refractive lenses to improve the design flexibility of NFT systems working with parallel beam illumination. Experimental results are presented.

S. Bará; C. Gómez-Reino

1989-01-01

428

Fourier-transform ghost imaging with pure far-field correlated thermal light  

SciTech Connect

Pure far-field correlated thermal light beams are created with phase grating, and Fourier-transform ghost imaging depending only on the far-field correlation is demonstrated experimentally. Theoretical analysis and the results of experimental investigation of this pure far-field correlated thermal light are presented. Applications which may be exploited with this imaging scheme are discussed.

Liu Honglin; Shen Xia; Han Shensheng [Key Laboratory for Quantum Optics and the Center for Cold Atom Physics of CAS, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, P.O. Box 800-211, Shanghai, 201800 (China); Zhu Daming [University of Science and Technology of China, Hefei, 230027 (China); University of Missouri-Kansas City, Kansas City, Missouri 64110 (United States)

2007-11-15

429

Investigation of the determination of respirable quartz on filter media using Fourier transform infrared spectrophotometry  

Microsoft Academic Search

The use of Fourier transform infrared spectrophotometry for the determination of quartz in respirable dust directly on filter media was investigated. Fifteen different 25-mm filters which might be used in a respirable dust sampler were examined. With the best of these, the limit of detection in practical operating conditions (three times the standard deviation of the blank) was estimated to

Lorberau

1989-01-01

430

Quasiparticle relaxation in Heavy Fermions studied using Inverse Fourier Transform of optical conductivity  

E-print Network

in discrete form, using the well known fast Fourier transform (FFT) algorithm [11]. Before the algorithm can rise to electrical resistance are independent from each other [1]. The central para- meter of the model,3]. The reciprocal of relaxation time, 1=t is commonly referred to as the scattering rate. The optical conductivity

Dordevic, Sasha V.

431

High Speed Countercurrent Chromatography/Fourier Transform Infrared (HSCCC/FT-IR) Spectrometry  

NASA Astrophysics Data System (ADS)

High Speed Countercurrent Chromatography/Fourier transform infrared (HSCCC/FT-IR) spectrometry is present-ed. High solute-to-solvent ratios can be obtained in separations performed using HSCCC. At these high solute concentrations it is possible to obtain spectra of solutes without solvent elimination, even in the presence of polar solvents, such as water and methanol.

Romanach, Rodolfo J.; de Haseth, James A.

1985-12-01

432

A test for second order stationarity of a time series based on the Discrete Fourier Transform  

E-print Network

A test for second order stationarity of a time series based on the Discrete Fourier Transform property, we construct a Portmanteau type test statistic for testing stationarity of the time series. It is shown that under the null of stationarity, the test statistic is approximately a chi square distribution

Subba Rao, Suhasini

433

Learning applications of multi-tasking signal analysis of Fourier transform based on smart mobile devices  

Microsoft Academic Search

This paper presents a viable approach and a new teaching and learning paradigm to enhance the effectiveness of teaching fast Fourier transform [1] and significantly improve the learning outcomes. By using the smart mobile devices, this approach establishes the links among concepts, abstract representations, and realistic applications which are often lacking in traditional instruction. Several mobile apps for real time

Zhengzhe Li; Teng Zhao; Dong Ren; Yang Zhang; Lei Wang

2012-01-01

434

Balloon-borne, He-cooled Fourier transform spectrometer for far infrared astronomy  

Microsoft Academic Search

Mounting a prototype version of the helium cooled German Infrared Laboratory (GIRL) spacelab Fourier transform spectrometer (FTS) on a balloon borne 1 m infrared telescope, and on a three-axis stabilized platform is proposed. The Michelson FTS utilizes both outputs. A Fabry-Perot masking filter passes radiation to the FTS only in bands containing lines of astrophysical interest. The reduction of the

M. F. Campbell; S. Drapatz

1985-01-01

435

GRAZING-ANGLE FOURIER TRANSFORM INFRARED SPECTROSCOPY FOR ONLINE SURFACE CLEANLINESS VERIFICATION. YEAR 1  

EPA Science Inventory

As part of the Online Surface Cleanliness Project, the Naval Facilities Engineering Service Center (NFESC) conducted a study of grazing-angle reflectance Fourier Transform Infrared (FTIR) Spectroscopy as a tool for online cleanliness verification at Department of Defense (DoD) cl...

436

Faster GPS via the Sparse Fourier Transform Haitham Hassanieh Fadel Adib Dina Katabi Piotr Indyk  

E-print Network

Faster GPS via the Sparse Fourier Transform Haitham Hassanieh Fadel Adib Dina Katabi Piotr Indyk, fadel, dk, indyk}@mit.edu ABSTRACT GPS is one of the most widely used wireless systems. A GPS re- ceiver the fastest GPS locking algorithm to date. The algorithm reduces the locking complexity to O(n log n). Fur

437

Emissions from smoldering combustion of biomass measured by open-path Fourier transform infrared spectroscopy  

Microsoft Academic Search

Biomass samples from a diverse range of ecosystems were burned in the Intermountain Fire Sciences Laboratory open combustion facility. Midinfrared spectra of the nascent emissions were acquired at several heights above the fires with a Fourier transform infrared spectrometer (FTIR) coupled to an open multipascell. In this report, the results from smoldering combustion during 24 fires are presented including production

Robert J. Yokelson; Ronald Susott; Darold E. Ward; James Reardon; David W. T. Griffith

1997-01-01

438

The Fourier transform solution for the Green's function of monoenergetic neutron transport theory  

E-print Network

Nearly 45 years ago, Ken Case published his seminal paper on the singular eigenfunction solution for the Green's function of the monoenergetic neutron transport equation with isotropic scattering. Previously, the solution had been obtained by Fourier transform. While it is apparent the two had to be equivalent, a convincing equivalence proof for general anisotropic scattering remained a challenge until now.

Barry D. ganapol

2014-03-17

439

Rheometrical detection of incipient blood clot formation by Fourier transform mechanical spectroscopy  

Microsoft Academic Search

We report a study of the coagulation of whole blood by oscillatory shear Fourier transform mechanical spectroscopy. The results include the first identification of the Gel Point of coagulating blood in terms of the Chambon–Winter Gel Point criterion and we show how this may be used as an appropriate basis for detecting the establishment of an incipient clot in samples

P. A. Evans; K. Hawkins; P. R. Williams; R. L. Williams

2008-01-01

440

A liquid helium cryostat for use in dispersive Fourier transform spectroscopy  

Microsoft Academic Search

A fully demountable liquid helium cryostat is described which has been constructed for measuring the optical constants of solids in the far infrared at low temperatures by dispersive Fourier transform spectroscopy. By firm location of the base plates of the liquid helium and liquid nitrogen cans in a metal reference plate in the fixed arm of a Michelson interferometer using

T. J. Parker; R. P. Lowndes

1979-01-01

441

An Example of Fourier Transforms of Orbital Integrals and their Endoscopic Transfer  

Microsoft Academic Search

For the Lie algebra sl2 over a p-adic eld, the Fourier transform of a regular orbital integral is expressed as an integral over all regular orbital integrals, with explicit coecients. This expression, unlike the Shalika germ expansion, is not restricted to orbits of small elements. The result gives quite an elementary access to a simple example of Waldspurger's recent theorem

Ulrich Everling

1998-01-01

442

The Kinetics of Mo(Co)6 Substitution Monitored by Fourier Transform Infrared Spectrophotometry.  

ERIC Educational Resources Information Center

Describes a physical chemistry experiment that uses Fourier transform (FTIR) spectrometers and microcomputers as a way of introducing students to the spectral storage and manipulation techniques associated with digitized data. It can be used to illustrate FTIR spectroscopy, simple kinetics, inorganic mechanisms, and Beer's Law. (TW)

Suslick, Kenneth S.; And Others

1987-01-01

443

Fourier Transform Infrared and Raman Spectroscopy for Characterization of Listeria monocytogenes Strains  

Microsoft Academic Search

The purpose of this study was to characterize the variation in biochemical composition of 89 strains of Listeria monocytogenes with different susceptibilities towards sakacin P, using Fourier transform infrared (FTIR) spectroscopy and Raman spectroscopy. The strains were also analyzed using amplified fragment length polymorphism (AFLP) analysis. Based on their susceptibilities to sakacin P, the 89 strains have previously been divided

Astrid Oust; T. Moretro; Kristine Naterstad; Ganesh D. Sockalingum; Isabelle Adt; Michel Manfait; Achim Kohler

2006-01-01

444

$(p,q)-$deformed Fibonacci and Lucas polynomials: characterization and Fourier integral transforms  

E-print Network

A full characterization of $(p,q)$-deformed Fibonacci and Lucas polynomials is given. These polynomials obey non-conventional three-term recursion relations. Their generating functions and Fourier integral transforms are explicitly computed and discussed. Relevant results known in the literature are examined as particular cases.

Mahouton Norbert Hounkonnou; Sama Arjika

2013-07-09

445

Software Development Kit for Multicore Acceleration Version 3.1 3D Fast Fourier Transform Library  

E-print Network

Software Development Kit for Multicore Acceleration Version 3.1 3D Fast Fourier Transform Library Programmer's Guide and API Reference #12;3D FFT Library Programmer's Guide and API Reference © Copyright IBM or disclosure restricted by GSA ADP Schedule Contract with IBM Corp. #12;3D FFT Library Programmer's Guide

446

Fourier Transform Infrared Absorption Study of Hexa(hexylthio)triphenylene: A Discotic Liquid Crystal  

Microsoft Academic Search

We have used Fourier transform infrared absorption spectroscopy to study the molecular motions of hexa(hexylthio)triphenylene as a function of temperature. Our measurements show pronounced changes in the CH stretching mode frequencies at the K ? H transition. (The H phase displays long range incommensurate helical order). However, the CH stretching mode frequencies show much less variation with temperature, suggesting that

W. K. Lee; P. A. Heiney; J. P. McCauley JR; A. B. Smith III

1991-01-01

447

Millimeter and Submillimeter Wave Dielectric Measurements of Household Powders Using Fourier Transform Spectroscopy  

Microsoft Academic Search

High resolution millimeter and submillimeter wave measurements of solids and powders are very difficult to acquire and have taken on a growing significance for security reasons. Utilizing a two-beam polarizing interferometer, the dielectric properties of household powders were obtained through Dispersive Fourier Transform Spectroscopy. The refractive index, absorption coefficient, real and imaginary permittivity, and loss tangent for talc, confectioner sugar,

Usman Khan; M. N. Afsar; Nicholas Nguyen

2006-01-01

448

Terahertz spectroscopy with a holographic Fourier transform spectrometer plus array detector using coherent synchrotron radiation  

SciTech Connect

By use of coherent terahertz synchrotron radiation, we experimentally tested a holographic Fourier transform spectrometer coupled to an array detector to determine its viability as a spectral device. Somewhat surprisingly, the overall performance strongly depends on the absorptivity of the birefringent lithium tantalate pixels in the array detector.

Nikolay I. Agladz, John Klopf, Gwyn Williams, Albert J. Sievers

2010-06-01

449

1880 Anal. Chem. 1987, 59,1880-1882 Californium-252 Plasma Desorption with Fourier Transform Mass  

E-print Network

for scanning instruments. Until re- cently PD has only been used with time-of-flight (TOF) mass spectrometers for obtaining PD/FT mass spectra for a variety of compounds with abundant molecular ion species of masses1880 Anal. Chem. 1987, 59,1880-1882 Californium-252 Plasma Desorption with Fourier Transform Mass

Chait, Brian T.

450

THE FOURIER-BASED SYNCHROSQUEEZING TRANSFORM T. Oberlin, S. Meignen and V. Perrier  

E-print Network

THE FOURIER-BASED SYNCHROSQUEEZING TRANSFORM T. Oberlin, S. Meignen and V. Perrier Laboratoire Jean. The synchrosqueezing is a post-processing method which circumvents the uncertainty relations, inherent to these linear of the synchrosqueezing to the STFT, and states a similar theoretical result. The emphasis is put on the differences

Paris-Sud XI, Université de

451

The data processing pipelines for the Herschel\\/SPIRE imaging Fourier transform spectrometer  

Microsoft Academic Search

We present an update to the data processing pipelines that generate calibrated spectral data products from the Spectral and Photometric Imaging Receiver (SPIRE), one of three scientific instruments onboard the European Space Agency's Herschel Space Observatory launched on 14 May 2009. The pipelines process telemetry from SPIRE's imaging Fourier Transform Spectrometer (FTS) taken in point source, jiggle- and raster-map observing

Trevor R. Fulton; Jean-Paul Baluteau; Dominique Benielli; Peter Davis-Imhof; Bruce M. Swinyard; Steve Guest; Christian Surace; Dave Clements; Pasquale Panuzzo; David A. Naylor; Edward Polehampton; Arnold Schwartz; Kevin Xu

2010-01-01

452

The data processing pipeline for the Herschel\\/SPIRE Imaging Fourier Transform Spectrometer  

Microsoft Academic Search

We present the data processing pipeline to generate calibrated data products from the Spectral and Photometric Imaging Receiver (SPIRE) imaging Fourier Transform Spectrometer. The pipeline processes telemetry from SPIRE point source, jiggle- and raster-map observations, producing calibrated spectra in low-, medium-, high-, and mixed low- and high- resolution modes. The spectrometer pipeline shares some elements with the SPIRE photometer pipeline,

Trevor R. Fultona; David A. Naylorb; Peter Davis-Imhofa; M. Swinyarde; Tanya L. Lime; Nanyao Luh; France Marseille

453

Fourier transform spectroscopy of the A1?-X1?+ transition of BH and BD  

NASA Astrophysics Data System (ADS)

The A1?-X1?+ transitions of BH and BD were recorded in emission near 4330 Å by Fourier transform spectroscopy. For BH improved line positions and molecular constants were determined from the analysis of the data. New bands of BD were found in our spectra. Alfred P. Sloan Fellow; Camille and Henry Dreyfus Teacher Scholar.

Fernando, W. T. M. L.; Bernath, P. F.

1991-02-01

454

Pulsed nozzle Fourier transform microwave spectrometer: Ideal to define hydrogen bond radius  

Microsoft Academic Search

A pulsed nozzle Fourier transform microwave (PNFTMW) spectrometer has been recently fabri- cated at the Indian Institute of Science. The basic design is the same as that of Balle and Flygare. How - ever, recent advances in microwave and computer technologies have helped in designing a state -of-the- art PNFTMW spectrometer. The range of the spectro- meter is from 2

E. Arunan; A. P. Tiwari; P. K. Mandal; P. C. Mathias

455

Reconstruction of multispectral image cubes from multiple-telescope array Fourier transform imaging spectrometer  

E-print Network

Reconstruction of multispectral image cubes from multiple- telescope array Fourier transform objects is more difficult, since the multispectral image cube is missing low spatial frequency information will present results for the simultaneous reconstruction of a multispectral image cube using simulated data

Fienup, James R.

456

ATMOSPHERIC MEASUREMENTS OF TRACE POLLUTANTS; LONG PATH FOURIER TRANSFORM INFRARED SPECTROSCOPY  

EPA Science Inventory

Described are the results of a four-year study to measure trace pollutant concentrations in polluted atmospheres by kilometer pathlength Fourier transform infrared (FT-IR) absorption spectroscopy. The study covers selected smog episodes during the years 1976 to 1979. During 1976 ...

457

Lecture Notes on the Fast Fourier Transform 1. Motivation: Digital Signal Processing  

E-print Network

Lecture Notes on the Fast Fourier Transform 1. Motivation: Digital Signal Processing Consider the system behaves. It turns out that, if the system is time invariant (does not change its behavior over time) and linear (roughly, gives twice the response to twice the signal), then its behavior

Vazirani, Umesh

458

Lecture Notes on the Fast Fourier Transform 1. Motivation: Digital Signal Processing  

E-print Network

Lecture Notes on the Fast Fourier Transform 1. Motivation: Digital Signal Processing Consider. It turns out that, if the system is time invariant does not change its behavior over time and linear roughly, gives twice the response to twice the signal, then its behavior is completely captured by its

Vazirani, Umesh

459

Measurement of ferrocyanides and oxyanions in waste sludges by Fourier transform infrared reflection methods  

NASA Astrophysics Data System (ADS)

Simulated waste sludges with compositions similar to some of the actual waste sludges stored in carbon steel tanks at the Hanford Site were measured for their ferrocyanide and oxyanion contents by Fourier transform infrared (FT-IR) reflection methods. The results indicated the viability of these methods to chemically characterize highly radioactive waste sludges.

Rebagay, Teofila V.; Dodd, D. A.; Jeppson, David W.

1994-01-01

460

JOURNAL DE PHYSIQUE Colloque C 2, supplkment au no 3-4, Tome 28, mars-ravril1967, page C 2 -58 A FAST FOURIER TRANSFORM TECHNIQUE  

E-print Network

A FAST FOURIER TRANSFORM TECHNIQUE AND ITS APPLICATION TO FOURIER SPECTROSCOPY (I) Concord Radiance. Abstract. - A description of a new method for computing Fourier transforms is given ; it was originated. The problem of computing Fourier transforms on digital computers is of great concern to many people

Boyer, Edmond

461

High-Resolution Fourier Transform Spectrum of the D 2O Molecule in the Region of the Second Triad of Interacting Vibrational States  

NASA Astrophysics Data System (ADS)

The high-resolution Fourier transform spectrum of the D 2O molecule was recorded in the 3200-4200 cm -1 region, where the bands of the second triad of interacting vibrational states are located. As a result of the theoretical analysis, both the rotational-vibrational structure of the (011) vibrational state was improved, and the rotational energies of the (110) and (030) vibrational states were determined for the first time up to rotational quantum numbers Jmax. = 15 and 14, respectively.

He, Sheng-gui; Ulenikov, O. N.; Onopenko, G. A.; Bekhtereva, E. S.; Wang, Xiang-huai; Hu, Shui-ming; Lin, Hai; Zhu, Qing-shi

2000-03-01

462

Estimation of motions in color image sequences using hypercomplex fourier transforms.  

PubMed

Although the motion estimation problem has been extensively studied, most of the proposed estimation approaches deal mainly with monochrome videos. The most usual way to apply them also in color image sequences is to process each color channel separately. A different, more sophisticated approach is to process the color channels in a "holistic" manner using quaternions, as proposed by Ell and Sangwine. In this paper, we extend standard spatiotemporal Fourier-based approaches to handle color image sequences, using the hypercomplex Fourier transform. We show that translational motions are manifested as energy concentration along planes in the hypercomplex 3-D Fourier domain and we describe a methodology to estimate the motions, based on this property. Furthermore, we compare the three-channels-separately approach with our approach and we show that the computational effort can be reduced by a factor of 1/3, using the hypercomplex Fourier transform. Also, we propose a simple, accompanying method to extract the moving objects in the hypercomplex Fourier domain. Our experimental results on synthetic and natural images verify our arguments throughout the paper. PMID:19095528

Alexiadis, Dimitrios S; Sergiadis, George D

2009-01-01

463

Improving axial resolution in spectral domain low-coherence interferometry through fast Fourier transform harmonic artifacts  

NASA Astrophysics Data System (ADS)

Low-coherence interferometric setups in the Fourier domain can experience false structures after the Fourier transform procedure due to signal saturation; in fact, these structures are located at multiple frequencies of the original signal, also referred to as harmonics. This study aids in a better understanding of this phenomenon. The aim of the present work was to show that these features can be used to improve differential axial resolution in highly reflective samples. Using an optical coherence tomography system and calibrated step height standards, it was possible to achieve a resolution greater than the light source coherence length.

Raele, Marcus Paulo; Tarelho, Luiz Vicente Gomes; da Silva Azeredo, Carlos Leonardo; Couceiro, Iakyra Borrakuens; Freitas, Anderson Zanardi

2014-07-01

464

Infrared absorption of CH3OSO detected with time-resolved Fourier-transform spectroscopy  

NASA Astrophysics Data System (ADS)

A step-scan Fourier-transform spectrometer coupled with a multipass absorption cell was employed to detect temporally resolved infrared absorption spectra of CH3OSO produced upon irradiation of a flowing gaseous mixture of CH3OS(O)Cl in N2 or CO2 at 248 nm. Two intense transient features with origins near 1152 and 994 cm-1 are assigned to syn-CH3OSO; the former is attributed to overlapping bands at 1154 +/- 3 and 1151 +/- 3 cm-1, assigned to the S=O stretching mixed with CH3 rocking (?8) and the S=O stretching mixed with CH3 wagging (?9) modes, respectively, and the latter to the C-O stretching (?10) mode at 994 +/- 6 cm-1. Two weak bands at 2991 +/- 6 and 2956 +/- 3 cm-1 are assigned as the CH3 antisymmetric stretching (?2) and symmetric stretching (?3) modes, respectively. Observed vibrational transition wavenumbers agree satisfactorily with those predicted with quantum-chemical calculations at level B3P86/aug-cc-pVTZ. Based on rotational parameters predicted at that level, the simulated rotational contours of these bands agree satisfactorily with experimental results. The simulation indicates that the S=O stretching mode of anti-CH3OSO near 1164 cm-1 likely makes a small contribution to the observed band near 1152 cm-1. A simple kinetic model of self-reaction is employed to account for the decay of CH3OSO and yields a second-order rate coefficient k = (4 +/- 2)×10-10 cm3 molecule-1 s-1.

Chen, Jin-Dah; Lee, Yuan-Pern

2011-03-01

465

Infrared absorption of CH3OSO detected with time-resolved Fourier-transform spectroscopy.  

PubMed

A step-scan Fourier-transform spectrometer coupled with a multipass absorption cell was employed to detect temporally resolved infrared absorption spectra of CH(3)OSO produced upon irradiation of a flowing gaseous mixture of CH(3)OS(O)Cl in N(2) or CO(2) at 248 nm. Two intense transient features with origins near 1152 and 994 cm(-1) are assigned to syn-CH(3)OSO; the former is attributed to overlapping bands at 1154 ± 3 and 1151 ± 3 cm(-1), assigned to the S=O stretching mixed with CH(3) rocking (?(8)) and the S=O stretching mixed with CH(3) wagging (?(9)) modes, respectively, and the latter to the C-O stretching (?(10)) mode at 994 ± 6 cm(-1). Two weak bands at 2991 ± 6 and 2956 ± 3 cm(-1) are assigned as the CH(3) antisymmetric stretching (?(2)) and symmetric stretching (?(3)) modes, respectively. Observed vibrational transition wavenumbers agree satisfactorily with those predicted with quantum-chemical calculations at level B3P86?aug-cc-pVTZ. Based on rotational parameters predicted at that level, the simulated rotational contours of these bands agree satisfactorily with experimental results. The simulation indicates that the S=O stretching mode of anti-CH(3)OSO near 1164 cm(-1) likely makes a small contribution to the observed band near 1152 cm(-1). A simple kinetic model of self-reaction is employed to account for the decay of CH(3)OSO and yields a second-order rate coefficient k=(4 ± 2)×10(-10) cm(3)molecule(-1)s(-1). PMID:21384966

Chen, Jin-Dah; Lee, Yuan-Pern

2011-03-01

466

A Study of Derivative Filters Using the Discrete Fourier Transform. Final Report M. S. Thesis  

NASA Technical Reports Server (NTRS)

Important properties of derivative (difference) filters using the discrete Fourier transform are investigated. The filters are designed using the derivative theorem of Fourier analysis. Because physical data are generally degraded by noise, the derivative filter is modified to diminish the effects of the noise, especially the noise amplification which normally occurs while differencing. The basis for these modifications is the reduction of those Fourier components for which the noise most dominates the data. The various filters are tested by applying them to find differences of two-dimensional data to which various amounts of signal dependent noise, as measured by a root mean square value, have been added. The modifications, circular and square ideal low-pass filters and a cut-off pyramid filter, are all found to reduce noise in the derivative without significantly degrading the result.

Ioup, G. E.

1980-01-01

467

A fast partial Fourier transform (FPFT) for data compression and filtering.  

SciTech Connect

A discrete Fourier transform (DFT) or the closely related discrete cosine transform (DCT) is often employed as part of a data compression scheme. This paper presents a fast partial Fourier transform (FPFT) algorithm that is useful for calculating a subset of M Fourier transform coefficients for a data set comprised of N points (M < N). This algorithm reduces to the standard DFT when M = 1 and it reduces to the radix-2, decimation-in-time FFT when M = N and N is a power of 2. The DFT requires on the order of MN complex floating point multiplications to calculate M coefficients for N data points, a complete FFT requires on the order of (N/2)log{sub 2}N multiplications independent of M, and the new FPFT algorithm requires on the order of (N/2)log{sub 2}M + N multiplications. The FPFT algorithm introduced in this paper could be readily adapted to parallel processing. In addition to data compression, the FPFT algorithm described in this paper might be useful for very narrow band filter operations that pass only a small number of non-zero frequency coefficients such that M << N.

Smith, Mark William

2010-07-01

468

The velocity synchronous discrete Fourier transform for order tracking in the field of rotating machinery  

NASA Astrophysics Data System (ADS)

Diagnostics of rotating machinery has developed significantly in the last decades, and industrial applications are spreading in different sectors. Most applications are characterized by varying velocities of the shaft and in many cases transients are the most critical to monitor. In these variable speed conditions, fault symptoms are clearer in the angular/order domains than in the common time/frequency ones. In the past, this issue was often solved by synchronously sampling data by means of phase locked circuits governing the acquisition; however, thanks to the spread of cheap and powerful microprocessors, this procedure is nowadays rarer; sampling is usually performed at constant time intervals, and the conversion to the order domain is made by means of digital signal processing techniques. In the last decades different algorithms have been proposed for the extraction of an order spectrum from a signal sampled asynchronously with respect to the shaft rotational velocity; many of them (the so called computed order tracking family) use interpolation techniques to resample the signal at constant angular increments, followed by a common discrete Fourier transform to shift from the angular domain to the order domain. A less exploited family of techniques shifts directly from the time domain to the order spectrum, by means of modified Fourier transforms. This paper proposes a new transform, named velocity synchronous discrete Fourier transform, which takes advantage of the instantaneous velocity to improve the quality of its result, reaching performances that can challenge the computed order tracking.

Borghesani, P.; Pennacchi, P.; Chatterton, S.; Ricci, R.

2014-02-01

469

Fourier Transform of the Stretched Exponential Function: Analytic Error Bounds, Double Exponential Transform, and Open-Source Implementation libkww  

E-print Network

The C library \\texttt{libkww} provides functions to compute the Kohlrausch-Williams-Watts function, i.e.\\ the Laplace-Fourier transform of the stretched (or compressed) exponential function $\\exp(-t^\\beta)$ for exponents $\\beta$ between 0.1 and 1.9 with sixteen-digits accuracy. Analytic error bounds are derived for the low and high frequency series expansions. For intermediate frequencies the numeric integration is enormously accelerated by using the Ooura-Mori double exponential transformation. The source code is available from the project home page \\url{http://apps.jcns.fz-juelich.de/doku/sc/kww}.

Joachim Wuttke

2009-11-25

470

A Discussion of the Discrete Fourier Transform Execution on a Typical Desktop PC  

NASA Technical Reports Server (NTRS)

This paper will discuss and compare the execution times of three examples of the Discrete Fourier Transform (DFT). The first two examples will demonstrate the direct implementation of the algorithm. In the first example, the Fourier coefficients are generated at the execution of the DFT. In the second example, the coefficients are generated prior to execution and the DFT coefficients are indexed at execution. The last example will demonstrate the Cooley- Tukey algorithm, better known as the Fast Fourier Transform. All examples were written in C executed on a PC using a Pentium 4 running at 1.7 Ghz. As a function of N, the total complex data size, the direct implementation DFT executes, as expected at order of N2 and the FFT executes at order of N log2 N. At N=16K, there is an increase in processing time beyond what is expected. This is not caused by implementation but is a consequence of the effect that machine architecture and memory hierarchy has on implementation. This paper will include a brief overview of digital signal processing, along with a discussion of contemporary work with discrete Fourier processing.

White, Michael J.

2006-01-01

471

High-resolution Fourier transform spectrum of H 2S in the region of the second hexade  

NASA Astrophysics Data System (ADS)

High-resolution Fourier transform infrared spectrum of H232S was recorded and analyzed in the region of the second hexade v=v1+{1}/{2}v2+v3=2.5. More than 1700 transitions were assigned to the 2 ?1 + ?2, ?1 + ?2 + ?3, ?1 + 3 ?2, 3 ?2 + ?3, 5 ?2, and ?2 + 2 ?3 bands with the maximum value of quantum number J equal to 18, 18, 13, 11, 13, and 9, respectively. The theoretical analysis was fulfilled with a Hamiltonian model which takes into account numerous resonance interactions between all the vibrational states in this polyad. By a least-square fitting, finally 505 upper energy levels were reproduced by 80 parameters with an rms deviation of 0.0019 cm -1.

Ulenikov, O. N.; Liu, A.-W.; Bekhtereva, E. S.; Gromova, O. V.; Hao, L.-Y.; Hu, S.-M.

2005-12-01

472

High-resolution Fourier transform spectrum of H 2S in the region of 8500-8900 cm -1  

NASA Astrophysics Data System (ADS)

High-resolution Fourier transform infrared spectrum of H 2S was recorded and analyzed in the region of the v=v1+{1}/{2}v2+v3=3.5 polyad. More than 450 transitions were assigned to the 3 ?1 + ?2 and 2 ?1 + ?2 + ?3 bands with the maximum values of quantum numbers J and Ka equal to 14, 7, and 14, 9 for these two bands, respectively. The theoretical analysis was fulfilled with the Hamiltonian which takes into account strong resonance interactions among the studied vibrational states (3 1 0), (2 1 1), and also "dark" states (0 3 2) and (2 3 0). The rms deviation is 0.0019 cm -1. The intensity borrowing effect in the doublets in the P-branch transitions of the 3 ?1 + ?2 and 2 ?1 + ?2 + ?3 bands is observed and discussed.

Ulenikov, O. N.; Liu, A.-W.; Bekhtereva, E. S.; Grebneva, S. V.; Deng, W.-P.; Gromova, O. V.; Hu, S.-M.

2004-11-01

473

High-Resolution Fourier Transform Spectrum of D 2O in the Region Near 0.97 ?m  

NASA Astrophysics Data System (ADS)

The high-resolution Fourier transform spectrum of the D 2O molecule were recorded and analyzed in the region near 0.97 ?m (10 200-10 440 cm -1) where the bands of the v=4 ( v= v1+ v2/2+ v3) polyad are located. Transitions belonging to the strongest band of the polyad, 3? 1+? 3, are assigned up to the value of the rotational angular momentum quantum number J=13. The presence of strong local resonance interactions allowed us to assign some transitions to the very weak band 4? 1. Upper states energies obtained on that basis were fitted with a Hamiltonian model which took into account resonance interactions between the states of the v=4 polyad. The derived spectroscopic parameters reproduce the overwhelming majority of assigned transitions within experimental accuracy.

Ulenikov, O. N.; Hu, Shui-Ming; Bekhtereva, E. S.; Onopenko, G. A.; He, Sheng-Gui; Wang, Xiang-Huai; Zheng, Jing-Jing; Zhu, Qing-Shi

2001-11-01

474

High-speed spectral domain optical coherence tomography using non-uniform fast Fourier transform  

PubMed Central

The useful imaging range in spectral domain optical coherence tomography (SD-OCT) is often limited by the depth dependent sensitivity fall-off. Processing SD-OCT data with the non-uniform fast Fourier transform (NFFT) can improve the sensitivity fall-off at maximum depth by greater than 5dB concurrently with a 30 fold decrease in processing time compared to the fast Fourier transform with cubic spline interpolation method. NFFT can also improve local signal to noise ratio (SNR) and reduce image artifacts introduced in post-processing. Combined with parallel processing, NFFT is shown to have the ability to process up to 90k A-lines per second. High-speed SD-OCT imaging is demonstrated at camera-limited 100 frames per second on an ex-vivo squid eye. PMID:21258551

Chan, Kenny K. H.; Tang, Shuo

2010-01-01

475

Stress wave calculations in composite plates using the fast Fourier transform.  

NASA Technical Reports Server (NTRS)

The protection of composite turbine fan blades against impact forces has prompted the study of dynamic stresses in composites due to transient loads. The mathematical model treats the laminated plate as an equivalent anisotropic material. The use of Mindlin's approximate theory of crystal plates results in five two-dimensional stress waves. Three of the waves are flexural and two involve in-plane extensional strains. The initial value problem due to a transient distributed transverse force on the plate is solved using Laplace and Fourier transforms. A fast computer program for inverting the two-dimensional Fourier transform is used. Stress contours for various stresses and times after application of load are obtained for a graphite fiber-epoxy matrix composite plate. Results indicate that the points of maximum stress travel along the fiber directions.

Moon, F. C.

1973-01-01

476

Gaseous effluent monitoring and identification using an imaging Fourier transform spectrometer  

SciTech Connect

We are developing an imaging Fourier transform spectrometer for chemical effluent monitoring. The system consists of a 2-D infrared imaging array in the focal plane of a Michelson interferometer. Individual images are coordinated with the positioning of a moving mirror in the Michelson interferometer. A three dimensional data cube with two spatial dimensions and one interferogram dimension is then Fourier transformed to produce a hyperspectral data cube with one spectral dimension and two spatial dimensions. The spectral range of the instrument is determined by the choice of optical components and the spectral range of the focal plane array. Measurements in the near UV, visible, near IR, and mid-IR ranges are possible with the existing instrument. Gaseous effluent monitoring and identification measurements will be primarily in the ``fingerprint`` region of the spectrum, ({lambda} = 8 to 12 {mu}m). Initial measurements of effluent using this imaging interferometer in the mid-IR will be presented.

Carter, M.R.; Bennett, C.L.; Fields, D.J.; Hernandez, J.

1993-10-01

477

Fourier transform spectrometer remote sensing of O2 A-band electric quadrupole transitions  

NASA Astrophysics Data System (ADS)

We observed electric quadrupole transitions in the O2 A-band, b1?g+?X3?g-(0,0), in high solar zenith angle atmospheric spectra recorded with the high-resolution solar-viewing Fourier transform spectrometer at Park Falls, WI. We identified 12 ?N=±3 transitions for the first time, including the first detection of NO-branch transitions and extended the TS-branch observations of Brault [J Mol Spectrosc 1980;80:384-8] up to N?=23. Additionally, we observed six electric quadrupole transitions of the ?N=-1 PO-branch. These observations demonstrate the excellent sensitivity and long-term stability of the new generation of solar-viewing Fourier transform spectrometers.

Miller, Charles E.; Wunch, Debra

2012-07-01

478

Tabletop single-shot extreme ultraviolet Fourier transform holography of an extended object.  

PubMed

We demonstrate single and multi-shot Fourier transform holography with the use of a tabletop extreme ultraviolet laser. The reference wave was produced by a Fresnel zone plate with a central opening that allowed the incident beam to illuminate the sample directly. The high reference wave intensity allows for larger objects to be imaged compared to mask-based lensless Fourier transform holography techniques. We obtain a spatial resolution of 169 nm from a single laser pulse and a resolution of 128 nm from an accumulation of 20 laser pulses for an object ~11x11?m(2) in size. This experiment utilized a tabletop extreme ultraviolet laser that produces a highly coherent ~1.2 ns laser pulse at 46.9 nm wavelength. PMID:23609701

Malm, Erik B; Monserud, Nils C; Brown, Christopher G; Wachulak, Przemyslaw W; Xu, Huiwen; Balakrishnan, Ganesh; Chao, Weilun; Anderson, Erik; Marconi, Mario C

2013-04-22

479

Simulation of micromechanical behavior of polycrystals: finite elements vs. fast Fourier transforms  

SciTech Connect

In this work, we compare finite element and fast Fourier transform approaches for the prediction of micromechanical behavior of polycrystals. Both approaches are full-field approaches and use the same visco-plastic single crystal constitutive law. We investigate the texture and the heterogeneity of the inter- and intragranular, stress and strain fields obtained from the two models. Additionally, we also look into their computational performance. Two cases - rolling of aluminium and wire drawing of tungsten - are used to evaluate the predictions of the two mode1s. Results from both the models are similar, when large grain distortions do not occur in the polycrystal. The finite element simulations were found to be highly computationally intensive, in comparison to the fast Fourier transform simulations.

Lebensohn, Ricardo A [Los Alamos National Laboratory; Prakash, Arun [IWM FREIBURG

2009-01-01

480

Diffractive imaging analysis of large-aperture segmented telescope based on partial Fourier transform  

NASA Astrophysics Data System (ADS)

Large-aperture segmented primary mirror will be widely used in next-generation space-based and ground-based telescopes. The effects of intersegment gaps, obstructions, position and figure errors of segments, which are all involved in the pupil plane, on the image quality metric should be analyzed using diffractive imaging theory. Traditional Fast Fourier Transform (FFT) method is very time-consuming and costs a lot of memory especially in dealing with large pupil-sampling matrix. A Partial Fourier Transform (PFT) method is first proposed to substantially speed up the computation and reduce memory usage for diffractive imaging analysis. Diffraction effects of a 6-meter segmented mirror including 18 hexagonal segments are simulated and analyzed using PFT method. The influence of intersegment gaps and position errors of segments on Strehl ratio is quantitatively analyzed by computing the Point Spread Function (PSF). By comparing simulation results with theoretical results, the correctness and feasibility of PFT method is confirmed.

Dong, Bing; Qin, Shun; Hu, Xinqi

2013-09-01

481

Effect of the fringe visibility on spectrum SNR of Fourier transform imaging spectrometer  

NASA Astrophysics Data System (ADS)

The principle of Fourier transform spectrometer is based on the relationship of Fourier-Transform between interferogram and spectrum. The spectral information of Fourier transform imaging spectrometer (FTIS) reconstructed from raw interferogram by data processing. So there are two kinds of signal-to-noise ratio (SNR) to evaluate instrument performance, one regarding interferogram and the other regarding reconstructed spectrum. Because the raw interferogram is intuitive, the interferogram SNR is studied usually. On the contrary, the spectrum SNR is studied less because of the complexity of the data processing from interferogram to spectrum. The research about the effect of the interference fringe visibility on the spectrum SNR is especially few. This paper present a research work on the relations between the interference fringe visibility and the spectrum SNR. Firstly, the reduction of fringe visibility caused by imaging lens defocus was analyzed. Secondly, the changes of the average spectrum signal and noise caused by the reduction of fringe visibility were calculated. For average spectrum signal, the math deductions are done base on Fourier transform theory. The average noise with different input signal optic-electrons number are simulated. the results show that the average spectrum signal is directly proportional to the fringe visibility, and the effect of fringe visibility on the noise related to signal can be ignorable. Finally, In order to demonstrate above results, the imaging experiment was done with white-light source, using LASIS (Large aperture static imaging spectrometer) based on Sagnac Interferometer. The average spectrum SNRs under different fringe visibility are calculated and analyzed. The experimental results show that: the average spectrum SNRs increase from 42.7 to 62.4.along with the fringe visibility increasing from 0.5051 to 0.687. the reconstructed spectrum SNR is directly proportional to the fringe visibility. As a result, the interferogram fringe visibility can be used to estimate the reconstructed spectrum SNR, and evaluate the performance of FTIS before data processing.

Wang, Shuang; Bin, Xiangli; Jing, Juanjuan; Pi, Haifeng

2013-08-01

482

Thermogravimetric coupled with Fourier transform infrared analysis study on thermal treatment of monopotassium phosphate residue  

Microsoft Academic Search

In China, safe disposal of hazardous waste is more and more a necessity, urged by rapid economic development. The pyrolysis\\u000a and combustion characteristics of a residue from producing monopotassium phosphate (monopotassium phosphate residue), considered\\u000a as a hazardous waste, were studied using a thermogravimetric, coupled with Fourier transform infrared analyzer (TG-FTIR).\\u000a Both pyrolysis and combustion runs can be subdivided into three

Yuheng Feng; Xuguang Jiang; Yong Chi; Xiaodong Li; Hongmei Zhu

2011-01-01

483

A fluctuation-induced plasma transport diagnostic based upon fast-Fourier transform spectral analysis  

NASA Technical Reports Server (NTRS)

A diagnostic, based on fast Fourier-transform spectral analysis techniques, that provides experimental insight into the relationship between the experimentally observable spectral characteristics of the fluctuations and the fluctuation-induced plasma transport is described. The model upon which the diagnostic technique is based and its experimental implementation is discussed. Some characteristic results obtained during the course of an experimental study of fluctuation-induced transport in the electric field dominated NASA Lewis bumpy torus plasma are presented.

Powers, E. J.; Kim, Y. C.; Hong, J. Y.; Roth, J. R.; Krawczonek, W. M.

1978-01-01

484

A low-complexity architecture of inverse fast Fourier transform for XDS  

Microsoft Academic Search

In this work, a low-complexity architecture of the inverse fast Fourier transform (IFFT) using the serial-input-parallel-output data flow is designed for digital subscriber line for any class (XDSL). Since input data in the XDSL are symmetric, the computation of the IFFT can be reduced to multiplication accumulation operations in the real part. Furthermore, consideration is taken to process all multiplication

Hsin-Horng Chen; O. T.-C. Chen; Heng-Cheng Yeh; Cheng-Shing Wu

2004-01-01

485

Monitoring the oxidation of edible oils by Fourier transform infrared spectroscopy  

Microsoft Academic Search

Edible fats and oils in their neat form are ideal candidates for Fourier transform infrared (FTIR) analysis, in either the\\u000a attenuated total reflectance or the transmission mode. FTIR spectroscopy provides a simple and rapid means of following complex\\u000a changes that take place as lipids oxidize. Safflower and cottonseed oils were oxidized under various conditions, and their\\u000a spectral changes were recorded

F. R. van de Voort; A. A. Ismail; J. Sedman; G. Emo

1994-01-01

486

Rapid quantitative determination of free fatty acids in fats and oils by fourier transform infrared spectroscopy  

Microsoft Academic Search

Rapid direct and indirect Fourier transform infrared (FTIR) spectroscopic methods were developed for the determination of\\u000a free fatty acids (FFA) in fats and oils based on both transmission and attenuated total reflectance approaches, covering an\\u000a analytical range of 0.2–8% FFA. Calibration curves were prepared by adding oleic acid to the oil chosen for analysis and measuring\\u000a the C=O band @

A. A. Ismail; F. R. van de Voort; G. Emo; J. Sedman

1993-01-01

487

Data processing pipeline for a time-sampled imaging Fourier transform spectrometer  

Microsoft Academic Search

ABSTRACT Imaging Fourier transform spectrometers ,(IFTS) are becoming ,the preferred systems ,for remote ,sensing spectral imaging applications because of their ability to provide, simultaneously, both high spatial and spectral resolution images ofa scene. IFTS can be operated in either step-and-integrate or rapid-scan modes, where it is common practice to sample interferograms at equal optical path difference intervals. The step-and-integrate mode

David A. Naylor; Trevor R. Fulton; Peter W. Davis; Ian M. Chapman; Brad G. Gom; D Locke; John V. Lindner; Nathan E. Nelson-fitzpatrick; Margaret K. Tahic; Gary R. Davis

488

Estimation of the magnitude-squared coherence function via overlapped fast Fourier transform processing  

Microsoft Academic Search

A method for estimating the magnitude-squared coherence function for two zero-mean wide-sense-stationary random processes is presented. The estimation technique utilizes the weighted overlapped segmentation fast Fourier transform approach. Analytical and empirical results for statistics of the estimator are presented. The analytical expressions are limited to the nonoverlapped case; empirical results show a decrease in bias and variance of the estimator

G. CLIFFORD CARTER; CHARLES H. KNAPP; ALBERT H. NUTTALL

1973-01-01

489

Implementation of the digital phase vocoder using the fast Fourier transform  

Microsoft Academic Search

This paper discusses a digital formulation of the phase vocoder, an analysis-synthesis system providing a parametric representation of a speech waveform by its short-time Fourier transform. Such a system is of interest both for data-rate reduction and for manipulating basic speech parameters. The system is designed to be an identity system in the absence of any parameter modifications. Computational efficiency

M. Portnoff

1976-01-01

490

Fourier-transform Raman spectroscopic study of natural waxes and resins. I  

NASA Astrophysics Data System (ADS)

The Fourier transform-Raman spectra of some natural waxes and resins that have been found in preparations of archaeological material have been identified non-destructively. Vibrational assignments are proposed which assist in the identification of the materials used; in one case, a sample of paper impregnated with a wax component, the presence of beeswax was identified. This work forms part of a programme for the characterisation of natural materials, which is addressed in their conservation and preservation.

Edwards, H. G. M.; Farwell, D. W.; Daffner, L.

1996-11-01

491

Using single buffers and data reorganization to implement a multi-megasample fast Fourier transform  

NASA Technical Reports Server (NTRS)

Data ordering in large fast Fourier transforms (FFT's) is both conceptually and implementationally difficult. Discribed here is a method of visualizing data orderings as vectors of address bits, which enables the engineer to use more efficient data orderings and reduce double-buffer memory designs. Also detailed are the difficulties and algorithmic solutions involved in FFT lengths up to 4 megasamples (Msamples) and sample rates up to 80 MHz.

Brown, R. D.

1992-01-01

492

FourierTransform Infrared Spectroscopy Studies of the Interaction of Functionalized Siloxane Polymers with Porous Silica  

Microsoft Academic Search

Adsorption behavior of the siloxane polymer, cyanopropylmethyl-phenyl-methyl-siloxane, in contact with a mesoporous silica has been investigated by Fourier-transform infrared spectroscopy (FT-IR) using a series of physically modified materials with different coating levels up to 20 w\\/w%. The nitrile stretch bands, which are observed in the 2150–2350 cm1 range, exhibited complex profiles due to a variety of interactions of the cyano

Anima Bose; Roger K. Gilpin; Mietek Jaroniec

2000-01-01

493

Fast wave-front reconstruction in large adaptive optics systems with use of the Fourier transform  

Microsoft Academic Search

Wave-front reconstruction with the use of the fast Fourier transform (FFT) and spatial filtering is shown to be computationally tractable and sufficiently accurate for use in large Shack-Hartmann-based adaptive optics systems (up to at least 10,000 actuators). This method is significantly faster than, and can have noise propa- gation comparable with that of, traditional vector-matrix-multiply reconstructors. The boundary problem that

Lisa A. Poyneer; Donald T. Gavel; James M. Brase

2002-01-01

494

Open-path Fourier transform infrared spectrometry characterization of low temperature combustion gases in biomass fuels  

Microsoft Academic Search

Accurate determination of gas concentration emitted during thermal degradation (pyrolysis) of biomass in forest fires is one of the keypoints in recent research on physical-based fire spread models. However, it is a very cumbersome task not well solved by classical invasive sensors and procedures. In this work, a methodology to use open-path Fourier transform-based infrared (OP-FTIR) spectrometry has been applied

A. J. de Castro; A. M. Lerma; F. López; M. Guijarro; C. Díez; C. Hernando; J. Madrigal

2007-01-01

495

Open-path Fourier transform infrared studies of large-scale laboratory biomass fires  

Microsoft Academic Search

A series of nine large-scale, open fires was conducted in the Intermountain Fire Sciences Laboratory (IFSL) controlled-environment combustion facility. The fuels were pure pine needles or sagebrush or mixed fuels simulating forest-floor, ground fires; crown fires; broadcast burns; and slash pile burns. Mid-infrared spectra of the smoke were recorded throughout each fire by open path Fourier transform infrared (FTIR) spectroscopy

Robert J. Yokelson; David W. T. Griffith; Darold E. Ward

1996-01-01

496

Accurate determination of the hydrogen concentration of silicon nitride layers by Fourier transform spectroscopy  

Microsoft Academic Search

In this study, we present a very accurate method of determining the hydrogen concentration of amorphous silicon nitride (SiN) layers by employing Fourier Transform IR Spectroscopy (FTIR). Our method comprises a very effective means of rapid and non-destructive in-line monitoring and quality control for the semiconductor industry. Amorphous SiN layers are essential for the semiconductor industry as an encapsulant for

Ingrid Jonak-Auer; Friedemar Kuchar

1998-01-01

497

An Imaging Fourier Transform Spectrometer for the Next Generation Space Telescope  

E-print Network

Due to its simultaneous deep imaging and integral field spectroscopic capability, an Imaging Fourier Transform Spectrograph (IFTS) is ideally suited to the Next Generation Space Telescope (NGST) mission, and offers opportunities for tremendous scientific return in many fields of astrophysical inquiry. We describe the operation and quantify the advantages of an IFTS for space applications. The conceptual design of the Integral Field Infrared Spectrograph (IFIRS) is a wide field (5'.3 x 5'.3) four-port imaging Michelson interferometer.

James R. Graham

1999-10-25

498

Estimation of phase derivatives using discrete chirp-Fourier-transform-based method.  

PubMed

Estimation of phase derivatives is an important task in many interferometric measurements in optical metrology. This Letter introduces a method based on discrete chirp-Fourier transform for accurate and direct estimation of phase derivatives, even in the presence of noise. The method is introduced in the context of the analysis of reconstructed interference fields in digital holographic interferometry. We present simulation and experimental results demonstrating the utility of the proposed method. PMID:19684794

Gorthi, Sai Siva; Rastogi, Pramod

2009-08-15

499

In-orbit performance of the Herschel/SPIRE imaging Fourier transform spectrometer  

NASA Astrophysics Data System (ADS)

The Spectral and Photometric Imaging Receiver (SPIRE) is one of three scientific instruments onboard the European Space Agency's Herschel Space Observatory launched on 14 May 2009. The low to medium resolution spectroscopic capability of SPIRE is provided by an imaging Fourier transform spectrometer of the Mach-Zehnder configuration. Results from the in flight performance verification phase of the SPIRE spectrometer are presented and conformance with the instrument design specifications is reviewed.

Naylor, David A.; Baluteau, Jean-Paul; Barlow, Mike J.; Benielli, Dominique; Ferlet, Marc; Fulton, Trevor R.; Griffin, Matthew J.; Grundy, Timothy; Imhof, Peter; Jones, Scott; King, Ken; Leeks, Sarah J.; Lim, Tanya L.; Lu, Nanyao; Makiwa, Gibion; Polehampton, Edward T.; Savini, Giorgio; Sidher, Sunil D.; Spencer, Locke D.; Surace, Christian; Swinyard, Bruce M.; Wesson, Roger

2010-07-01

500

A reconstruction technique for three-dimensional porous media using image analysis and Fourier transforms  

Microsoft Academic Search

A truncated gaussian method based on Fourier transforms is proposed to generate periodic 3D porous structure from a 2D image of the sample. This technique improves a previous method developed by Quiblier [Quiblier, J.A., 1984. A new three-dimensional modeling technique for studying porous media. J. Colloid Interface Sci 98, 84–102] and Adler et al. [Adler, P.M., Jacquin, C.G., Quiblier, J.A.,

Z. R. Liang; C. P. Fernandes; F. S. Magnani; P. C. Philippi

1998-01-01