NASA Astrophysics Data System (ADS)
Chang, Chun; Huang, Benxiong; Xu, Zhengguang; Li, Bin
2015-12-01
A partial-response-pulse-shaped 16-ary quadrature amplitude modulation (16QAM) format called quadrature duoquaternary (QDQ) modulation, which can achieve higher spectral efficiency than Nyquist-pulse-shaped 16QAM and realize super-Nyquist wavelength-division-multiplexing (WDM) transmission, is proposed. The dual-polarized QDQ (DP-QDQ) modulation principle and coherent reception based on digital signal processing (DSP) are presented. The performance of the DP-QDQ scheme is investigated in 32-GBaud super-Nyquist-WDM systems by simulation. The simulation results show that DP-QDQ has only a 1.3 dB optical-signal-to-noise-ratio (OSNR) penalty for the 28-GHz-spaced 5-channel super-Nyquist-WDM case relative to the single-channel case. Compared with Nyquist-pulse-shaped 16QAM, DP-QDQ not only has a higher spectral efficiency, but also a lower sensitivity to sampling time error and a better dispersion tolerance. The 28-GHz-spaced 5-channel super-Nyquist-WDM DP-QDQ system can successfully implement 1520-km transmission at the forward-error-correction (FEC) bit-error-rate (BER) requirements.
NASA Technical Reports Server (NTRS)
Fines, P.; Aghvami, A. H.
1990-01-01
The performance of a low bit rate (64 Kb/s) all digital 16-ary Differentially Encoded Quadrature Amplitude Modulation (16-DEQAM) demodulator operating over a mobile satellite channel, is considered. The synchronization and detection techniques employed to overcome the Rician channel impairments, are described. The acquisition and steady state performance of this modem, are evaluated by computer simulation over AWGN and RICIAN channels. The results verify the suitability of the 16-DEQAM transmission over slowly faded and/or mildly faded channels.
Development of a coded 16-ary CPFSK coherent demodulator
NASA Technical Reports Server (NTRS)
Clarke, Ken; Davis, Robert; Roesch, Jim
1988-01-01
Theory and hardware are described for a proof-of-concept 16-ary continuous phase frequency shift keying (16-CPFSK) digital modem. The 16 frequencies are spaced every 1/16th baud rate for 2 bits/sec/Hz operation. Overall rate 3/4 convolutional coding is incorporated. The demodulator differs significantly from typical quadrature phase detector approaches in that phase is coherently measured by processing the baseband output of a frequency discriminator. Baud rate phase samples from the baseband processor are decoded to yield the original data stream. The method of encoding onto the 16-ary phase nodes, together with convolutional coding gain, results in near quad PSK (QPSK) performance. The modulated signal is of constant envelope; thus the power amplifier can be saturated for peak performance. The spectrum is inherently bandlimited and requires no RF filter.
Double-Referential Holography and Spatial Quadrature Amplitude Modulation
NASA Astrophysics Data System (ADS)
Zukeran, Keisuke; Okamoto, Atsushi; Takabayashi, Masanori; Shibukawa, Atsushi; Sato, Kunihiro; Tomita, Akihisa
2013-09-01
We proposed a double-referential holography (DRH) that allows phase-detection without external additional beams. In the DRH, phantom beams, prepared in the same optical path as signal beams and preliminary multiplexed in a recording medium along with the signal, are used to produce interference fringes on an imager for converting a phase into an intensity distribution. The DRH enables stable and high-accuracy phase detection independent of the fluctuations and vibrations of the optical system owing to medium shift and temperature variation. Besides, the collinear arrangement of the signal and phantom beams leads to the compactness of the optical data storage system. We conducted an experiment using binary phase modulation signals for verifying the DRH operation. In addition, 38-level spatial quadrature amplitude modulation signals were successfully reproduced with the DRH by numerical simulation. Furthermore, we verified that the distributed phase-shifting method moderates the dynamic range consumption for the exposure of phantom beams.
Modulator-free quadrature amplitude modulation signal synthesis
NASA Astrophysics Data System (ADS)
Liu, Zhixin; Kakande, Joseph; Kelly, Brian; O'Carroll, John; Phelan, Richard; Richardson, David J.; Slavík, Radan
2014-12-01
The ability to generate high-speed on-off-keyed telecommunication signals by directly modulating a semiconductor laser’s drive current was one of the most exciting prospective applications of the nascent field of laser technology throughout the 1960s. Three decades of progress led to the commercialization of 2.5 Gbit s-1-per-channel submarine fibre optic systems that drove the growth of the internet as a global phenomenon. However, the detrimental frequency chirp associated with direct modulation forced industry to use external electro-optic modulators to deliver the next generation of on-off-keyed 10 Gbit s-1 systems and is absolutely prohibitive for today’s (>)100 Gbit s-1 coherent systems, which use complex modulation formats (for example, quadrature amplitude modulation). Here we use optical injection locking of directly modulated semiconductor lasers to generate complex modulation format signals showing distinct advantages over current and other currently researched solutions.
Modulator-free quadrature amplitude modulation signal synthesis
Liu, Zhixin; Kakande, Joseph; Kelly, Brian; O’Carroll, John; Phelan, Richard; Richardson, David J.; Slavík, Radan
2014-01-01
The ability to generate high-speed on–off-keyed telecommunication signals by directly modulating a semiconductor laser’s drive current was one of the most exciting prospective applications of the nascent field of laser technology throughout the 1960s. Three decades of progress led to the commercialization of 2.5 Gbit s−1-per-channel submarine fibre optic systems that drove the growth of the internet as a global phenomenon. However, the detrimental frequency chirp associated with direct modulation forced industry to use external electro-optic modulators to deliver the next generation of on–off-keyed 10 Gbit s−1 systems and is absolutely prohibitive for today’s (>)100 Gbit s−1 coherent systems, which use complex modulation formats (for example, quadrature amplitude modulation). Here we use optical injection locking of directly modulated semiconductor lasers to generate complex modulation format signals showing distinct advantages over current and other currently researched solutions. PMID:25523757
A Simple Approximation for the Symbol Error Rate of Triangular Quadrature Amplitude Modulation
NASA Astrophysics Data System (ADS)
Duy, Tran Trung; Kong, Hyung Yun
In this paper, we consider the error performance of the regular triangular quadrature amplitude modulation (TQAM). In particular, using an accurate exponential bound of the complementary error function, we derive a simple approximation for the average symbol error rate (SER) of TQAM over Additive White Gaussian Noise (AWGN) and fading channels. The accuracy of our approach is verified by some simulation results.
Schrenk, Bernhard; Dris, Stefanos; Bakopoulos, Paraskevas; Lazarou, Ioannis; Voigt, Karsten; Zimmermann, Lars; Avramopoulos, Hercules
2012-08-01
Optical quadrature amplitude modulation (QAM) is experimentally demonstrated with a low-complexity modulator based on a semiconductor optical amplifier and electroabsorption modulator. Flexible amplitude/phase format transmission is achieved. The applicability of octary QAM for coherent optical access networks with sustainable 3 Gb/s per-user bandwidth is investigated for a long reach of 100 km, and its compatibility with a potentially high split is verified. PMID:22859139
NASA Technical Reports Server (NTRS)
Dobson, Chris C.; Jones, Jonathan E.; Chavers, Greg
2003-01-01
A polychromatic microwave quadrature interferometer has been characterized using several laboratory plasmas. Reflections between the transmitter and the receiver have been observed, and the effects of including reflection terms in the data reduction equation have been examined. An error analysis which includes the reflections, modulation of the scene beam amplitude by the plasma, and simultaneous measurements at two frequencies has been applied to the empirical database, and the results are summarized. For reflection amplitudes around 1096, the reflection terms were found to reduce the calculated error bars for electron density measurements by about a factor of 2. The impact of amplitude modulation is also quantified. In the complete analysis, the mean error bar for high- density measurements is 7.596, and the mean phase shift error for low-density measurements is 1.2". .
Performance of a Coded Non-Square Quadrature Amplitude Modulation Scheme over Fading Channels
NASA Astrophysics Data System (ADS)
Li, L.; Divsalar, D.; Dolinar, S.
2004-02-01
It is shown that a non-square (NS) 2^(2n+1)-ary quadrature amplitude modulation (QAM) can be decomposed into a single-parity-check (SPC) block encoder and a memoryless modulator with independent in-phase (I) and quadrature (Q) symbol mapping. When NS-2^(2n+1)-QAM is concatenated with a forward-error-correcting (FEC) code, iterative demodulation and decoding of the FEC code and the inherent SPC code of NS-2^(2n+1)-QAM exploits the modulation's inherent memory and its independent I- and Q-channel mapping and demapping. The capacity and the bit-/symbol-error-rate (BER/SER) performance of coded and uncoded NS-2^(2n+1)-QAM systems are given for both additive white Gaussian noise (AWGN) channels and Rayleigh fading channels and are compared to those of other conventional 2^(2n+1)-ary systems. Simulation results show that, with iterative demodulation and decoding, coded NS-8QAM outperforms three conventional 8-ary systems by at least 0.65 dB on AWGN channels and by at least 0.57 dB on Rayleigh fading channels at BER = 10^(-5), when the FEC code is a concatenation of (15,11) Hamming codes with rate-1 accumulator codes, while coded NS-32QAM outperforms standard 32QAM by about 0.45 dB on AWGN channels and by about 0.27 dB on Rayleigh fading channels.
Khaleghi, Salman; Chitgarha, Mohammad Reza; Yilmaz, Omer F; Tur, Moshe; Haney, Michael W; Langrock, Carsten; Fejer, Martin M; Willner, Alan E
2013-05-15
We experimentally demonstrate a reconfigurable optical converter/encoder for quadrature amplitude modulated (QAM) signals. The system utilizes nonlinear wavelength multicasting, conversion-dispersion delays, and simultaneous nonlinear multiplexing and sampling. We show baud rate tunability (31 and 20 Gbaud) and reconfigurable conversions from lower-order QAM signals to higher-order QAM signals (e.g., 64-QAM). PMID:23938882
Digital services using quadrature amplitude modulation (QAM) over CATV analog DWDM system
NASA Astrophysics Data System (ADS)
Yeh, JengRong; Selker, Mark D.; Trail, J.; Piehler, David; Levi, Israel
2000-04-01
Dense Wavelength Division Multiplexing (DWDM) has recently gained great popularity as it provides a cost effective way to increase the transmission capacity of the existing fiber cable plant. For a long time, Dense WDM was exclusively used for baseband digital applications, predominantly in terrestrial long haul networks and in some cases in metropolitan and enterprise networks. Recently, the performance of DWDM components and frequency-stabilized lasers has substantially improved while the costs have down significantly. This makes a variety of new optical network architectures economically viable. The first commercial 8- wavelength DWDM system designed for Hybrid Fiber Coax networks was reported in 1998. This type of DWDM system utilizes Sub-Carrier Multiplexing (SCM) of Quadrature Amplitude Modulated (QAM) signals to transport IP data digital video broadcast and Video on Demand on ITU grid lightwave carriers. The ability of DWDM to provide scalable transmission capacity in the optical layer with SCM granularity is now considered by many to be the most promising technology for future transport and distribution of broadband multimedia services.
NASA Technical Reports Server (NTRS)
Cao, Chang-Qi
1996-01-01
The amplitude and transverse quadrature component squeezing of coherent light in high Q cavity by injection of atoms of two-photon transition are studied. The Golubev-Sokolov master equation and generating function approach are utilized to derive the exact variances of photon number and of transverse quadrature component as function of t. The correlation functions and power spectrums of photon number noise and of output photon current noise are also investigated.
Symbol rate identification for auxiliary amplitude modulation optical signal
NASA Astrophysics Data System (ADS)
Wei, Junyu; Dong, Zhi; Huang, Zhiping; Zhang, Yimeng
2016-09-01
In this paper, we creatively propose and demonstrate a method for symbol rate identification (SRI) of auxiliary amplitude modulation (AAM) optical signal based on asynchronous delay-tap sampling (ADTS) and average magnitude difference function (AMDF). The method can accurately estimate symbol rate and has large transmission impairments tolerance. Furthermore, it can be realized in the digital signal processor (DSP) with low logical resources because of multiplication-free. In order to improve the accuracy of SRI, the peak to valley ratio (PTVR) of AMDF is introduced into our method for blind chromatic dispersion (CD) compensation. The results of the numerical simulations show that the overall maximum SRI error is smaller 0.079% for return-to-zero (RZ) on-off keying (OOK), RZ differential phase-shift keying (DPSK), RZ differential quadrature phase-shift keying (DQPSK) and RZ 16-ary quadrature amplitude modulation (QAM) with 50% duty cycles.
Yue, Yang; Zhang, Bo; Wang, Qiang; Lofland, Rob; O'Neil, Jason; Anderson, Jon
2016-03-21
Dual-polarization quadrature amplitude modulation (DP-QAM) is one of the feasible paths towards 100-Gb/s, 400-Gb/s and 1-Tb/s optical fiber communications systems. For DP-QAM transmitter, the time mismatch between the in-phase and quadrature (IQ) or x-polarized and y-polarized (XY) tributary channels is known as the IQ or XY skew. Large uncompensated IQ or XY skew can significantly degrade the optical fiber communications system performance. Sometimes, time-interleaved return-to-zero (RZ) DP signal is preferred with lower nonlinear polarization scattering induced penalty. In this work, detection and alignment of DP-QAM transmitter IQ and XY skews using reconfigurable interference is experimentally demonstrated. For IQ skew detection, a total dynamic range of 26.4 dB is achieved with ~1-dB power change for 0.5-ps skew from well alignment. For XY skew detection, it shows 23.2-dB dynamic range, and ~1.5-dB power change is achieved for 1-ps XY skew. Fast detection algorithm for arbitrary skew is also proposed and experimentally verified. The scheme is compatible with different modulation formats, flexible data sequences, and variable waveforms. PMID:27136859
Quadrature amplitude modulation (QAM) using binary-driven coupling-modulated rings
NASA Astrophysics Data System (ADS)
Karimelahi, Samira; Sheikholeslami, Ali
2016-05-01
We propose and fully analyze a compact structure for DAC-free pure optical QAM modulation. The proposed structure is the first ring resonator-based DAC-free QAM modulator reported in the literature, to the best of our knowledge. The device consists of two segmented add-drop Mach Zehnder interferometer-assisted ring modulators (MZIARM) in an IQ configuration. The proposed architecture is investigated based on the parameters from SOI technology where various key design considerations are discussed. We have included the loss in the MZI arms in our analysis of phase and amplitude modulation using MZIARM for the first time and show that the imbalanced loss results in a phase error. The output level linearity is also studied for both QAM-16 and QAM-64 not only based on optimizing RF segment lengths but also by optimizing the number of segments. In QAM-16, linearity among levels is achievable with two segments while in QAM-64 an additional segment may be required.
NASA Technical Reports Server (NTRS)
Kifle, Muli; Vanderaar, Mark
1994-01-01
Union bounds and Monte Carlo simulation Bit-Error-Rate (BER) performance results are presented for various 32-ary and 64-ary Quadrature Amplitude Modulation (QAM) schemes. Filtered and unfiltered modulation formats are compared for the best packing arrangement in peak power limited systems. It is verified that circular constellations which populate as many symbols as possible at the peak magnitude offer the best performance. For example: a 32-ary QAM scheme based on concentric circles offers about 1.05 dB better peak power improvement at a BER of 10(exp -6) over the scheme optimized for average power using triangular symbol packing. This peak power improvement increases to 1.25 dB for comparable 64-ary QAM schemes. This work serves as a precursor to determine the feasibility of a combined modem/codec that can accommodate Broadband Integrated Services Digital Network (B-ISDN) at a rate of 155.52 Mbps through typical transponder bandwidths of 36 MHz and 54 MHz.
Quadrature Mixer LO Leakage Suppression Through Quadrature DC Bias
BALDWIN, JESSE G; DUBBERT, DALE F.
2002-05-01
A new concept has been developed which allows direct-to-RF conversion of digitally synthesized waveforms. The concept named Quadrature Error Corrected Digital Waveform Synthesis (QECDWS) employs quadrature amplitude and phase predistortion to the complex waveform to reduce the undesirable quadrature image. Another undesirable product of QECDWS-based RF conversion is the Local Oscillator (LO) leakage through the quadrature upconverter (mixer). A common technique for reducing this LO leakage is to apply a quadrature bias to the mixer I and Q inputs. This report analyzes this technique through theory, lab measurement, and data analysis for a candidate quadrature mixer for Synthetic Aperture Radar (SAR) applications.
Ishimura, Shota; Kikuchi, Kazuro
2015-03-01
We apply the eight-state trellis-coded modulation (TCM) using signal constellations of four-dimensional M-ary quadrature-amplitude modulation (4D-MQAM) to optical communication systems for the first time to our knowledge. In the TCM scheme, the free distance of the trellis diagram is equal to the minimum distance between constellation points in partitioned subsets, which enlarges the coding gain effectively. In fact, its asymptotic power efficiency is 3-dB larger than that of the set-partitioned 4D-MQAM (SP-4D-MQAM) format, while their spectral efficiencies are the same. Such theoretical predictions are confirmed through computer simulations on eight-state TCM with constellations of 4D-4QAM (i.e., 4D quadrature phase-shift keying: 4D-QPSK) and 4D-16QAM. In particular, eight-state TCM with 4D-QPSK constellations is practically important because of its simple encoder structure, relatively low computational cost, and high coding gain against dual-polarization QPSK (DP-QPSK) and SP-4D-QPSK. Through measurements of its bit-error rate (BER) performance, we confirm that the coding gain against DP-QPSK is about 3 dB at BER=10(-3). PMID:25836886
Receiver Architecture for 12.5 Gb/s 16-ary Pulse Position Modulation (PPM) Signaling
Mendez, A J; Gagliardi, R M; Hernandez, V J; Bennett, C V
2008-07-11
PPM is a signaling scheme that enables the transmission of multiple bits per symbol [1]. It has found favor in the regime of free space optical communications ('FSO' or 'Lasercom'); however, PPM has yet to be widely applied to fiber optic-based communications. Its limitation in fiber results from the exceedingly high bandwidth requirements needed to electronically process a directly detected pulse, especially as the symbol rate increases and the pulse width correspondingly decreases. As a solution, we introduced the concept of a virtual quadrant receiver for receiving 1.25 Gb/s 4-ary PPM, where photonic processing reduced the number of required electronic components [2]. In this paper, we extend these photonic process techniques to a 16-ary, 12.5 Gb/s (10 Gb/s plus 8B/10B line coding) PPM communications system for fiber optic avionics, wherein much of the receiver processing is enabled by techniques based on planar lightwave circuits (PLCs). The architecture is applicable to higher input data rates and M-ary PPM. In the following, we present the PPM encoding and decoding architectures and numerically simulated results.
NASA Astrophysics Data System (ADS)
Wang, Jin; Cao, Yongsheng; Chen, Fushen
2015-01-01
We present the performance analysis of a spectral amplitude code labeled system with 100 Gb/s polarization division multiplexed (PDM) differential quadrature phase shift keying payload in simulation. Direct detection is chosen to demodulate the PDM payload by applying a polarization tracker, while 4-bits of the 156 Mb/s spectral amplitude code label is coherently detected with a scheme of frequency-swept coherent detection. We optimize the payload laser linewidth as well as the frequency spacing between the payload and label. For back-to-back system and 96 km transmission, label eye opening factors are 0.95 and 0.94, respectively, while payload optical signal-to-noise ratios are 20.6 dB and 22.0 dB, and the payload received optical powers are -15.0 dBm and -14.5 dBm for a bit error rate value of 10-9. The results show that both the payload and label have good transmission performances after long-haul transmission in a standard single mode fiber and dispersion compensating fiber, and the payload could be well demodulated after 288 km transmission.
NASA Astrophysics Data System (ADS)
Kikuchi, Nobuhiko
2005-11-01
The optical multilevel modulation is one of the attractive candidates to significantly increase the channel bit rate and total capacity of future optical fiber communications. We review various multilevel modulation schemes proposed to date, including our experimental results of the 8-level and 16-level APSK modulation/demodulation schemes at 10 Gsymbol/s. We also discuss the advantages and disadvantages, and future issues of the optical multilevel modulation schemes.
Positive quadrature formulas III
NASA Astrophysics Data System (ADS)
Peherstorfer, Franz
2008-12-01
First we discuss briefly our former characterization theorem for positive interpolation quadrature formulas (abbreviated qf), provide an equivalent characterization in terms of Jacobi matrices, and give links and applications to other qf, in particular to Gauss-Kronrod quadratures and recent rediscoveries. Then for any polynomial t_n which generates a positive qf, a weight function (depending on n ) is given with respect to which t_n is orthogonal to mathbb{P}_{n-1} . With the help of this result an asymptotic representation of the quadrature weights is derived. In general the asymptotic behaviour is different from that of the Gaussian weights. Only under additional conditions do the quadrature weights satisfy the so-called circle law. Corresponding results are obtained for positive qf of Radau and Lobatto type.
Buchenauer, C.J.
1981-09-23
The quadrature phase angle phi (t) of a pair of quadrature signals S/sub 1/(t) and S/sub 2/(t) is digitally encoded on a real time basis by a quadrature digitizer for fractional phi (t) rotational excursions and by a quadrature up/down counter for full phi (t) rotations. The pair of quadrature signals are of the form S/sub 1/(t) = k(t) sin phi (t) and S/sub 2/(t) = k(t) cos phi (t) where k(t) is a signal common to both. The quadrature digitizer and the quadrature up/down counter may be used together or singularly as desired or required. Optionally, a digital-to-analog converter may follow the outputs of the quadrature digitizer and the quadrature up/down counter to provide an analog signal output of the quadrature phase angle phi (t).
Buchenauer, C. Jerald
1984-01-01
The quadrature phase angle .phi.(t) of a pair of quadrature signals S.sub.1 (t) and S.sub.2 (t) is digitally encoded on a real time basis by a quadrature digitizer for fractional .phi.(t) rotational excursions and by a quadrature up/down counter for full .phi.(t) rotations. The pair of quadrature signals are of the form S.sub.1 (t)=k(t) sin .phi.(t) and S.sub.2 (t)=k(t) cos .phi.(t) where k(t) is a signal common to both. The quadrature digitizer and the quadrature up/down counter may be used together or singularly as desired or required. Optionally, a digital-to-analog converter may follow the outputs of the quadrature digitizer and the quadrature up/down counter to provide an analog signal output of the quadrature phase angle .phi.(t).
Quadrature wavelength scanning interferometry.
Moschetti, Giuseppe; Forbes, Alistair; Leach, Richard K; Jiang, Xiang; O'Connor, Daniel
2016-07-10
A novel method to double the measurement range of wavelength scanning interferometery (WSI) is described. In WSI the measured optical path difference (OPD) is affected by a sign ambiguity, that is, from an interference signal it is not possible to distinguish whether the OPD is positive or negative. The sign ambiguity can be resolved by measuring an interference signal in quadrature. A method to obtain a quadrature interference signal for WSI is described, and a theoretical analysis of the advantages is reported. Simulations of the advantages of the technique and of signal errors due to nonideal quadrature are discussed. The analysis and simulation are supported by experimental measurements to show the improved performances. PMID:27409307
NASA Astrophysics Data System (ADS)
Monien, H.
2010-04-01
Gaussian quadrature is a well-known technique for numerical integration. Recently Gaussian quadrature with respect to discrete measures corresponding to finite sums has found some new interest. In this paper we apply these ideas to infinite sums in general and give an explicit construction for the weights and abscissae of Gaussian formulas. The abscissae of the Gaussian summation have a very interesting asymptotic distribution function with a kink singularity. We apply the Gaussian summation technique to two problems which have been discussed in the literature. We find that the Gaussian summation has a very rapid convergence rate for the Hardy-Littlewood sum for a large range of parameters.
Quadrature, Interpolation and Observability
NASA Technical Reports Server (NTRS)
Hodges, Lucille McDaniel
1997-01-01
Methods of interpolation and quadrature have been used for over 300 years. Improvements in the techniques have been made by many, most notably by Gauss, whose technique applied to polynomials is referred to as Gaussian Quadrature. Stieltjes extended Gauss's method to certain non-polynomial functions as early as 1884. Conditions that guarantee the existence of quadrature formulas for certain collections of functions were studied by Tchebycheff, and his work was extended by others. Today, a class of functions which satisfies these conditions is called a Tchebycheff System. This thesis contains the definition of a Tchebycheff System, along with the theorems, proofs, and definitions necessary to guarantee the existence of quadrature formulas for such systems. Solutions of discretely observable linear control systems are of particular interest, and observability with respect to a given output function is defined. The output function is written as a linear combination of a collection of orthonormal functions. Orthonormal functions are defined, and their properties are discussed. The technique for evaluating the coefficients in the output function involves evaluating the definite integral of functions which can be shown to form a Tchebycheff system. Therefore, quadrature formulas for these integrals exist, and in many cases are known. The technique given is useful in cases where the method of direct calculation is unstable. The condition number of a matrix is defined and shown to be an indication of the the degree to which perturbations in data affect the accuracy of the solution. In special cases, the number of data points required for direct calculation is the same as the number required by the method presented in this thesis. But the method is shown to require more data points in other cases. A lower bound for the number of data points required is given.
Optically controlled quadrature coupler on silicon substrate
NASA Astrophysics Data System (ADS)
Bhadauria, Avanish; Sharma, Sonia; Sonania, Shikha; Akhtar, Jamil
2016-03-01
In this paper, we have proposed and studied an optically controlled quadrature coupler fabricated on silicon substrate. The optically controlled quadrature coupler can be realized by terminating its coupled or through ports by optically induced load. Simulation and experimental results show that by varying optical intensity, we can control the phase and amplitude of output RF signal and can realize optically controlled reflection type attenuator, reflection type phase-shifter and ultrafast switches. The new kind of proposed device can be useful for ultra-fast signal processing and modulation schemes in high speed communication especially in QPSK modulation. The optical control has several advantages over conventional techniques such as MEMS and other semiconductor switching, which have several inherent disadvantages and limitations like low response time, low power handling capacity, device parasitic and non-linearity.
NASA Astrophysics Data System (ADS)
Yeh, Chien-Hung; Chen, Hsing-Yu; Chow, Chi-Wai; Wu, Yu-Fu
2012-01-01
We use a commercially available 1.2 GHz bandwidth reflective semiconductor optical amplifier (RSOA)--based optical network unit (ONU) to achieve 10-gbits/s upstream traffic for an optical orthogonal frequency division multiplexing (OFDM) long-reach passive optical network (LR-PON). This is the first time the 64--quadrature amplitude modulation (QAM) OFDM format has been applied to RSOA-ONU to achieve a 75 km fiber transmission length. In the proposed LR-PON, the upstream power penalty of 5.2 dB at the bit error rate of 3.8×10-3 is measured by using a 64-QAM OFDM modulation after the 75 km fiber transmission without dispersion compensation.
Regenerative Fourier transformation for dual-quadrature regeneration of multilevel rectangular QAM.
Sorokina, Mariia; Sygletos, Stylianos; Ellis, Andrew; Turitsyn, Sergei
2015-07-01
We propose a new nonlinear optical loop mirror based configuration capable of regenerating regular rectangular quadrature amplitude modulated (QAM) signals. The scheme achieves suppression of noise distortion on both signal quadratures through the realization of two orthogonal regenerative Fourier transformations. Numerical simulations show the performance of the scheme for high constellation complexities (including 256-QAM formats). PMID:26125381
Quadrature mixture LO suppression via DSW DAC noise dither
Dubbert, Dale F.; Dudley, Peter A.
2007-08-21
A Quadrature Error Corrected Digital Waveform Synthesizer (QECDWS) employs frequency dependent phase error corrections to, in effect, pre-distort the phase characteristic of the chirp to compensate for the frequency dependent phase nonlinearity of the RF and microwave subsystem. In addition, the QECDWS can employ frequency dependent correction vectors to the quadrature amplitude and phase of the synthesized output. The quadrature corrections cancel the radars' quadrature upconverter (mixer) errors to null the unwanted spectral image. A result is the direct generation of an RF waveform, which has a theoretical chirp bandwidth equal to the QECDWS clock frequency (1 to 1.2 GHz) with the high Spurious Free Dynamic Range (SFDR) necessary for high dynamic range radar systems such as SAR. To correct for the problematic upconverter local oscillator (LO) leakage, precision DC offsets can be applied over the chirped pulse using a pseudo-random noise dither. The present dither technique can effectively produce a quadrature DC bias which has the precision required to adequately suppress the LO leakage. A calibration technique can be employed to calculate both the quadrature correction vectors and the LO-nulling DC offsets using the radar built-in test capability.
Digital quadrature phase detection
Smith, J.A.; Johnson, J.A.
1992-05-26
A system for detecting the phase of a frequency or phase modulated signal that includes digital quadrature sampling of the frequency or phase modulated signal at two times that are one quarter of a cycle of a reference signal apart, determination of the arctangent of the ratio of a first sampling of the frequency or phase modulated signal to the second sampling of the frequency or phase modulated signal, and a determination of quadrant in which the phase determination is increased by 2[pi] when the quadrant changes from the first quadrant to the fourth quadrant and decreased by 2[pi] when the quadrant changes from the fourth quadrant to the first quadrant whereby the absolute phase of the frequency or phase modulated signal can be determined using an arbitrary reference convention. 6 figs.
Digital quadrature phase detection
Smith, James A.; Johnson, John A.
1992-01-01
A system for detecting the phase of a frequency of phase modulated signal that includes digital quadrature sampling of the frequency or phase modulated signal at two times that are one quarter of a cycle of a reference signal apart, determination of the arctangent of the ratio of a first sampling of the frequency or phase modulated signal to the second sampling of the frequency or phase modulated signal, and a determination of quadrant in which the phase determination is increased by 2.pi. when the quadrant changes from the first quadrant to the fourth quadrant and decreased by 2.pi. when the quadrant changes from the fourth quadrant to the first quadrant whereby the absolute phase of the frequency or phase modulated signal can be determined using an arbitrary reference convention.
Wave-Based Inversion & Imaging for the Optical Quadrature Microscope
Lehman, S K
2005-10-27
The Center for Subsurface Sensing & Imaging System's (CenSSIS) Optical Quadrature Microscope (OQM) is a narrow band visible light microscope capable of measuring both amplitude and phase of a scattered field. We develop a diffraction tomography, that is, wave-based, scattered field inversion and imaging algorithm, for reconstructing the refractive index of the scattering object.
Optimized quadrature surface coil designs
Kumar, Ananda; Bottomley, Paul A.
2008-01-01
Background Quadrature surface MRI/MRS detectors comprised of circular loop and figure-8 or butterfly-shaped coils offer improved signal-to-noise-ratios (SNR) compared to single surface coils, and reduced power and specific absorption rates (SAR) when used for MRI excitation. While the radius of the optimum loop coil for performing MRI at depth d in a sample is known, the optimum geometry for figure-8 and butterfly coils is not. Materials and methods The geometries of figure-8 and square butterfly detector coils that deliver the optimum SNR are determined numerically by the electromagnetic method of moments. Figure-8 and loop detectors are then combined to create SNR-optimized quadrature detectors whose theoretical and experimental SNR performance are compared with a novel quadrature detector comprised of a strip and a loop, and with two overlapped loops optimized for the same depth at 3 T. The quadrature detection efficiency and local SAR during transmission for the three quadrature configurations are analyzed and compared. Results The SNR-optimized figure-8 detector has loop radius r8 ∼ 0.6d, so r8/r0 ∼ 1.3 in an optimized quadrature detector at 3 T. The optimized butterfly coil has side length ∼ d and crossover angle of ≥ 150° at the center. Conclusions These new design rules for figure-8 and butterfly coils optimize their performance as linear and quadrature detectors. PMID:18057975
Length Scales in Bayesian Automatic Adaptive Quadrature
NASA Astrophysics Data System (ADS)
Adam, Gh.; Adam, S.
2016-02-01
Two conceptual developments in the Bayesian automatic adaptive quadrature approach to the numerical solution of one-dimensional Riemann integrals [Gh. Adam, S. Adam, Springer LNCS 7125, 1-16 (2012)] are reported. First, it is shown that the numerical quadrature which avoids the overcomputing and minimizes the hidden floating point loss of precision asks for the consideration of three classes of integration domain lengths endowed with specific quadrature sums: microscopic (trapezoidal rule), mesoscopic (Simpson rule), and macroscopic (quadrature sums of high algebraic degrees of precision). Second, sensitive diagnostic tools for the Bayesian inference on macroscopic ranges, coming from the use of Clenshaw-Curtis quadrature, are derived.
Radio frequency path characterization for wide band quadrature amplitude modulation
Bracht, R.
1998-12-31
Remote, high speed, high explosive wave front monitoring requires very high bandwidth telemetry to allow transmission of diagnostic data before the explosion destroys the sensor system itself. The main motivation for this study is that no known existing implementation of this sort has been applied to realistic weapons environments. These facts have prompted the research and gathering of data that can be used to extrapolate towards finding the best modulation method for this application. In addition to research of similar existing analysis and testing operations, data was recently captured from a Joint Test Assembly (JTA) Air Launched Cruise Missile (ALCM) flight.
Quadrature formulas for Fourier coefficients
NASA Astrophysics Data System (ADS)
Bojanov, Borislav; Petrova, Guergana
2009-09-01
We consider quadrature formulas of high degree of precision for the computation of the Fourier coefficients in expansions of functions with respect to a system of orthogonal polynomials. In particular, we show the uniqueness of a multiple node formula for the Fourier-Tchebycheff coefficients given by Micchelli and Sharma and construct new Gaussian formulas for the Fourier coefficients of a function, based on the values of the function and its derivatives.
Microwave photonic quadrature filter based on an all-optical programmable Hilbert transformer.
Huang, Thomas X H; Yi, Xiaoke; Minasian, Robert A
2011-11-15
A microwave photonic quadrature filter, new to our knowledge, based on an all-optical Hilbert transformer is presented. It is based on mapping of a Hilbert transform transfer function between the optical and electrical domains, using a programmable Fourier-domain optical processor and high-speed photodiodes. The technique enables the realization of an extremely wide operating bandwidth, tunable programmable bandwidth, and a highly precise amplitude and phase response. Experimental results demonstrate a microwave quadrature filter from 10 to 20 GHz, which achieves an amplitude imbalance of less than ±0.23 dB and a phase imbalance of less than ±0.5°. PMID:22089590
Error Analysis of Quadrature Rules. Classroom Notes
ERIC Educational Resources Information Center
Glaister, P.
2004-01-01
Approaches to the determination of the error in numerical quadrature rules are discussed and compared. This article considers the problem of the determination of errors in numerical quadrature rules, taking Simpson's rule as the principal example. It suggests an approach based on truncation error analysis of numerical schemes for differential…
Parametric generation of quadrature squeezing of mirrors in cavity optomechanics
Liao, Jie-Qiao; Law, C. K.
2011-03-15
We propose a method to generate quadrature-squeezed states of a moving mirror in a Fabry-Perot cavity. This is achieved by exploiting the fact that when the cavity is driven by an external field with a large detuning, the moving mirror behaves as a parametric oscillator. We show that parametric resonance can be reached approximately by modulating the driving field amplitude at a frequency matching the frequency shift of the mirror. The parametric resonance leads to an efficient generation of squeezing, which is limited by the thermal noise of the environment.
A generalized discrepancy and quadrature error bound
NASA Astrophysics Data System (ADS)
Hickernell, F. J.
1998-01-01
An error bound for multidimensional quadrature is derived that includes the Koksma-Hlawka inequality as a special case. This error bound takes the form of a product of two terms. One term, which depends only on the integrand, is defined as a generalized variation. The other term, which depends only on the quadrature rule, is defined as a generalized discrepancy. The generalized discrepancy is a figure of merit for quadrature rules and includes as special cases the L-p-star discrepancy and P-alpha that arises in the study of lattice rules.
Gaussian quadrature formulae for arbitrary positive measures.
Fernandes, Andrew D; Atchley, William R
2006-01-01
We present computational methods and subroutines to compute Gaussian quadrature integration formulas for arbitrary positive measures. For expensive integrands that can be factored into well-known forms, Gaussian quadrature schemes allow for efficient evaluation of high-accuracy and -precision numerical integrals, especially compared to general ad hoc schemes. In addition, for certain well-known density measures (the normal, gamma, log-normal, Student's t, inverse-gamma, beta, and Fisher's F) we present exact formulae for computing the respective quadrature scheme. PMID:19455218
Cao, Yuan; Chan, Erwin H W; Wang, Xudong; Feng, Xinhuan; Guan, Bai-ou
2015-10-15
A photonic microwave quadrature filter is presented. It has a very simple structure, very low phase imbalance, and high signal-to-noise ratio performance. Experimental results are presented that demonstrate a photonic microwave quadrature filter with a 3 dB operating frequency range of 10.5-26.5 GHz, an amplitude and phase imbalance of less than ±0.3 dB and ±0.15°, and a signal-to-noise ratio of more than 121 dB in a 1 Hz noise bandwidth. PMID:26469589
Antenna-array, phase quadrature tracking system
NASA Technical Reports Server (NTRS)
Cubley, H. D.
1970-01-01
Phase relationship between input signals appearing on widely-spaced parallel connected antenna elements in array is automatically adjusted in phase quadrature tracking system. Compact and lightweight design permit use in wide variety of airborne communications networks.
Structured eigenvalue problems for rational gauss quadrature
NASA Astrophysics Data System (ADS)
Fasino, Dario; Gemignani, Luca
2007-08-01
The connection between Gauss quadrature rules and the algebraic eigenvalue problem for a Jacobi matrix was first exploited in the now classical paper by Golub and Welsch (Math. Comput. 23(106), 221?230, 1969). From then on many computational problems arising in the construction of (polynomial) Gauss quadrature formulas have been reduced to solving direct and inverse eigenvalue problems for symmetric tridiagonals. Over the last few years (rational) generalizations of the classical Gauss quadrature formulas have been studied, i.e., formulas integrating exactly in spaces of rational functions. This paper wants to illustrate that stable and efficient procedures based on structured numerical linear algebra techniques can also be devised for the solution of the eigenvalue problems arising in the field of rational Gauss quadrature.
Calculates Angular Quadrature Weights and Cosines.
Energy Science and Technology Software Center (ESTSC)
1988-02-18
DSNQUAD calculates the angular quadrature weights and cosines for use in CCC-254/ANISN-ORNL. The subroutines in DSNQUAD were lifted from the XSDRN-PM code, which is supplied with the CCC-475/ SCALIAS-77 package.
Past and Future SOHO-Ulysses Quadratures
NASA Technical Reports Server (NTRS)
Suess, Steven; Poletto, G.
2006-01-01
With the launch of SOHO, it again became possible to carry out quadrature observations. In comparison with earlier observations, the new capabilities of coronal spectroscopy with UVCS and in situ ionization state and composition with Ulysses/SWICS enabled new types of studies. Results from two studies serve as examples: (i) The acceleration profile of wind from small coronal holes. (ii) A high-coronal reconnecting current sheet as the source of high ionization state Fe in a CME at Ulysses. Generally quadrature observations last only for a few days, when Ulysses is within ca. 5 degrees of the limb. This means luck is required for the phenomenon of interest to lie along the radial direction to Ulysses. However, when Ulysses is at high southern latitude in winter 2007 and high northern latitude in winter 2008, there will be unusually favorable configurations for quadrature observations with SOHO and corresponding bracketing limb observations from STEREO A/B. Specifically, Ulysses will be within 5 degrees of the limb from December 2006 to May 2007 and within 10 degrees of the limb from December 2007 to May 2008. These long-lasting quadratures and bracketing STEREO A/B observations overcome the limitations inherent in the short observation intervals of typical quadratures. Furthermore, ionization and charge state measurements like those on Ulysses will also be made on STEREO and these will be essential for identification of CME ejecta - one of the prime objectives for STEREO.
Quadrature formulae for problems in mechanics
NASA Astrophysics Data System (ADS)
Milovanović, Gradimir V.; Igić, Tomislav; Tončev, Novica
2012-09-01
The fast progress in recent years in symbolic computation and variable-precision arithmetic provide a possibility for generating the recursion coefficients in the three-term recurrence relation for orthogonal polynomials with respect to several nonclassical weight functions, as well as the construction of the corresponding quadrature rules of Gaussian type. Such quadratures are very important in many applications in engineering (fracture mechanics, damage mechanics, etc.), as well as in other computational and applied sciences. The boundary element method (BEM), finite element method (FEM), methods for solving integral equations, etc. very often require the numerical evaluation of one dimensional or multiple integrals with singular or near singular integrands with a high precision. In this paper we give some improvements of quadrature rules of Gaussian type with logarithmic and/or algebraic singularities. A numerical examples is included.
Summation Paths in Clenshaw-Curtis Quadrature
NASA Astrophysics Data System (ADS)
Adam, S.; Adam, Gh.
2016-02-01
Two topics concerning the use of Clenshaw-Curtis quadrature within the Bayesian automatic adaptive quadrature approach to the numerical solution of Riemann integrals are considered. First, it is found that the efficient floating point computation of the coefficients of the Chebyshev series expansion of the integrand is to be done within a mathematical structure consisting of the union of coefficient families ordered into complete binary trees. Second, the scrutiny of the decay rates of the involved even and odd rank Chebyshev expansion coefficients with the increase of their rank labels enables the definition of Bayesian decision paths for the advancement to the numerical output.
Composite Gauss-Legendre Quadrature with Error Control
ERIC Educational Resources Information Center
Prentice, J. S. C.
2011-01-01
We describe composite Gauss-Legendre quadrature for determining definite integrals, including a means of controlling the approximation error. We compare the form and performance of the algorithm with standard Newton-Cotes quadrature. (Contains 1 table.)
Runge-Kutta based generalized convolution quadrature
NASA Astrophysics Data System (ADS)
Lopez-Fernandez, Maria; Sauter, Stefan
2016-06-01
We present the Runge-Kutta generalized convolution quadrature (gCQ) with variable time steps for the numerical solution of convolution equations for time and space-time problems. We present the main properties of the method and a convergence result.
Gauss-Laguerre interval quadrature rule
NASA Astrophysics Data System (ADS)
Milovanovic, Gradimir V.; Cvetkovic, Aleksandar S.
2005-10-01
In this paper we prove the existence and uniqueness of the Gaussian interval quadrature formula with respect to the generalized Laguerre weight function. An algorithm for numerical construction has also investigated and some suitable solutions are proposed. A few numerical examples are included.
Error Bounds for Quadrature Methods Involving Lower Order Derivatives
ERIC Educational Resources Information Center
Engelbrecht, Johann; Fedotov, Igor; Fedotova, Tanya; Harding, Ansie
2003-01-01
Quadrature methods for approximating the definite integral of a function f(t) over an interval [a,b] are in common use. Examples of such methods are the Newton-Cotes formulas (midpoint, trapezoidal and Simpson methods etc.) and the Gauss-Legendre quadrature rules, to name two types of quadrature. Error bounds for these approximations involve…
NASA Astrophysics Data System (ADS)
Warger, William C., II; Newmark, Judith A.; Zhao, Bing; Warner, Carol M.; DiMarzio, Charles A.
2006-02-01
Present imaging techniques used in in vitro fertilization (IVF) clinics are unable to produce accurate cell counts in developing embryos past the eight-cell stage. We have developed a method that has produced accurate cell counts in live mouse embryos ranging from 13-25 cells by combining Differential Interference Contrast (DIC) and Optical Quadrature Microscopy. Optical Quadrature Microscopy is an interferometric imaging modality that measures the amplitude and phase of the signal beam that travels through the embryo. The phase is transformed into an image of optical path length difference, which is used to determine the maximum optical path length deviation of a single cell. DIC microscopy gives distinct cell boundaries for cells within the focal plane when other cells do not lie in the path to the objective. Fitting an ellipse to the boundary of a single cell in the DIC image and combining it with the maximum optical path length deviation of a single cell creates an ellipsoidal model cell of optical path length deviation. Subtracting the model cell from the Optical Quadrature image will either show the optical path length deviation of the culture medium or reveal another cell underneath. Once all the boundaries are used in the DIC image, the subtracted Optical Quadrature image is analyzed to determine the cell boundaries of the remaining cells. The final cell count is produced when no more cells can be subtracted. We have produced exact cell counts on 5 samples, which have been validated by Epi-Fluorescence images of Hoechst stained nuclei.
Uniform positive-weight quadratures for discrete ordinate transport calculations
Carew, J.F.; Zamonsky, G.
1999-02-01
Mechanical quadratures that allow systematic improvement and solution convergence are derived for application of the discrete ordinates method to the Boltzmann transport equation. the quadrature directions are arranged on n latitudinal levels, are uniformly distributed over the unit sphere, and have positive weights. Both a uniform and equal-weight quadrature set UE{sub n} and a uniform and Gauss-weight quadrature set UG{sub n} are derived. These quadratures have the advantage over the standard level-symmetric LQ{sub n} quadrature sets in that the weights are positive for all orders, and the solution may be systematically converged by increasing the order of the quadrature set. As the order of the quadrature is increased the points approach a uniform continuous distribution on the unit sphere and the quadrature is invariant with respect to spatial rotations. The numerical integrals converge for continuous functions as the order of the quadrature is increased. Numerical calculations were performed to evaluate the application of the UE{sub n} quadrature set. Comparisons of the exact moments and those calculated using the UE{sub n} quadrature set demonstrate that the moment integrals are performed accurately except for distributions that are very sharply peaked along the direction of the polar axis. A series of DORT transport calculations of the >1-Mev neutron flux for a typical reactor core/pressure vessel geometry were also carried out. These calculations employed the UE{sub n} (n = 6, 10, 12, 18, and 24) quadratures and indicate that the UE{sub n} solutions have converged to within {approximately}0.5%. The UE{sub 24} solutions were also found to be more accurate than the calculations performed with the S{sub 16} level-symmetric quadratures.
Exponential fitting quadrature rule for functional equations
NASA Astrophysics Data System (ADS)
Cardone, A.; Paternoster, B.; Santomauro, G.
2012-09-01
A Gaussian quadrature rule for periodic integrand function is presented. The weights and nodes depend on the frequency of the problem and they are constructed by following the exponential fitting theory. The composite rule based on this formula is derived. The analysis of the error is carried out and it proves that the exponentially fitted Gaussian rule is more accurate than the classical Gauss-Legendre rule when oscillatory functions are treated. Some numerical tests are presented.
Modeling of optical quadrature microscopy for imaging mouse embryos
NASA Astrophysics Data System (ADS)
Warger, William C., II; DiMarzio, Charles A.
2008-02-01
Optical quadrature microscopy (OQM) has been shown to provide the optical path difference through a mouse embryo, and has led to a novel method to count the total number of cells further into development than current non-toxic imaging techniques used in the clinic. The cell counting method has the potential to provide an additional quantitative viability marker for blastocyst transfer during in vitro fertilization. OQM uses a 633 nm laser within a modified Mach-Zehnder interferometer configuration to measure the amplitude and phase of the signal beam that travels through the embryo. Four cameras preceded by multiple beamsplitters record the four interferograms that are used within a reconstruction algorithm to produce an image of the complex electric field amplitude. Here we present a model for the electric field through the primary optical components in the imaging configuration and the reconstruction algorithm to calculate the signal to noise ratio when imaging mouse embryos. The model includes magnitude and phase errors in the individual reference and sample paths, fixed pattern noise, and noise within the laser and detectors. This analysis provides the foundation for determining the imaging limitations of OQM and the basis to optimize the cell counting method in order to introduce additional quantitative viability markers.
NASA Astrophysics Data System (ADS)
Gabriel, C.; Aiello, A.; Berg-Johansen, S.; Marquardt, Ch.; Leuchs, G.
2012-07-01
Quadrature squeezed cylindrically polarized modes contain entanglement not only in the polarization and spatial electric field variables but also between these two degrees of freedom [C. Gabriel et al., Phys. Rev. Lett. 106, 060502 (2011)]. In this paper we present tools to generate and detect this entanglement. Experimentally we demonstrate the generation of quadrature squeezing in cylindrically polarized modes by mode transforming a squeezed Gaussian mode. Specifically, -1.2 dB ± 0.1 dB of amplitude squeezing are achieved in the radially and azimuthally polarized mode. Furthermore, theoretically it is shown how the entanglement contained within these modes can be measured and how strong the quantum correlations are, depending on the measurement scheme.
Gauss Legendre Quadrature Formulae for Tetrahedra
NASA Astrophysics Data System (ADS)
Rathod, H. T.; Venkatesudu, B.; Nagaraja, K. V.
2005-09-01
In this paper we consider the Gauss Legendre quadrature method for numerical integration over the standard tetrahedron: {(x, y, z)|0 = x, y, z = 1, x + y + z = 1} in the Cartesian three-dimensional (x, y, z) space. The mathematical transformation from the (x, y, z) space to (?, ?, ?) space is described to map the standard tetrahedron in (x, y, z) space to a standard 2-cube: {(?, ?, ?)| - 1 = ?, ?,? = 1} in the (?, ?, ?) space. This overcomes the difficulties associated with the derivation of new weight co-efficients and sampling points. The effectiveness of the formulae is demonstrated by applying them to the integration of three nonpolynomial and three polynomial functions.
Positive interpolatory quadrature formulas and para-orthogonal polynomials
NASA Astrophysics Data System (ADS)
Bultheel, Adhemar; Daruis, Leyla; Gonzalez-Vera, Pablo
2005-07-01
We establish a relation between quadrature formulas on the interval [-1,1] that approximate integrals of the form and Szego quadrature formulas on the unit circle that approximate integrals of the form . The functions [mu](x) and [omega]([theta]) are assumed to be weight functions on [-1,1] and [-[pi],[pi
Correlated quadratures of resonance fluorescence and the generalized uncertainty relation
NASA Technical Reports Server (NTRS)
Arnoldus, Henk F.; George, Thomas F.; Gross, Rolf W. F.
1994-01-01
Resonance fluorescence from a two-state atom has been predicted to exhibit quadrature squeezing below the Heisenberg uncertainty limit, provided that the optical parameters (Rabi frequency, detuning, laser linewidth, etc.) are chosen carefully. When the correlation between two quadratures of the radiation field does not vanish, however, the Heisenberg limit for quantum fluctuations might be an unrealistic lower bound. A generalized uncertainty relation, due to Schroedinger, takes into account the possible correlation between the quadrature components of the radiation, and it suggests a modified definition of squeezing. We show that the coherence between the two levels of a laser-driven atom is responsible for the correlation between the quadrature components of the emitted fluorescence, and that the Schrodinger uncertainty limit increases monotonically with the coherence. On the other hand, the fluctuations in the quadrature field diminish with an increasing coherence, and can disappear completely when the coherence reaches 1/2, provided that certain phase relations hold.
Method of differential-phase/absolute-amplitude QAM
Dimsdle, Jeffrey William
2007-07-03
A method of quadrature amplitude modulation involving encoding phase differentially and amplitude absolutely, allowing for a high data rate and spectral efficiency in data transmission and other communication applications, and allowing for amplitude scaling to facilitate data recovery; amplitude scale tracking to track-out rapid and severe scale variations and facilitate successful demodulation and data retrieval; 2.sup.N power carrier recovery; incoherent demodulation where coherent carrier recovery is not possible or practical due to signal degradation; coherent demodulation; multipath equalization to equalize frequency dependent multipath; and demodulation filtering.
Method of differential-phase/absolute-amplitude QAM
Dimsdle, Jeffrey William
2008-10-21
A method of quadrature amplitude modulation involving encoding phase differentially and amplitude absolutely, allowing for a high data rate and spectral efficiency in data transmission and other communication applications, and allowing for amplitude scaling to facilitate data recovery; amplitude scale tracking to track-out rapid and severe scale variations and facilitate successful demodulation and data retrieval; 2.sup.N power carrier recovery; incoherent demodulation where coherent carrier recovery is not possible or practical due to signal degradation; coherent demodulation; multipath equalization to equalize frequency dependent multipath; and demodulation filtering.
Method of differential-phase/absolute-amplitude QAM
Dimsdle, Jeffrey William
2007-07-17
A method of quadrature amplitude modulation involving encoding phase differentially and amplitude absolutely, allowing for a high data rate and spectral efficiency in data transmission and other communication applications, and allowing for amplitude scaling to facilitate data recovery; amplitude scale tracking to track-out rapid and severe scale variations and facilitate successful demodulation and data retrieval; 2.sup.N power carrier recovery; incoherent demodulation where coherent carrier recovery is not possible or practical due to signal degradation; coherent demodulation; multipath equalization to equalize frequency dependent multipath; and demodulation filtering.
Method of differential-phase/absolute-amplitude QAM
Dimsdle, Jeffrey William
2007-10-02
A method of quadrature amplitude modulation involving encoding phase differentially and amplitude absolutely, allowing for a high data rate and spectral efficiency in data transmission and other communication applications, and allowing for amplitude scaling to facilitate data recovery; amplitude scale tracking to track-out rapid and severe scale variations and facilitate successful demodulation and data retrieval; 2.sup.N power carrier recovery; incoherent demodulation where coherent carrier recovery is not possible or practical due to signal degradation; coherent demodulation; multipath equalization to equalize frequency dependent multipath; and demodulation filtering.
Method of differential-phase/absolute-amplitude QAM
Dimsdle, Jeffrey William
2009-09-01
A method of quadrature amplitude modulation involving encoding phase differentially and amplitude absolutely, allowing for a high data rate and spectral efficiency in data transmission and other communication applications, and allowing for amplitude scaling to facilitate data recovery; amplitude scale tracking to track-out rapid and severe scale variations and facilitate successful demodulation and data retrieval; 2.sup.N power carrier recovery; incoherent demodulation where coherent carrier recovery is not possible or practical due to signal degradation; coherent demodulation; multipath equalization to equalize frequency dependent multipath; and demodulation filtering.
NASA Technical Reports Server (NTRS)
Caves, C. M.; Schumaker, B. L.
1985-01-01
A new formalism for analyzing two-photon devices, such as parametric amplifiers and phase-conjugate mirrors, is proposed in part I, focusing on the properties and the significance of the quadrature-phase amplitudes and two-mode squeezed states. Time-stationary quasi-probability noise is also detailed for the case of Gaussian noise, and uncertainty principles for the quadrature-phase amplitudes are outlined, as well as some important properties of the two-mode states. Part II establishes a mathematical foundation for the formalism, with introduction of a vector notation for compact representation of two-mode properties. Fundamental unitary operators and special quantum states are also examined with an emphasis on the two-mode squeezed states. The results are applied to a previously studied degenerate limit (epsilon = 0).
Two-frequency-dependent Gauss quadrature rules
NASA Astrophysics Data System (ADS)
Kim, Kyung Joong
2005-02-01
We construct two-frequency-dependent Gauss quadrature rules which can be applied for approximating the integration of the product of two oscillatory functions with different frequencies [beta]1 and [beta]2 of the forms,yi(x)=fi,1(x) cos([beta]ix)+fi,2(x) sin([beta]ix), i=1,2,where the functions fi,j(x) are smooth. A regularization procedure is presented to avoid the singularity of the Jacobian matrix of nonlinear system of equations which is induced as one frequency approaches the other frequency. We provide numerical results to compare the accuracy of the classical Gauss rule and one- and two-frequency-dependent rules.
The May 1997 SOHO-Ulysses Quadrature
NASA Technical Reports Server (NTRS)
Suess, Steven T.; Poletto, G.; Romoli, M.; Neugebauer, M.; Goldstein, B. E.; Simnett, G.
2000-01-01
We present results from the May 1997 SOHO-Ulysses quadrature, near sunspot minimum. Ulysses was at 5.1 AU, 100 north of the solar equator, and off the east limb. It was, by chance, also at the very northern edge of the streamer belt. Nevertheless, SWOOPS detected only slow, relatively smooth wind and there was no direct evidence of fast wind from the northern polar coronal hole or of mixing with fast wind. LASCO images show that the streamer belt at 10 N was narrow and sharp at the beginning and end of the two week observation interval, but broadened in the middle. A corresponding change in density, but not flow speed, occurred at Ulysses. Coronal densities derived from UVCS show that physical parameters in the lower corona are closely related to those in the solar wind, both over quiet intervals and in transient events on the limb. One small transient observed by both LASCO and UVCS is analyzed in detail.
Quadrature conductivity: A quantitative indicator of bacterial abundance in porous media
Chi Zhang; Andre Revil; Yoshiko Fujita; Junko Munakata-Marr; George Redden
2014-09-01
ABSTRACT The abundance and growth stages of bacteria in subsurface porous media affect the concentrations and distributions of charged species within the solid-solution interfaces. Therefore, spectral induced polarization (SIP) measurements can be used to monitor changes in bacterial biomass and growth stage. Our goal was to gain a better understanding of the SIP response of bacteria present in a porous material. Bacterial cell surfaces possess an electric double layer and therefore become polarized in an electric field. We performed SIP measurements over the frequency range of 0.1–1 kHz on cell suspensions alone and cell suspensions mixed with sand at four pore water conductivities. We used Zymomonas mobilis at four different cell densities (in- cluding the background). The quadrature conductivity spectra exhibited two peaks, one around 0.05–0.10 Hz and the other around 1–10 Hz. Because SIP measurements on bacterial suspensions are typically made at frequencies greater than 1 Hz, these peaks have not been previously reported. In the bac-terial suspensions in growth medium, the quadrature conduc-tivity at peak I was linearly proportional to the density of the bacteria. For the case of the suspensions mixed with sands, we observed that peak II presented a smaller increase in the quadrature conductivity with the cell density. A comparison of the experiments with and without sand grains illustrated the effect of the porous medium on the overall quadrature con- ductivity response (decrease in the amplitude and shift of the peaks to the lower frequencies). Our results indicate that for a given porous medium, time-lapse SIP has potential for mon- itoring changes in bacterial abundance within porous media.
Power flow control using quadrature boosters
NASA Astrophysics Data System (ADS)
Sadanandan, Sandeep N.
A power system that can be controlled within security constraints would be an advantage to power planners and real-time operators. Controlling flows can lessen reliability issues such as thermal limit violations, power stability problems, and/or voltage stability conditions. Control of flows can also mitigate market issues by reducing congestion on some lines and rerouting power to less loaded lines or onto preferable paths. In the traditional control of power flows, phase shifters are often used. More advanced methods include using Flexible AC Transmission System (FACTS) Controllers. Some examples include Thyristor Controlled Series Capacitors, Synchronous Series Static Compensators, and Unified Power Flow Controllers. Quadrature Boosters (QBs) have similar structures to phase-shifters, but allow for higher voltage magnitude during real power flow control. In comparison with other FACTS controllers QBs are not as complex and not as expensive. The present study proposes to use QBs to control power flows on a power system. With the inclusion of QBs, real power flows can be controlled to desired scheduled values. In this thesis, the linearized power flow equations used for power flow analysis were modified for the control problem. This included modifying the Jacobian matrix, the power error vector, and calculating the voltage injected by the quadrature booster for the scheduled real power flow. Two scenarios were examined using the proposed power flow control method. First, the power flow in a line in a 5-bus system was modified with a QB using the method developed in this thesis. Simulation was carried out using Matlab. Second, the method was applied to a 30-bus system and then to a 118-bus system using several QBs. In all the cases, the calculated values of the QB voltages led to desired power flows in the designated line.
Bakhtiari, Zahra; Sawchuk, Alexander A
2015-04-20
We describe and demonstrate an all-optical tunable phase- preserving scheme for multilevel amplitude regeneration based on coherent optical wave mixing using a polarizer for optical star 8-quadrature-amplitude modulation (star-8QAM) and star-16QAM signals with a power ratio of 1:5. Amplitude noise can be efficiently suppressed on both amplitude levels. A regeneration factor of nearly 5 for the higher-amplitude level of star-8QAM and 3 for lower-amplitude level are achieved. The system robustness against nonlinear phase noise originating from the Gordon-Mollenauer effect in a 150 km transmission line is investigated using the proposed amplitude regenerator. PMID:25969093
NASA Astrophysics Data System (ADS)
Warger, William C., II; Newmark, Judith A.; Chang, ChihChing; Brooks, Dana H.; Warner, Carol M.; DiMarzio, Charles A.
2005-03-01
The Multifunctional Staring Mode Microscope was developed to permit three modes of imaging for cell counting in mouse embryos: Optical Quadrature, Differential Interference Contrast (DIC), and Fluorescence Imaging. The Optical Quadrature Microscope, consisting of a modified Mach-Zender Interferometer, uses a 632.8 nm laser to measure the amplitude and phase of the signal beam that travels through the embryo. Four cameras, preceded by multiple beamsplitters, are used to read the four interferograms, which are then combined to produce an image of the complex electric field amplitude. The phase of the complex amplitude is then unwrapped using a 2-D phase unwrap algorithm and images of optical path length are produced. To combine the additional modes of DIC and Fluorescence Imaging with the Optical Quadrature Microscope, a 632.8 nm narrow bandpass beamsplitter was placed at the output of the microscope. This allows the laser light to continue through the Mach-Zender while all other wavelengths are reflected at 90 degrees to another camera. This was effective in combining the three modes as the fluorescence wavelength for the Hoechst stain is well below the bandpass window of the beamsplitter. Both live and fixed samples have been successfully imaged in all three modes. Accuracy in cell counting was achieved by using the DIC image for detecting cell boundaries and the Optical Quadrature image for phase mapping to determine where cells overlap. The final results were verified by Hoechst fluorescence imaging to count the individual nuclei. Algorithms are currently being refined so larger cell counts can be done more efficiently.
First CFOA-based explicit-current-output quadrature sinusoidal oscillators using grounded capacitors
NASA Astrophysics Data System (ADS)
Lahiri, Abhirup; Jaikla, Winai; Siripruchyanun, Montree
2013-02-01
To date, no current-feedback operational amplifier (CFOA)-based sinusoidal oscillator has been reported which provides all the following features simultaneously: (i) current-mode quadrature sinusoidal oscillator providing two explicit-current-outputs (ECOs) from high output impedance terminals, (ii) employing no more than three CFOA ICs and six passive components, which include two grounded capacitors, (iii) offers independent tuning of the condition of oscillation (CO) via a resistor and (iv) provides tunability of the ratio of amplitudes of the generated quadrature ECOs via a separate resistor. To the best of authors' knowledge, this article reports first CFOA-based QOs in current-mode (i.e. providing two ECO signals). Experimental results using AD844 CFOA ICs from Analog Devices have been included to verify the workability of the proposed oscillator circuits. An example automatic gain control (AGC) loop to regulate the oscillation amplitude and control the THD has also been used and verified using SPICE simulations using the AD844 macro-model.
Algorithm 699 - A new representation of Patterson's quadrature formulae
NASA Technical Reports Server (NTRS)
Krogh, Fred T.; Van Snyder, W.
1991-01-01
A method is presented to reduce the number of coefficients necessary to represent Patterson's quadrature formulae. It also reduces the amount of storage necessary for storing function values, and produces slightly smaller error in evaluating the formulae.
Experimental study of quadrature spring rate at tuned dry gyro
NASA Astrophysics Data System (ADS)
Hayakawa, Yoshiaki; Murayama, Naoshi
A survey result on the mechanism of quadrature spring rate occurring at the tuned dry gyro is given. It is noted that the quadrature spring rate is a damping torque. This damping torque is similar to the spring reaction torque generated by the flexure displacement angles and drives the gyro rotor back to a balanced position. In order to investigate the mechanism of damping occurring at the gyro rotor, the relation between surrounding gas pressure and damping factor under gyro nonoperating was measured. Furthermore, the drag torque acting on the gyro rotor was measured by the back EMF method at different surrounding gas pressure. As a result of these testings, it was found out that the quadrature spring rate was generated by gas movement of the flexure around and drag forces due to bearing loss and windage loss, and the mechanism and magnitude of each damping torque which are contributor to the quadrature spring rate were extracted separately.
Squeezing quadrature rotation in the acoustic band via optomechanics
NASA Astrophysics Data System (ADS)
Guccione, Giovanni; Slatyer, Harry J.; Carvalho, André R. R.; Buchler, Ben C.; Lam, Ping Koy
2016-03-01
We examine the use of optomechanically generated squeezing to obtain a sensitivity enhancement for interferometers in the gravitational-wave band. The intrinsic dispersion characteristics of optomechanical squeezing around the mechanical frequency are able to produce squeezing at different quadratures over the spectrum, a feature required by gravitational-wave interferometers to beat the standard quantum limit over an extended frequency range. Under realistic assumptions we show that the amount of available squeezing and the intrinsic quadrature rotation may provide, compared to similar amounts of fixed-quadrature squeezing, a detection advantage. A significant challenge for this scheme, however, is the amount of excess noise that is generated in the unsqueezed quadrature at frequencies near the mechanical resonance.
Optical encryption system using quadrature multiplexing
NASA Astrophysics Data System (ADS)
Islam, Mohammed Nazrul; Alam, Mohammad S.
2006-08-01
Optical security systems have attracted much research interest recently for information security and fraud deterrent applications. A number of encryption techniques have been proposed in the literature, which includes double random-phase encryption, polarization encoding, encryption and verification using a multiplexed minimum average correlation energy phase-encrypted filter. Most of these reports employ a pseudo-random code for each information to be encrypted, where it requires individual storage capacity or transmission channel for further processing of each information. The objective of this paper is to develop an optical encryption system employing quadrature multiplexing to enhance the storage/transmission capacity of the system. Two information signals are encrypted using the same code but employing two orthogonal functions and then they are multiplexed together in the same domain. As the orthogonal functions have zero cross-correlation between them, so the encrypted information are expected to be unaffected by each other. Each encryption and multiplexing process can accommodate two information signals for a single code and a single storage cell or transmission channel. The same process can be performed in multiple steps to increase the multiplexing capability of the system. For decryption purpose, the composite encoded signal is correlated using the appropriate code and the appropriate function. The proposed technique has been found to work excellent in computer simulation with binary as well as gray level images. It has also been verified that the encrypted images remain secure, because no unwanted reproduction is possible without having the appropriate code and function.
Two integrator loop quadrature oscillators: A review
Soliman, Ahmed M.
2012-01-01
A review of the two integrator loop oscillator circuits providing two quadrature sinusoidal output voltages is given. All the circuits considered employ the minimum number of capacitors namely two except one circuit which uses three capacitors. The circuits considered are classified to four different classes. The first class includes floating capacitors and floating resistors and the active building blocks realizing these circuits are the Op Amp or the OTRA. The second class employs grounded capacitors and includes floating resistors and the active building blocks realizing these circuits are the DCVC or the unity gain cells or the CFOA. The third class employs grounded capacitors and grounded resistors and the active building blocks realizing these circuits are the CCII. The fourth class employs grounded capacitors and no resistors and the active building blocks realizing these circuits are the TA. Transformation methods showing the generation of different classes from each other is given in details and this is one of the main objectives of this paper. PMID:25685396
All-atomic generation and noise-quadrature filtering of squeezed vacuum in hot Rb vapor
NASA Astrophysics Data System (ADS)
Horrom, Travis; Romanov, Gleb; Novikova, Irina; Mikhailov, Eugeniy E.
2013-01-01
With our all-atomic squeezing and filtering setup, we demonstrate control over the noise amplitudes and manipulation of the frequency-dependent squeezing angle of a squeezed vacuum quantum state by passing it through an atomic medium with electromagnetically induced transparency (EIT). We generate low sideband frequency squeezed vacuum using the polarization self-rotation effect in a hot Rb vapor cell, and direct it through a second atomic vapor subject to EIT conditions. We use the frequency-dependent absorption of the EIT window to demonstrate an example of squeeze amplitude attenuation and squeeze angle rotation of the quantum noise quadratures of the squeezed probe. These studies have implications for quantum memory and storage as well as gravitational wave interferometric detectors.
Orthogonal rational functions and quadrature on an interval
NASA Astrophysics Data System (ADS)
van Deun, J.; Bultheel, A.
2003-04-01
Rational functions with real poles and poles in the complex lower half-plane, orthogonal on the real line, are well known. Quadrature formulas similar to the Gauss formulas for orthogonal polynomials have been studied. We generalize to the case of arbitrary complex poles and study orthogonality on a finite interval. The zeros of the orthogonal rational functions are shown to satisfy a quadratic eigenvalue problem. In the case of real poles, these zeros are used as nodes in the quadrature formulas.
An exponentially fitted quadrature rule over unbounded intervals
NASA Astrophysics Data System (ADS)
Conte, D.; Paternoster, B.; Santomauro, G.
2012-09-01
A new class of quadrature formulae for the computation of integrals over unbounded intervals with oscillating integrand is illustrated. Such formulae are a generalization of the gaussian quadrature formulae by exploiting the Exponential Fitting theory. The coefficients depend on the frequency of oscillation, in order to improve the accuracy of the solution. The construction of the methods with 1, 2 and 3 nodes is described, together with the comparison of the order of accuracy with respect to classical formulae.
Gaussian quadrature inference for continuous-variable quantum key distribution
NASA Astrophysics Data System (ADS)
Gyongyosi, L.; Imre, S.
2016-05-01
We propose the Gaussian quadrature inference (GQI) method for multicarrier continuous-variable quantum key distribution (CVQKD). A multicarrier CVQKD protocol utilizes Gaussian subcarrier quantum continuous variables (CV) for information transmission. The GQI framework provides a minimal error estimate of the quadratures of the CV quantum states from the discrete, measured noisy subcarrier variables. GQI utilizes the fundamentals of regularization theory and statistical information processing. We characterize GQI for multicarrier CVQKD, and define a method for the statistical modeling and processing of noisy Gaussian subcarrier quadratures. We demonstrate the results through the adaptive multicarrier quadrature division (AMQD) scheme. We introduce the terms statistical secret key rate and statistical private classical information, which quantities are derived purely by the statistical functions of GQI. We prove the secret key rate formulas for a multiple access multicarrier CVQKD via the AMQD-MQA (multiuser quadrature allocation) scheme. The framework can be established in an arbitrary CVQKD protocol and measurement setting, and are implementable by standard low-complexity statistical functions, which is particularly convenient for an experimental CVQKD scenario.
The Fall 2000 and Fall 2001 SOHO-Ulysses Quadratures
NASA Technical Reports Server (NTRS)
Suess, S. T.; Poletto, G.
2000-01-01
SOHO-Ulysses quadrature occurs when the SOHO-Sun-Ulysses included angle is 90 degrees. It is only at such times that the same plasma leaving the Sun in the direction of Ulysses can first be remotely analyzed with SOHO instruments and then later be sampled in situ by Ulysses instruments. The quadratures in December 2000 and 2001 are of special significance because Ulysses will be near the south and north heliographic poles, respectively, and the solar cycle will be near sunspot maximum. Quadrature geometry is sometimes confusing and observations are influenced by solar rotation. The Fall 2000 and 2001 quadratures are more complex than usual because Ulysses is not in a true polar orbit and the orbital speed of Ulysses about the Sun is becoming comparable to the speed of SOHO about the Sun. In 2000 Ulysses will always be slightly behind the pole but will appear to hang over the pole for over two months because it is moving around the Sun in the same direction as SOHO. In 20001, Ulysses will be slightly in front of the pole so that its footpoint will be directly observable. Detailed plots will be shown of the relative positions of SOHO and Ulysses will their relative positions. In neither case is true quadrature actually achieved, but this works to the observers advantage in 2001.
The Fall 2000 and Fall 2001 SOHO-Ulysses Quadratures
NASA Technical Reports Server (NTRS)
Suess, S. T.; Poletto, G.; Rose, M. Franklin (Technical Monitor)
2001-01-01
SOHO-Ulysses quadrature occurs when the SOHO-Sun-Ulysses included angle is 90 degrees. It is only at such times that the same plasma leaving the Sun in the direction of Ulysses can first be remotely analyzed with SOHO instruments and then later be sampled in situ by Ulysses instruments. The quadratures in December 2000 and 2001 are of special significance because Ulysses will be near the south and north heliographic poles, respectively, and the solar cycle will be near sunspot maximum. Quadrature geometry is sometimes confusing and observations are influenced by solar rotation. The Fall 2000 and 2001 quadratures are more complex than usual because Ulysses is not in a true polar orbit and the orbital speed of Ulysses about the Sun is becoming comparable to the speed of SOHO about the Sun. In 2000 Ulysses will always be slightly behind the pole but will appear to hang over the pole for over two months because it is moving around the Sun in the same direction as SOHO. In 2001 Ulysses will be slightly in front of the pole so that its footpoint will be directly observable. Detailed plots will be shown of the relative positions of SOHO and Ulysses will their relative positions. In neither case is true quadrature actually achieved, but this works to the observers advantage in 2001.
Gauss Quadratures - the Keystone of Lattice Boltzmann Models
NASA Astrophysics Data System (ADS)
Piaud, Benjamin; Blanco, Stéphane; Fournier, Richard; Ambruş, Victor Eugen; Sofonea, Victor
2014-01-01
In this paper, we compare two families of Lattice Boltzmann (LB) models derived by means of Gauss quadratures in the momentum space. The first one is the HLB(N;Qx,Qy,Qz) family, derived by using the Cartesian coordinate system and the Gauss-Hermite quadrature. The second one is the SLB(N;K,L,M) family, derived by using the spherical coordinate system and the Gauss-Laguerre, as well as the Gauss-Legendre quadratures. These models order themselves according to the maximum order N of the moments of the equilibrium distribution function that are exactly recovered. Microfluidics effects (slip velocity, temperature jump, as well as the longitudinal heat flux that is not driven by a temperature gradient) are accurately captured during the simulation of Couette flow for Knudsen number (kn) up to 0.25.
Discrete Ordinate Quadrature Selection for Reactor-based Eigenvalue Problems
Jarrell, Joshua J; Evans, Thomas M; Davidson, Gregory G
2013-01-01
In this paper we analyze the effect of various quadrature sets on the eigenvalues of several reactor-based problems, including a two-dimensional (2D) fuel pin, a 2D lattice of fuel pins, and a three-dimensional (3D) reactor core problem. While many quadrature sets have been applied to neutral particle discrete ordinate transport calculations, the Level Symmetric (LS) and the Gauss-Chebyshev product (GC) sets are the most widely used in production-level reactor simulations. Other quadrature sets, such as Quadruple Range (QR) sets, have been shown to be more accurate in shielding applications. In this paper, we compare the LS, GC, QR, and the recently developed linear-discontinuous finite element (LDFE) sets, as well as give a brief overview of other proposed quadrature sets. We show that, for a given number of angles, the QR sets are more accurate than the LS and GC in all types of reactor problems analyzed (2D and 3D). We also show that the LDFE sets are more accurate than the LS and GC sets for these problems. We conclude that, for problems where tens to hundreds of quadrature points (directions) per octant are appropriate, QR sets should regularly be used because they have similar integration properties as the LS and GC sets, have no noticeable impact on the speed of convergence of the solution when compared with other quadrature sets, and yield more accurate results. We note that, for very high-order scattering problems, the QR sets exactly integrate fewer angular flux moments over the unit sphere than the GC sets. The effects of those inexact integrations have yet to be analyzed. We also note that the LDFE sets only exactly integrate the zeroth and first angular flux moments. Pin power comparisons and analyses are not included in this paper and are left for future work.
Error estimates for Gaussian quadratures of analytic functions
NASA Astrophysics Data System (ADS)
Milovanovic, Gradimir V.; Spalevic, Miodrag M.; Pranic, Miroslav S.
2009-12-01
For analytic functions the remainder term of Gaussian quadrature formula and its Kronrod extension can be represented as a contour integral with a complex kernel. We study these kernels on elliptic contours with foci at the points ±1 and the sum of semi-axes [varrho]>1 for the Chebyshev weight functions of the first, second and third kind, and derive representation of their difference. Using this representation and following Kronrod's method of obtaining a practical error estimate in numerical integration, we derive new error estimates for Gaussian quadratures.
The development of accurate and efficient methods of numerical quadrature
NASA Technical Reports Server (NTRS)
Feagin, T.
1973-01-01
Some new methods for performing numerical quadrature of an integrable function over a finite interval are described. Each method provides a sequence of approximations of increasing order to the value of the integral. Each approximation makes use of all previously computed values of the integrand. The points at which new values of the integrand are computed are selected in such a way that the order of the approximation is maximized. The methods are compared with the quadrature methods of Clenshaw and Curtis, Gauss, Patterson, and Romberg using several examples.
An Algorithm to Evaluate Imbalances of Quadrature Mixers
NASA Astrophysics Data System (ADS)
Asami, Koji; Arai, Michiaki
It is essential, as bandwidths of wireless communications get wider, to evaluate the imbalances among quadrature mixer ports, in terms of carrier phase offset, IQ gain imbalance, and IQ skew. Because it is time consuming to separate skew, gain imbalance and carrier phase offset evaluation during test is often performed using a composite value, without separation of the imbalance factors. This paper describes an algorithm for enabling separation among quadrature mixer gain imbalance, carrier phase offset, and skew. Since the test time is reduced by the proposed method, it can be applied during high volume production testing.
Trapezoidal rule quadrature algorithms for MIMD distributed memory computers
Lyness, J.N.; Plowman, S.E.
1994-08-01
An approach to multi-dimensional quadrature, designed to exploit parallel architectures, is described. This involves transforming the integral in such a way that an accurate result is given by the trapezoidal rule; and by evaluating the resulting sum in a manner which may be efficiently implemented on parallel architectures. This approach is to be implemented in the Liverpool NAG transputer library.
From Lobatto Quadrature to the Euler Constant "e"
ERIC Educational Resources Information Center
Khattri, Sanjay Kumar
2010-01-01
Based on the Lobatto quadrature, we develop several new closed form approximations to the mathematical constant "e." For validating effectiveness of our approximations, a comparison of our results to the existing approximations is also presented. Another objective of our work is to inspire students to formulate other better approximations by using…
Gaussian rational quadrature formulas for ill-scaled integrands
NASA Astrophysics Data System (ADS)
Illán González, J. R.
2009-12-01
A flexible treatment of Gaussian quadrature formulas based on rational functions is given to evaluate the integral , when f is meromorphic in a neighborhood V of the interval I and W(x) is an ill-scaled weight function. Some numerical tests illustrate the power of this approach in comparison with Gautschi's method.
Archimedes Quadrature of the Parabola: A Mechanical View
ERIC Educational Resources Information Center
Oster, Thomas J.
2006-01-01
In his famous quadrature of the parabola, Archimedes found the area of the region bounded by a parabola and a chord. His method was to fill the region with infinitely many triangles each of whose area he could calculate. In his solution, he stated, without proof, three preliminary propositions about parabolas that were known in his time, but are…
Applying Quadrature Rules with Multiple Nodes to Solving Integral Equations
Hashemiparast, S. M.; Avazpour, L.
2008-09-01
There are many procedures for the numerical solution of Fredholm integral equations. The main idea in these procedures is accuracy of the solution. In this paper, we use Gaussian quadrature with multiple nodes to improve the solution of these integral equations. The application of this method is illustrated via some examples, the related tables are given at the end.
Extraction of quadrature phase information from multiple pulse NMR signals
NASA Technical Reports Server (NTRS)
Rhim, W.-K.; Burum, D. P.; Vaughan, R. W.
1976-01-01
A multiple pulse sequence (8-pulse sequence) used for high-resolution solid state NMR is analyzed with regard to the information available from each of the four wide sampling windows. It is demonstrated that full quadrature phase information can be obtained using only a single phase detector and that, for the commonly encountered situation where the spectral width is much less than the folding frequency, the signals from the various windows can be combined easily using standard complex Fourier transform software. An improvement in the signal-to-noise ratio equal to the square root of 3 is obtained over either standard single or quadrature phase detection schemes. Procedures for correcting spectral distortions are presented.
On a quadrature formula of Gori and Micchelli
NASA Astrophysics Data System (ADS)
Yang, Shijun
2005-04-01
Sparked by Bojanov (J. Comput. Appl. Math. 70 (1996) 349), we provide an alternate approach to quadrature formulas based on the zeros of the Chebyshev polynomial of the first kind for any weight function w introduced and studied in Gori and Micchelli (Math. Comp. 65 (1996) 1567), thereby improving on their observations. Upon expansion of the divided differences, we obtain explicit expressions for the corresponding Cotes coefficients in Gauss-Turan quadrature formulas for and I(fTn;w) for a Gori-Micchelli weight function. It is also interesting to mention what has been neglected for about 30 years by the literature is that, as a consequence of expansion of the divided differences in the special case when , the solution of the famous Turan's Problem 26 raised in 1980 was in fact implied by a result of Micchelli and Rivlin (IBM J. Res. Develop. 16 (1972) 372) in 1972. Some concluding comments are made in the final section.
Accurate Computation of Gaussian Quadrature for Tension Powers
NASA Astrophysics Data System (ADS)
Singer, Saša
2007-09-01
We consider Gaussian quadrature formulæ which exactly integrate a system of tension powers 1,x,x2,…,xn-3, sinh(px), cosh(px), on a given interval [a,b], where n⩾4 is an even integer and p>0 is a given tension parameter. In some applications it is essential that p can be changed dynamically, and we need an efficient "on-demand" algorithm that calculates the nodes and weights of Gaussian quadrature formulas for many different values of p, which are not known in advance. It is an interesting numerical challenge to achieve the required full machine precision accuracy in such an algorithm, for all possible values of p. By exploiting various analytic and numerical techniques, we show that this can be done efficiently for all reasonably low values of n that are of any practical importance.
Quadrature formulae for classes of functions of low smoothness
Nursultanov, E D; Tleukhanova, N T
2003-10-31
For Sobolev and Korobov spaces of functions of several variables a quadrature formula with explicitly defined coefficients and nodes is constructed. This formula is precise for trigonometric polynomials with harmonics from the corresponding step hyperbolic cross. The error of the quadrature formula in the classes W{sup {alpha}}{sub p}[0,1]{sup n}, E{sup {alpha}}[0,1]{sup n} is o((ln M){sup {beta}}/M{sup {alpha}}), where M is the number of nodes and {beta} is a parameter depending on the class. The problem of the approximate calculation of multiple integrals for functions in W{sup {alpha}}{sub p}[0,1]{sup n} is considered in the case when this class does not lie in the space of continuous functions, that is, for {alpha}{<=}1/p.
Efficient quadrature multichannel processor algorithms for MCD applications
NASA Astrophysics Data System (ADS)
Corden, I. R.; Carrasco, R. A.
1992-06-01
The forthcoming third generation of satellites incorporating multichannel demodulator (MCD) processors, and the needs apparent within aviation systems, induce the requirement for efficient band processing algorithms with specific regard to the quadrature processing arrangement. This paper presents a coherent z-domain formulation of the pertinent digital transmultiplexer algorithms for the on-board processing (OBP) scenario, with a view to establishig a set of desirable algorithmic properties suitable for the preferred complex oriented quadrature processing algorithms. Stemming from the principles set forth, an ensemble of new algorithms based upon mixes of Hilbert transforming and real transform algorithms is presented, wherein the established concepts relating to the telephone network transmultiplexer algorithms are able to be exploited in certain cases. Further, the computational load of one of the methods is lower than that of a known prominent OBP related technique. The computational necessities of the various algorithms are laid down for comparative purposes in addition to the mathematical descriptions.
Best quadrature formula on Sobolev class with Chebyshev weight
NASA Astrophysics Data System (ADS)
Xie, Congcong
2008-05-01
Using best interpolation function based on a given function information, we present a best quadrature rule of function on Sobolev class KWr[-1,1] with Chebyshev weight. The given function information means that the values of a function f[set membership, variant]KWr[-1,1] and its derivatives up to r-1 order at a set of nodes x are given. Error bounds are obtained, and the method is illustrated by some examples.
Some new applications of truncated Gauss-Laguerre quadrature formulas
NASA Astrophysics Data System (ADS)
Mastroianni, G.; Monegato, G.
2008-12-01
We show how truncated Gauss-Laguerre quadrature formulas can be used to produce accurate approximations and high rates of convergence, also when they are applied to integrand functions having only an algebraic type decay to zero at infinity. The approach presented in the paper is proposed for the computation of integrals and for the construction of Nyström type interpolants for some second kind integral equations.
Solar Wind Characteristics from SOHO-Sun-Ulysses Quadrature Observations
NASA Technical Reports Server (NTRS)
Poletto, Giannina; Suess, Steve T.; Six, N. Frank (Technical Monitor)
2002-01-01
Over the past few years, we have been running SOHO (Solar and Heliospheric Observatory)-Sun-Ulysses quadrature campaigns, aimed at comparing the plasma properties at coronal altitudes with plasma properties at interplanetary distances. Coronal plasma has been observed by SOHO experiments: mainly, we used LASCO (Large Angle and Spectrometric Coronagraph Experiment) data to understand the overall coronal configuration at the time of quadratures and analyzed SUMER (Solar Ultraviolet Measurements of Emitted Radiation), CDS (Coronal Diagnostic Spectrometer) and UVCS (Ultraviolet Coronagraph Spectrometer) data to derive its physical characteristics. At interplanetary distances, SWICS (Solar Wind Ion Composition Spectrometer) and SWOOPS (Solar Wind Observation over the Poles of the Sun) aboard Ulysses provided us with interplanetary plasma data. Here we report on results from some of the campaigns. We notice that, depending on the geometry of the quadrature, i.e. on whether the radial to Ulysses traverses the corona at high or low latitudes, we are able to study different kinds of solar wind. In particular, a comparison between low-latitude and high-latitude wind, allowed us to provide evidence for differences in the acceleration of polar, fast plasma and equatorial, slow plasma: the latter occurring at higher levels and through a more extended region than fast wind. These properties are shared by both the proton and heavy ions outflows. Quadrature observations may provide useful information also on coronal vs. in situ elemental composition. To this end, we analyzed spectra taken in the corona, at altitudes ranging between approx. 1.02 and 2.2 solar radii, and derived the abundances of a number of ions, including oxygen and iron. Values of the O/Fe ratio, at coronal levels, have been compared with measurements of this ratio made by SWICS at interplanetary distances. Our results are compared with previous findings and predictions from modeling efforts.
NASA Astrophysics Data System (ADS)
Ghasemi, Seiyed E.; Hatami, M.; Hatami, J.; Sahebi, S. A. R.; Ganji, D. D.
2016-02-01
In this paper, flow analysis for a non-Newtonian third grade blood in coronary and femoral arteries is simulated numerically. Blood is considered as the third grade non-Newtonian fluid under periodic body acceleration motion and pulsatile pressure gradient. Differential Quadrature Method (DQM) and Crank Nicholson Method (CNM) are used to solve the Partial Differential Equation (PDE) governing equation by which a good agreement between them was observed in the results. The influences of some physical parameters such as amplitude, lead angle and body acceleration frequency on non-dimensional velocity and profiles are considered. For instance, the results show that increasing the amplitude, Ag, and reducing the lead angle of body acceleration, ϕ, make higher velocity profiles in the center line of both arteries.
Statistical Quadrature Evolution for Continuous-Variable Quantum Key Distribution
NASA Astrophysics Data System (ADS)
Gyongyosi, Laszlo; Imre, Sandor
2016-05-01
We propose a statistical quadrature evolution (SQE) method for multicarrier continuous-variable quantum key distribution (CVQKD). A multicarrier CVQKD protocol utilizes Gaussian subcarrier quantum continuous variables (CV) for information transmission. The SQE framework provides a minimal error estimate of the quadratures of the CV quantum states from the discrete, measured noisy subcarrier variables. We define a method for the statistical modeling and processing of noisy Gaussian subcarrier quadratures. We introduce the terms statistical secret key rate and statistical private classical information, which quantities are derived purely by the statistical functions of our method. We prove the secret key rate formulas for a multiple access multicarrier CVQKD. The framework can be established in an arbitrary CVQKD protocol and measurement setting, and are implementable by standard low-complexity statistical functions, which is particularly convenient for an experimental CVQKD scenario. This work was partially supported by the GOP-1.1.1-11-2012-0092 project sponsored by the EU and European Structural Fund, by the Hungarian Scientific Research Fund - OTKA K-112125, and by the COST Action MP1006.
Discrete ordinates with new quadrature sets and modified source conditions
Ganguly, K.; Allen, E.J., Victory, H.D. Jr. )
1989-01-01
A major shortcoming of the discrete ordinates method with the Gauss-Legendre quadrature set is that when the number of secondaries per primary c and the order of approximation N are not too large, all the (N + 1)v (the flux being of the form exp({minus}x/v)) lie in ({minus}1,1). It is known, however, that the largest v{sub j} corresponding to the asymptotic flux is greater than unity. The Legendre polynomial used for obtaining the quadrature set is orthogonal with respect to weight unity in the range ({minus}1,1). However, the Case and Zweifel eigenfunctions derived from the exact solution of one-speed transport theory are orthogonal with respect to a complicated weight function w({mu}) and {mu} in the half-range and full-range cases, respectively. In this paper, the authors have used a set of orthogonal polynomials with respect to w ({mu}) to develop quadrature sets to be used in the discrete ordinates calculation.
Fast evaluation of quadrature formulae on the sphere
NASA Astrophysics Data System (ADS)
Keiner, Jens; Potts, Daniel
2008-03-01
Recently, a fast approximate algorithm for the evaluation of expansions in terms of standard mathrm{L}^2left(mathbb{S}^2right) -orthonormal spherical harmonics at arbitrary nodes on the sphere mathbb{S}^2 has been proposed in [S. Kunis and D. Potts. Fast spherical Fourier algorithms. JE Comput. Appl. Math., 161:75-98, 2003]. The aim of this paper is to develop a new fast algorithm for the adjoint problem which can be used to compute expansion coefficients from sampled data by means of quadrature rules. We give a formulation in matrix-vector notation and an explicit factorisation of the spherical Fourier matrix based on the former algorithm. Starting from this, we obtain the corresponding factorisation of the adjoint spherical Fourier matrix and are able to describe the associated algorithm for the adjoint transformation which can be employed to evaluate quadrature rules for arbitrary weights and nodes on the sphere. We provide results of numerical tests showing the stability of the obtained algorithm using as examples classical Gauss-Legendre and Clenshaw-Curtis quadrature rules as well as the HEALPix pixelation scheme and an equidistribution.
Testing the Empirical Shock Arrival Model Using Quadrature Observations
NASA Technical Reports Server (NTRS)
Gopalswamy, N.; Makela, P.; Xie, H.; Yashiro, S.
2013-01-01
The empirical shock arrival (ESA) model was developed based on quadrature data from Helios (in situ) and P-78 (remote sensing) to predict the Sun-Earth travel time of coronal mass ejections (CMEs). The ESA model requires earthward CME speed as input, which is not directly measurable from coronagraphs along the Sun-Earth line. The Solar Terrestrial Relations Observatory (STEREO) and the Solar and Heliospheric Observatory (SOHO) were in quadrature during 20102012, so the speeds of Earth-directed CMEs were observed with minimal projection effects. We identified a set of 20 full halo CMEs in the field of view of SOHO that were also observed in quadrature by STEREO. We used the earthward speed from STEREO measurements as input to the ESA model and compared the resulting travel times with the observed ones from L1 monitors. We find that the model predicts the CME travel time within about 7.3 h, which is similar to the predictions by the ENLIL model. We also find that CME-CME and CME-coronal hole interaction can lead to large deviations from model predictions.
An Application of the Quadrature-Free Discontinuous Galerkin Method
NASA Technical Reports Server (NTRS)
Lockard, David P.; Atkins, Harold L.
2000-01-01
The process of generating a block-structured mesh with the smoothness required for high-accuracy schemes is still a time-consuming process often measured in weeks or months. Unstructured grids about complex geometries are more easily generated, and for this reason, methods using unstructured grids have gained favor for aerodynamic analyses. The discontinuous Galerkin (DG) method is a compact finite-element projection method that provides a practical framework for the development of a high-order method using unstructured grids. Higher-order accuracy is obtained by representing the solution as a high-degree polynomial whose time evolution is governed by a local Galerkin projection. The traditional implementation of the discontinuous Galerkin uses quadrature for the evaluation of the integral projections and is prohibitively expensive. Atkins and Shu introduced the quadrature-free formulation in which the integrals are evaluated a-priori and exactly for a similarity element. The approach has been demonstrated to possess the accuracy required for acoustics even in cases where the grid is not smooth. Other issues such as boundary conditions and the treatment of non-linear fluxes have also been studied in earlier work This paper describes the application of the quadrature-free discontinuous Galerkin method to a two-dimensional shear layer problem. First, a brief description of the method is given. Next, the problem is described and the solution is presented. Finally, the resources required to perform the calculations are given.
Fast wavelength-scanning interferometry technique with derivative detection of quadrature signals
NASA Astrophysics Data System (ADS)
Číp, O.; Mikel, B.; Lazar, J.
2006-04-01
We present a laser interferometer where a narrow-line width tuneable VCSEL laser (Vertical-Cavity Surface-Emitting Laser) working at 760 nm is used. For the detection of an absolute distance, we have used a fast wavelength-scanning interferometry technique. In the first part of the work we introduce the absolute laser interferometer as a demonstrator for research of a digital detection of quadrature signals (X-cos and Y-sin). This interferometer uses polarized beams and magnitude division of interference fringes. The wavelength of VCSEL laser is swept with the mode-hop free tuning range more than 1.2 nm, by means of the amplitude modulation of the injection current. At the same time, the operating temperature of the VCSEL is stabilized with a fast digital temperature controller. We control the wavelength value and whole tuning process of the laser with the frequency lock to selected modes of an external Fabry-Perot etalon. Except the frequency lock, the Fabry-Perot mode spectrum identifies wavelength-tuning interval of VCSEL during each sweep. A digital signal processor (DSP) is heart of the control and detection system. It samples intensity signal from Fabry- Perot etalon and X-Y quadrature signals from the detection unit of the interferometer. After 1 nm sweep of the VCSEL wavelength, we obtain a number of passed interference fringes and the number of passed Fabry-Perot resonance modes, at the same time. On basis of these measured quantities we are able to calculate the instantaneous value of the optical path length difference between the measuring and reference arm of the demonstrational interferometer. The other part of the work is oriented to research and experimental testing of the digital detection of quadrature signals (X-cos and Y-sin) processed only on basis of one intensity signal (X-axis) that is produced by a simple photo-detector. On basis of traditional inversion function arctan(Y/X) we are able to determine instantaneous phase between interference
Optical performance monitoring technique using software-based synchronous amplitude histograms.
Choi, H G; Chang, J H; Kim, Hoon; Chung, Y C
2014-10-01
We propose and demonstrate a simple technique to monitor both the optical signal-to-noise ratio (OSNR) and chromatic dispersion (CD) by using the software-based synchronous amplitude histogram (SAH) analysis. We exploit the software-based synchronization technique to construct SAHs from the asynchronously sampled intensities of the signal. The use of SAHs facilitates the accurate extraction of the monitoring parameters at the center of the symbol. Thus, unlike in the case of using the technique based on the asynchronous amplitude histogram (AAH), this technique is not affected by the transient characteristics of the modulated signals. The performance of the proposed monitoring technique is evaluated experimentally by using 10-Gbaud quadrature phase-shift keying (QPSK) and quadrature amplitude modulation (QAM) signals over wide ranges of OSNR and CD. We also evaluate the robustness of the proposed technique to the signal's transient characteristics. PMID:25321978
Advanced quadratures and periodic boundary conditions in parallel 3D S{sub n} transport
Manalo, K.; Yi, C.; Huang, M.; Sjoden, G.
2013-07-01
Significant updates in numerical quadratures have warranted investigation with 3D Sn discrete ordinates transport. We show new applications of quadrature departing from level symmetric (S{sub 2}o). investigating 3 recently developed quadratures: Even-Odd (EO), Linear-Discontinuous Finite Element - Surface Area (LDFE-SA), and the non-symmetric Icosahedral Quadrature (IC). We discuss implementation changes to 3D Sn codes (applied to Hybrid MOC-Sn TITAN and 3D parallel PENTRAN) that can be performed to accommodate Icosahedral Quadrature, as this quadrature is not 90-degree rotation invariant. In particular, as demonstrated using PENTRAN, the properties of Icosahedral Quadrature are suitable for trivial application using periodic BCs versus that of reflective BCs. In addition to implementing periodic BCs for 3D Sn PENTRAN, we implemented a technique termed 'angular re-sweep' which properly conditions periodic BCs for outer eigenvalue iterative loop convergence. As demonstrated by two simple transport problems (3-group fixed source and 3-group reflected/periodic eigenvalue pin cell), we remark that all of the quadratures we investigated are generally superior to level symmetric quadrature, with Icosahedral Quadrature performing the most efficiently for problems tested. (authors)
Decision-directed automatic gain control for MAPSK systems. [M-ary Amplitude and Phase Shift Keying
NASA Technical Reports Server (NTRS)
Weber, W. J., III
1974-01-01
An automatic gain control (AGC) loop is presented for use with M-ary amplitude and phase shift keying (MAPSK) systems. The gain control amplifier is regulated by an error signal formed by the difference between the estimated amplitude level and the received amplitude level. The AGC performance is thus independent of the short-term average received signal energy. AGC loop analysis and simulation is presented for M-ary amplitude shift keying and quadrature amplitude shift keying. The AGC is shown to have a negligible degradation on the symbol probability of error for most practical cases. A generalized AGC for an arbitrary MAPSK system is presented.
Quadrature rules with multiple nodes for evaluating integrals with strong singularities
NASA Astrophysics Data System (ADS)
Milovanovic, Gradimir V.; Spalevic, Miodrag M.
2006-05-01
We present a method based on the Chakalov-Popoviciu quadrature formula of Lobatto type, a rather general case of quadrature with multiple nodes, for approximating integrals defined by Cauchy principal values or by Hadamard finite parts. As a starting point we use the results obtained by L. Gori and E. Santi (cf. On the evaluation of Hilbert transforms by means of a particular class of Turan quadrature rules, Numer. Algorithms 10 (1995), 27-39; Quadrature rules based on s-orthogonal polynomials for evaluating integrals with strong singularities, Oberwolfach Proceedings: Applications and Computation of Orthogonal Polynomials, ISNM 131, Birkhauser, Basel, 1999, pp. 109-119). We generalize their results by using some of our numerical procedures for stable calculation of the quadrature formula with multiple nodes of Gaussian type and proposed methods for estimating the remainder term in such type of quadrature formulae. Numerical examples, illustrations and comparisons are also shown.
Chen, Hua-Pin
2014-01-01
The electronically tunable quadrature oscillator using a single multiple-output current controlled current differencing transconductance amplifier (MO-CCCDTA) and grounded passive components is presented. The proposed configuration uses a single MO-CCCDTA, two grounded capacitors and one grounded resistor. Two high-output impedance quadrature current signals and two quadrature voltage signals with 90° phase difference. The oscillation condition and oscillation frequency of the proposed quadrature oscillator are independently controllable. The use of only grounded passive components makes the proposed circuit ideal for integrated circuit implementation. PMID:25121124
Experimental demonstration of microring quadrature phase-shift keying modulators.
Dong, Po; Xie, Chongjin; Chen, Long; Fontaine, Nicolas K; Chen, Young-kai
2012-04-01
Advanced optical modulation formats are a key technology to increase the capacity of optical communication networks. Mach-Zehnder modulators are typically used to generate various modulation formats. Here, we report the first experimental demonstration of quadrature phase-shift keying (QPSK) modulation using compact microring modulators. Generation of 20 Gb/s QPSK signals is demonstrated with 30 μm radius silicon ring modulators with drive voltages of ~6 V. These compact QPSK modulators may be used in miniature optical transponders for high-capacity optical data links. PMID:22466187
Noise-cancelling quadrature magnetic position, speed and direction sensor
Preston, Mark A.; King, Robert D.
1996-01-01
An array of three magnetic sensors in a single package is employed with a single bias magnet for sensing shaft position, speed and direction of a motor in a high magnetic noise environment. Two of the three magnetic sensors are situated in an anti-phase relationship (i.e., 180.degree. out-of-phase) with respect to the relationship between the other of the two sensors and magnetically salient target, and the third magnetic sensor is situated between the anti-phase sensors. The result is quadrature sensing with noise immunity for accurate relative position, speed and direction measurements.
NASA Astrophysics Data System (ADS)
Honma, Satoshi; Sekiguchi, Toru
2014-09-01
The utilization of spatial quadrature amplitude modulation (SQAM) signals with amplitude and phase modulation is a simple method used to improve storage capacity in a holographic data storage system. We propose a multilevel phase and amplitude modulation method for holographic memories with a programmable phase modulator (PPM). In this method, holographic page data is recorded by a two-step exposure process for different phase-modulated data. There is no need to adjust the positions of spatial light modulators (SLM) with high accuracy because we use only one spatial modulator. We estimate the quality of 16 SQAM signals produced by our technique.
Amplitude and phase modulation of radiation in a travelling-wave amplifier based on a laser diode
Bogatov, A P; D'yachkov, N V; Drakin, A E; Gushchik, T I
2013-08-31
An analytical solution (in quadratures) to the problem of propagation of quasi-monochromatic optical signal in a semiconductor amplifier under harmonic modulation of its pump current is obtained for the first time. It is shown that the modulation of the output radiation has amplitude and phase features. The relation is found between the coefficients of the amplitude and phase modulation with the effect of gain saturation taken into account. Adequacy of the results obtained is confirmed experimentally. (control of laser radiation parameters)
Calculating scattering amplitudes efficiently
Dixon, L.
1996-01-01
We review techniques for more efficient computation of perturbative scattering amplitudes in gauge theory, in particular tree and one- loop multi-parton amplitudes in QCD. We emphasize the advantages of (1) using color and helicity information to decompose amplitudes into smaller gauge-invariant pieces, and (2) exploiting the analytic properties of these pieces, namely their cuts and poles. Other useful tools include recursion relations, special gauges and supersymmetric rearrangements. 46 refs., 11 figs.
The Nature of the Nodes, Weights and Degree of Precision in Gaussian Quadrature Rules
ERIC Educational Resources Information Center
Prentice, J. S. C.
2011-01-01
We present a comprehensive proof of the theorem that relates the weights and nodes of a Gaussian quadrature rule to its degree of precision. This level of detail is often absent in modern texts on numerical analysis. We show that the degree of precision is maximal, and that the approximation error in Gaussian quadrature is minimal, in a…
A Family of Exponential Fitting Direct Quadrature Methods for Volterra Integral Equations
NASA Astrophysics Data System (ADS)
Cardone, A.; Ferro, M.; Ixaru, L. Gr.; Paternoster, B.
2010-09-01
A new class of direct quadrature methods for the solution of Volterra Integral Equations with periodic solution is illustrated. Such methods are based on an exponential fitting gaussian quadrature formula, whose coefficients depend on the problem parameters, in order to better reproduce the behavior the analytical solution. The construction of the methods is described, together with the analysis of the order of accuracy.
General n-dimensional quadrature transform and its application to interferogram demodulation.
Servin, Manuel; Quiroga, Juan Antonio; Marroquin, Jose Luis
2003-05-01
Quadrature operators are useful for obtaining the modulating phase phi in interferometry and temporal signals in electrical communications. In carrier-frequency interferometry and electrical communications, one uses the Hilbert transform to obtain the quadrature of the signal. In these cases the Hilbert transform gives the desired quadrature because the modulating phase is monotonically increasing. We propose an n-dimensional quadrature operator that transforms cos(phi) into -sin(phi) regardless of the frequency spectrum of the signal. With the quadrature of the phase-modulated signal, one can easily calculate the value of phi over all the domain of interest. Our quadrature operator is composed of two n-dimensional vector fields: One is related to the gradient of the image normalized with respect to local frequency magnitude, and the other is related to the sign of the local frequency of the signal. The inner product of these two vector fields gives us the desired quadrature signal. This quadrature operator is derived in the image space by use of differential vector calculus and in the frequency domain by use of a n-dimensional generalization of the Hilbert transform. A robust numerical algorithm is given to find the modulating phase of two-dimensional single-image closed-fringe interferograms by use of the ideas put forward. PMID:12747439
NASA Technical Reports Server (NTRS)
Smith, A. C.; Yang, H.
1989-01-01
The quadrature phase detection technique was used to simultaneously monitor the phase and amplitude of a toneburst signal normally reflected from an adhesively bonded steel-to-rubber interface. The measured phase was found to show a positive shift for all bonded samples with respect to the disbonded state - the phase shift being larger for samples with weaker bonds, as manifested by smaller values of applied tensile loads at failure. A model calculation, which incorporates the concept of interfacial strength into the usual problem of wave propagation in multilayered media, was used to deduce a bond-quality parameter from an experimentally measured phase shift. This bond-quality parameter was found to be correlated with the tensile strength of the adhesive bonds at failure loads.
Bandwidth Efficient Wireless Digital Modem Developed
NASA Technical Reports Server (NTRS)
Kifle, Muli
1999-01-01
NASA Lewis Research Center has developed a digital approach for broadcasting highfidelity audio (nearly compact disk (CD) quality sound) in the commercial frequencymodulated (FM) broadcast band. This digital approach provides a means of achieving high data transmission rates with low hardware complexity--including low mass, size, and power consumption. Lewis has completed the design and prototype development of a bandwidth-efficient digital modem (modulator and demodulator) that uses a spectrally efficient modulation scheme: 16-ary rectangular quadrature amplitude modulation, or 16- ary QAM. The digital implementation is based strictly on inexpensive, commercial off-theshelf digital signal processing (DSP) hardware to perform up and down conversions and pulse shaping. The digital modem transmits data at rates up to 76 kilobits per second (kbps), which is almost 3 times faster than standard 28.8-kbps telephone modems. In addition, the modem offers improved power and spectral performance, flexible operation, and low-cost implementation.
Quadrature phase interferometer for high resolution force spectroscopy
NASA Astrophysics Data System (ADS)
Paolino, Pierdomenico; Aguilar Sandoval, Felipe A.; Bellon, Ludovic
2013-09-01
In this article, we present a deflection measurement setup for Atomic Force Microscopy (AFM). It is based on a quadrature phase differential interferometer: we measure the optical path difference between a laser beam reflecting above the cantilever tip and a reference beam reflecting on the static base of the sensor. A design with very low environmental susceptibility and another allowing calibrated measurements on a wide spectral range are described. Both enable a very high resolution (down to 2.5 × 10^{-15} m/sqrtHz), illustrated by thermal noise measurements on AFM cantilevers. They present an excellent long-term stability and a constant sensitivity independent of the optical phase of the interferometer. A quick review shows that our precision is equaling or out-performing the best results reported in the literature, but for a much larger deflection range, up to a few μm.
Quadrature phase interferometer for high resolution force spectroscopy
Paolino, Pierdomenico; Aguilar Sandoval, Felipe A.; Bellon, Ludovic
2013-09-15
In this article, we present a deflection measurement setup for Atomic Force Microscopy (AFM). It is based on a quadrature phase differential interferometer: we measure the optical path difference between a laser beam reflecting above the cantilever tip and a reference beam reflecting on the static base of the sensor. A design with very low environmental susceptibility and another allowing calibrated measurements on a wide spectral range are described. Both enable a very high resolution (down to 2.5×10{sup −15} m/√(Hz)), illustrated by thermal noise measurements on AFM cantilevers. They present an excellent long-term stability and a constant sensitivity independent of the optical phase of the interferometer. A quick review shows that our precision is equaling or out-performing the best results reported in the literature, but for a much larger deflection range, up to a few μm.
Weighted discrete least-squares polynomial approximation using randomized quadratures
NASA Astrophysics Data System (ADS)
Zhou, Tao; Narayan, Akil; Xiu, Dongbin
2015-10-01
We discuss the problem of polynomial approximation of multivariate functions using discrete least squares collocation. The problem stems from uncertainty quantification (UQ), where the independent variables of the functions are random variables with specified probability measure. We propose to construct the least squares approximation on points randomly and uniformly sampled from tensor product Gaussian quadrature points. We analyze the stability properties of this method and prove that the method is asymptotically stable, provided that the number of points scales linearly (up to a logarithmic factor) with the cardinality of the polynomial space. Specific results in both bounded and unbounded domains are obtained, along with a convergence result for Chebyshev measure. Numerical examples are provided to verify the theoretical results.
Quadrature phase interferometer for high resolution force spectroscopy.
Paolino, Pierdomenico; Aguilar Sandoval, Felipe A; Bellon, Ludovic
2013-09-01
In this article, we present a deflection measurement setup for Atomic Force Microscopy (AFM). It is based on a quadrature phase differential interferometer: we measure the optical path difference between a laser beam reflecting above the cantilever tip and a reference beam reflecting on the static base of the sensor. A design with very low environmental susceptibility and another allowing calibrated measurements on a wide spectral range are described. Both enable a very high resolution (down to 2.5×10(-15) m/√Hz), illustrated by thermal noise measurements on AFM cantilevers. They present an excellent long-term stability and a constant sensitivity independent of the optical phase of the interferometer. A quick review shows that our precision is equaling or out-performing the best results reported in the literature, but for a much larger deflection range, up to a few μm. PMID:24089852
Terahertz single-shot quadrature phase-shifting interferometry.
Földesy, Péter
2012-10-01
A single-shot quadrature phase-shifting interferometry architecture is presented that is applicable to antenna coupled detector technologies. The method is based on orthogonally polarized object and reference beams and on linear and circular polarization sensitive antennas in space-division multiplexing. The technique can be adapted to two-, three-, and four-step and Gabor holography recordings. It is also demonstrated that the space-division multiplexing does not necessarily cause sparse sampling. A sub-THz detector array is presented containing multiple on-chip antennas and FET plasma wave detectors implemented in a 90 nm complementary metal-oxide semiconductor technology. As an example, two-step phase-shifting reconstruction results are given at 360 GHz. PMID:23027273
Quadrature squeezed photons from a two-level system.
Schulte, Carsten H H; Hansom, Jack; Jones, Alex E; Matthiesen, Clemens; Le Gall, Claire; Atatüre, Mete
2015-09-10
Resonance fluorescence arises from the interaction of an optical field with a two-level system, and has played a fundamental role in the development of quantum optics and its applications. Despite its conceptual simplicity, it entails a wide range of intriguing phenomena, such as the Mollow-triplet emission spectrum, photon antibunching and coherent photon emission. One fundamental aspect of resonance fluorescence--squeezing in the form of reduced quantum fluctuations in the single photon stream from an atom in free space--was predicted more than 30 years ago. However, the requirement to operate in the weak excitation regime, together with the combination of modest oscillator strength of atoms and low collection efficiencies, has continued to necessitate stringent experimental conditions for the observation of squeezing with atoms. Attempts to circumvent these issues had to sacrifice antibunching, owing to either stimulated forward scattering from atomic ensembles or multi-photon transitions inside optical cavities. Here, we use an artificial atom with a large optical dipole enabling 100-fold improvement of the photon detection rate over the natural atom counterpart and reach the necessary conditions for the observation of quadrature squeezing in single resonance-fluorescence photons. By implementing phase-dependent homodyne intensity-correlation detection, we demonstrate that the electric field quadrature variance of resonance fluorescence is three per cent below the fundamental limit set by vacuum fluctuations, while the photon statistics remain antibunched. The presence of squeezing and antibunching simultaneously is a fully non-classical outcome of the wave-particle duality of photons. PMID:26322581
Residual Distribution Schemes for Conservation Laws Via Adaptive Quadrature
NASA Technical Reports Server (NTRS)
Barth, Timothy; Abgrall, Remi; Biegel, Bryan (Technical Monitor)
2000-01-01
This paper considers a family of nonconservative numerical discretizations for conservation laws which retains the correct weak solution behavior in the limit of mesh refinement whenever sufficient order numerical quadrature is used. Our analysis of 2-D discretizations in nonconservative form follows the 1-D analysis of Hou and Le Floch. For a specific family of nonconservative discretizations, it is shown under mild assumptions that the error arising from non-conservation is strictly smaller than the discretization error in the scheme. In the limit of mesh refinement under the same assumptions, solutions are shown to satisfy an entropy inequality. Using results from this analysis, a variant of the "N" (Narrow) residual distribution scheme of van der Weide and Deconinck is developed for first-order systems of conservation laws. The modified form of the N-scheme supplants the usual exact single-state mean-value linearization of flux divergence, typically used for the Euler equations of gasdynamics, by an equivalent integral form on simplex interiors. This integral form is then numerically approximated using an adaptive quadrature procedure. This renders the scheme nonconservative in the sense described earlier so that correct weak solutions are still obtained in the limit of mesh refinement. Consequently, we then show that the modified form of the N-scheme can be easily applied to general (non-simplicial) element shapes and general systems of first-order conservation laws equipped with an entropy inequality where exact mean-value linearization of the flux divergence is not readily obtained, e.g. magnetohydrodynamics, the Euler equations with certain forms of chemistry, etc. Numerical examples of subsonic, transonic and supersonic flows containing discontinuities together with multi-level mesh refinement are provided to verify the analysis.
Greenblatt, M.H.
1958-03-25
This patent pertains to pulse amplitude analyzers for sorting and counting a serles of pulses, and specifically discloses an analyzer which ls simple in construction and presents the puise height distribution visually on an oscilloscope screen. According to the invention, the pulses are applied to the vertical deflection plates of an oscilloscope and trigger the horizontal sweep. Each pulse starts at the same point on the screen and has a maximum amplitude substantially along the same vertical line. A mask is placed over the screen except for a slot running along the line where the maximum amplitudes of the pulses appear. After the slot has been scanned by a photocell in combination with a slotted rotating disk, the photocell signal is displayed on an auxiliary oscilloscope as vertical deflection along a horizontal time base to portray the pulse amplitude distribution.
Lewis, I.A.D.
1956-05-15
This patent pentains to an electrical pulse amplitude analyzer, capable of accepting input pulses having a separation between adjacent pulses in the order of one microsecond while providing a large number of channels of classification. In its broad aspect the described pulse amplitude analyzer utilizes a storage cathode ray tube und control circuitry whereby the amplitude of the analyzed pulses controls both the intensity and vertical defiection of the beam to charge particular spots in horizontal sectors of the tube face as the beam is moved horizontally across the tube face. As soon as the beam has swept the length of the tube the information stored therein is read out by scanning individually each horizontal sector corresponding to a certain range of pulse amplitudes and applying the output signal from each scan to separate indicating means.
Topics in Scattering Amplitudes
NASA Astrophysics Data System (ADS)
Dennen, Tristan Lucas
In Part 1, we combine on-shell methods with the six-dimensional helicity formalism of Cheung and O'Connell to construct tree-level and multiloop scattering amplitudes. As a nontrivial multiloop example, we confirm that the recently constructed four-loop four-point amplitude of N=4 super-Yang-Mills theory, including nonplanar contributions, is valid for dimensions less than or equal to six. We demonstrate that the tree-level amplitudes of maximal super-Yang-Mills theory in six dimensions, when stripped of their overall momentum and supermomentum delta functions, are covariant with respect to the six-dimensional dual conformal group. We demonstrate that this property is also present for loop amplitudes. In Part 2, we explore consequences of the recently discovered duality between color and kinematics, which states that kinematic numerators in a diagrammatic expansion of gauge-theory amplitudes can be arranged to satisfy Jacobi-like identities in one-to-one correspondence to the associated color factors. The related squaring relations express gravity amplitudes in terms of gauge-theory ingredients. We then present a Yang-Mills Lagrangian whose diagrams through five points manifestly satisfy the duality between color and kinematics. Finally, we compute the coefficient of the potential three-loop divergence in pure N=4 supergravity and show that it vanishes, contrary to expectations from symmetry arguments.
Multidimensional Hermite-Gaussian quadrature formulae and their application to nonlinear estimation
NASA Technical Reports Server (NTRS)
Mcreynolds, S. R.
1975-01-01
A simplified technique is proposed for calculating multidimensional Hermite-Gaussian quadratures that involves taking the square root of a matrix by the Cholesky algorithm rather than computation of the eigenvectors of the matrix. Ways of reducing the dimension, number, and order of the quadratures are set forth. If the function f(x) under the integral sign is not well approximated by a low-order algebraic expression, the order of the quadrature may be reduced by factoring f(x) into an expression that is nearly algebraic and one that is Gaussian.
NASA Technical Reports Server (NTRS)
Desmarais, R. N.
1975-01-01
Computer programs for computing Gaussian quadrature abscissas and weights are described. For the classical case the programs use Laguerre iteration to compute abscissas as zeros of orthogonal polynomials. The polynomials are evaluated from known recursion coefficients. The nonclassical case is handled similarly except that the recursion coefficients are computed by numerical integration. A sample problem, with input and output, is presented to illustrate the use of the programs. It computes the quadrature abscissas and weights associated with the weight function over the interval (0,1) for quadrature orders from 16 to 96 in increments of 8.
NASA Astrophysics Data System (ADS)
Knizhnerman, Leonid
2010-01-01
Stability of passing from Gaussian quadrature data to the Lanczos recurrence coefficients is considered. Special attention is paid to estimates explicitly expressed in terms of quadrature data and not having weights in denominators. It has been shown that the recent approach, exploiting integral representation of Hankel determinants, implies quantitative improvement of D. Laurie's constructive estimate. It has also been demonstrated that a particular implementation on the Hankel determinant approach gives an estimate being unimprovable up to a coefficient; the corresponding example involves quadrature data with a small but not too small weight. It follows that polynomial increase of a general case upper bound in terms of the dimension is unavoidable.
NASA Astrophysics Data System (ADS)
Bauman, Brian J.; Xiao, Hong
2010-08-01
Forbes introduced the usage of Gaussian quadratures in optical design for circular pupils and fields, and for a specific visible wavelength band. In this paper, Gaussian quadrature methods of selecting rays in ray-tracing are derived for noncircular pupil shapes, such as obscured and vignetted apertures. In addition, these methods are generalized for square fields, and for integrating performance over arbitrary wavelength bands. Integration over wavelength is aided by the use of a novel chromatic coordinate. These quadratures achieve low calculations with fewer rays (by orders of magnitude) than uniform sampling schemes.
Reissner-Mindlin Legendre Spectral Finite Elements with Mixed Reduced Quadrature
Brito, K. D.; Sprague, M. A.
2012-10-01
Legendre spectral finite elements (LSFEs) are examined through numerical experiments for static and dynamic Reissner-Mindlin plate bending and a mixed-quadrature scheme is proposed. LSFEs are high-order Lagrangian-interpolant finite elements with nodes located at the Gauss-Lobatto-Legendre quadrature points. Solutions on unstructured meshes are examined in terms of accuracy as a function of the number of model nodes and total operations. While nodal-quadrature LSFEs have been shown elsewhere to be free of shear locking on structured grids, locking is demonstrated here on unstructured grids. LSFEs with mixed quadrature are, however, locking free and are significantly more accurate than low-order finite-elements for a given model size or total computation time.
NASA Astrophysics Data System (ADS)
Evans, W. A. B.; Torre, A.
2012-11-01
The paper focusses on the advantages of using high-order Gauss-Legendre quadratures for the precise evaluation of integrals with both smooth and rapidly changing integrands. Aspects of their precision are analysed in the light of Gauss' error formula. Some "test examples" are considered and evaluated in multiple precision to ≈ 200 significant decimal digits with David Bailey's multiprecision package to eliminate truncation/rounding errors. The increase of precision on doubling the number of subintervals is analysed, the relevant quadrature attribute being the precision increment. In order to exemplify the advantages that high-order quadrature afford, the technique is then used to evaluate several plots of the Rayleigh-Sommerfeld diffraction integral for axi-symmetric source fields defined on a planar aperture. A comparison of the high-order quadrature method against various FFT-based methods is finally given.
Cui, Junning; He, Zhangqiang; Jiu, Yuanwei; Tan, Jiubin; Sun, Tao
2016-09-01
The demand for minimal cyclic nonlinearity error in laser interferometry is increasing as a result of advanced scientific research projects. Research shows that the quadrature phase error is the main effect that introduces cyclic nonlinearity error, and polarization-mixing cross talk during beam splitting is the main error source that causes the quadrature phase error. In this paper, a new homodyne quadrature laser interferometer configuration based on nonpolarization beam splitting and balanced interference between two circularly polarized laser beams is proposed. Theoretical modeling indicates that the polarization-mixing cross talk is elaborately avoided through nonpolarizing and Wollaston beam splitting, with a minimum number of quadrature phase error sources involved. Experimental results show that the cyclic nonlinearity error of the interferometer is up to 0.6 nm (peak-to-valley value) without any correction and can be further suppressed to 0.2 nm with a simple gain and offset correction method. PMID:27607285
Information entropy of Gegenbauer polynomials and Gaussian quadrature
NASA Astrophysics Data System (ADS)
Sánchez-Ruiz, Jorge
2003-05-01
In a recent paper (Buyarov V S, López-Artés P, Martínez-Finkelshtein A and Van Assche W 2000 J. Phys. A: Math. Gen. 33 6549-60), an efficient method was provided for evaluating in closed form the information entropy of the Gegenbauer polynomials C(lambda)n(x) in the case when lambda = l in Bbb N. For given values of n and l, this method requires the computation by means of recurrence relations of two auxiliary polynomials, P(x) and H(x), of degrees 2l - 2 and 2l - 4, respectively. Here it is shown that P(x) is related to the coefficients of the Gaussian quadrature formula for the Gegenbauer weights wl(x) = (1 - x2)l-1/2, and this fact is used to obtain the explicit expression of P(x). From this result, an explicit formula is also given for the polynomial S(x) = limnrightarrowinfty P(1 - x/(2n2)), which is relevant to the study of the asymptotic (n rightarrow infty with l fixed) behaviour of the entropy.
Electronically Tunable Differential Integrator: Linear Voltage Controlled Quadrature Oscillator
Nandi, Rabindranath; Pattanayak, Sandhya; Das, Sagarika
2015-01-01
A new electronically tunable differential integrator (ETDI) and its extension to voltage controlled quadrature oscillator (VCQO) design with linear tuning law are proposed; the active building block is a composite current feedback amplifier with recent multiplication mode current conveyor (MMCC) element. Recently utilization of two different kinds of active devices to form a composite building block is being considered since it yields a superior functional element suitable for improved quality circuit design. The integrator time constant (τ) and the oscillation frequency (ωo) are tunable by the control voltage (V) of the MMCC block. Analysis indicates negligible phase error (θe) for the integrator and low active ωo-sensitivity relative to the device parasitic capacitances. Satisfactory experimental verifications on electronic tunability of some wave shaping applications by the integrator and a double-integrator feedback loop (DIFL) based sinusoid oscillator with linear fo variation range of 60 KHz~1.8 MHz at low THD of 2.1% are verified by both simulation and hardware tests. PMID:27347537
Quantitative phase imaging using grating-based quadrature phase interferometer
NASA Astrophysics Data System (ADS)
Wu, Jigang; Yaqoob, Zahid; Heng, Xin; Cui, Xiquan; Yang, Changhuei
2007-02-01
In this paper, we report the use of holographic gratings, which act as the free-space equivalent of the 3x3 fiber-optic coupler, to perform full field phase imaging. By recording two harmonically-related gratings in the same holographic plate, we are able to obtain nontrivial phase shift between different output ports of the gratings-based Mach-Zehnder interferometer. The phase difference can be adjusted by changing the relative phase of the recording beams when recording the hologram. We have built a Mach-Zehnder interferometer using harmonically-related holographic gratings with 600 and 1200 lines/mm spacing. Two CCD cameras at the output ports of the gratings-based Mach-Zehnder interferometer are used to record the full-field quadrature interferograms, which are subsequently processed to reconstruct the phase image. The imaging system has ~12X magnification with ~420μmx315μm field-of-view. To demonstrate the capability of our system, we have successfully performed phase imaging of a pure phase object and a paramecium caudatum.
Radiation transport modeling using extended quadrature method of moments
NASA Astrophysics Data System (ADS)
Vikas, V.; Hauck, C. D.; Wang, Z. J.; Fox, R. O.
2013-08-01
The radiative transfer equation describes the propagation of radiation through a material medium. While it provides a highly accurate description of the radiation field, the large phase space on which the equation is defined makes it numerically challenging. As a consequence, significant effort has gone into the development of accurate approximation methods. Recently, an extended quadrature method of moments (EQMOM) has been developed to solve univariate population balance equations, which also have a large phase space and thus face similar computational challenges. The distinct advantage of the EQMOM approach over other moment methods is that it generates moment equations that are consistent with a positive phase space density and has a moment inversion algorithm that is fast and efficient. The goal of the current paper is to present the EQMOM method in the context of radiation transport, to discuss advantages and disadvantages, and to demonstrate its performance on a set of standard one-dimensional benchmark problems that encompass optically thin, thick, and transition regimes. Special attention is given in the implementation to the issue of realizability—that is, consistency with a positive phase space density. Numerical results in one dimension are promising and lay the foundation for extending the same framework to multiple dimensions.
Electronically Tunable Differential Integrator: Linear Voltage Controlled Quadrature Oscillator.
Nandi, Rabindranath; Pattanayak, Sandhya; Venkateswaran, Palaniandavar; Das, Sagarika
2015-01-01
A new electronically tunable differential integrator (ETDI) and its extension to voltage controlled quadrature oscillator (VCQO) design with linear tuning law are proposed; the active building block is a composite current feedback amplifier with recent multiplication mode current conveyor (MMCC) element. Recently utilization of two different kinds of active devices to form a composite building block is being considered since it yields a superior functional element suitable for improved quality circuit design. The integrator time constant (τ) and the oscillation frequency (ω o ) are tunable by the control voltage (V) of the MMCC block. Analysis indicates negligible phase error (θ e ) for the integrator and low active ω o -sensitivity relative to the device parasitic capacitances. Satisfactory experimental verifications on electronic tunability of some wave shaping applications by the integrator and a double-integrator feedback loop (DIFL) based sinusoid oscillator with linear f o variation range of 60 KHz~1.8 MHz at low THD of 2.1% are verified by both simulation and hardware tests. PMID:27347537
A fast method of numerical quadrature for p-version finite element matrices
NASA Technical Reports Server (NTRS)
Hinnant, Howard E.
1993-01-01
A new technique of numerical quadrature especially suited for p-version finite element matrices is presented. This new technique separates the integrand into two parts, and numerically operates on each part separately. The objective of this scheme is to minimize the computational cost of integrating the entire element matrix as opposed to minimizing the cost of integrating a single function. The efficiency of the new technique is compared with Gaussian quadrature and found to take a small fraction of the computational effort.
Optimization and Experimentation of Dual-Mass MEMS Gyroscope Quadrature Error Correction Methods
Cao, Huiliang; Li, Hongsheng; Kou, Zhiwei; Shi, Yunbo; Tang, Jun; Ma, Zongmin; Shen, Chong; Liu, Jun
2016-01-01
This paper focuses on an optimal quadrature error correction method for the dual-mass MEMS gyroscope, in order to reduce the long term bias drift. It is known that the coupling stiffness and demodulation error are important elements causing bias drift. The coupling stiffness in dual-mass structures is analyzed. The experiment proves that the left and right masses’ quadrature errors are different, and the quadrature correction system should be arranged independently. The process leading to quadrature error is proposed, and the Charge Injecting Correction (CIC), Quadrature Force Correction (QFC) and Coupling Stiffness Correction (CSC) methods are introduced. The correction objects of these three methods are the quadrature error signal, force and the coupling stiffness, respectively. The three methods are investigated through control theory analysis, model simulation and circuit experiments, and the results support the theoretical analysis. The bias stability results based on CIC, QFC and CSC are 48 °/h, 9.9 °/h and 3.7 °/h, respectively, and this value is 38 °/h before quadrature error correction. The CSC method is proved to be the better method for quadrature correction, and it improves the Angle Random Walking (ARW) value, increasing it from 0.66 °/√h to 0.21 °/√h. The CSC system general test results show that it works well across the full temperature range, and the bias stabilities of the six groups’ output data are 3.8 °/h, 3.6 °/h, 3.4 °/h, 3.1 °/h, 3.0 °/h and 4.2 °/h, respectively, which proves the system has excellent repeatability. PMID:26751455
Reinforcing Saccadic Amplitude Variability
ERIC Educational Resources Information Center
Paeye, Celine; Madelain, Laurent
2011-01-01
Saccadic endpoint variability is often viewed as the outcome of neural noise occurring during sensorimotor processing. However, part of this variability might result from operant learning. We tested this hypothesis by reinforcing dispersions of saccadic amplitude distributions, while maintaining constant their medians. In a first experiment we…
Directional dual-tree complex wavelet packet transforms for processing quadrature signals.
Serbes, Gorkem; Gulcur, Halil Ozcan; Aydin, Nizamettin
2016-03-01
Quadrature signals containing in-phase and quadrature-phase components are used in many signal processing applications in every field of science and engineering. Specifically, Doppler ultrasound systems used to evaluate cardiovascular disorders noninvasively also result in quadrature format signals. In order to obtain directional blood flow information, the quadrature outputs have to be preprocessed using methods such as asymmetrical and symmetrical phasing filter techniques. These resultant directional signals can be employed in order to detect asymptomatic embolic signals caused by small emboli, which are indicators of a possible future stroke, in the cerebral circulation. Various transform-based methods such as Fourier and wavelet were frequently used in processing embolic signals. However, most of the times, the Fourier and discrete wavelet transforms are not appropriate for the analysis of embolic signals due to their non-stationary time-frequency behavior. Alternatively, discrete wavelet packet transform can perform an adaptive decomposition of the time-frequency axis. In this study, directional discrete wavelet packet transforms, which have the ability to map directional information while processing quadrature signals and have less computational complexity than the existing wavelet packet-based methods, are introduced. The performances of proposed methods are examined in detail by using single-frequency, synthetic narrow-band, and embolic quadrature signals. PMID:25388779
Performance of Low-Density Parity-Check Coded Modulation
NASA Technical Reports Server (NTRS)
Hamkins, Jon
2010-01-01
This paper reports the simulated performance of each of the nine accumulate-repeat-4-jagged-accumulate (AR4JA) low-density parity-check (LDPC) codes [3] when used in conjunction with binary phase-shift-keying (BPSK), quadrature PSK (QPSK), 8-PSK, 16-ary amplitude PSK (16- APSK), and 32-APSK.We also report the performance under various mappings of bits to modulation symbols, 16-APSK and 32-APSK ring scalings, log-likelihood ratio (LLR) approximations, and decoder variations. One of the simple and well-performing LLR approximations can be expressed in a general equation that applies to all of the modulation types.
Compensation of a distorted N-fold orbital angular momentum multicasting link using adaptive optics.
Li, Shuhui; Wang, Jian
2016-04-01
By using an adaptive feedback correction technique, we experimentally demonstrate turbulence compensation for free-space four-fold and eight-fold 16-ary quadrature amplitude modulation (16-QAM) carrying orbital angular momentum (OAM) multicasting links. The performance of multicasted OAM beams through emulated atmospheric turbulence and adaptive optics assisted compensation loop is investigated. The experimental results show that the scheme can efficiently compensate for the atmospheric turbulence induced distortions, i.e., reducing power fluctuation of multicasted OAM channels, suppressing inter-channel crosstalk, and improving the bit-error rate (BER) performance. PMID:27192267
All-optical multi-channel wavelength conversion of Nyquist 16 QAM signal using a silicon waveguide.
Long, Yun; Liu, Jun; Hu, Xiao; Wang, Andong; Zhou, Linjie; Zou, Kaiheng; Zhu, Yixiao; Zhang, Fan; Wang, Jian
2015-12-01
We experimentally demonstrate on-chip all-optical multi-channel wavelength conversion of Nyquist 16 ary quadrature amplitude modulation (16 QAM) signal in a silicon waveguide. The measured optical signal-to-noise ratio (OSNR) penalties of wavelength conversion are ∼2 dB. The observed constellations of converted idlers indicate favorable performance of silicon-waveguide-based multi-channel wavelength conversion. We also experimentally study and compare the phase-conjugated wavelength conversion by degenerate four-wave mixing (FWM) and transparent wavelength conversion by non-degenerate FWM in the silicon waveguide. PMID:26625029
Flexible digital modulation and coding synthesis for satellite communications
NASA Technical Reports Server (NTRS)
Vanderaar, Mark; Budinger, James; Hoerig, Craig; Tague, John
1991-01-01
An architecture and a hardware prototype of a flexible trellis modem/codec (FTMC) transmitter are presented. The theory of operation is built upon a pragmatic approach to trellis-coded modulation that emphasizes power and spectral efficiency. The system incorporates programmable modulation formats, variations of trellis-coding, digital baseband pulse-shaping, and digital channel precompensation. The modulation formats examined include (uncoded and coded) binary phase shift keying (BPSK), quatenary phase shift keying (QPSK), octal phase shift keying (8PSK), 16-ary quadrature amplitude modulation (16-QAM), and quadrature quadrature phase shift keying (Q squared PSK) at programmable rates up to 20 megabits per second (Mbps). The FTMC is part of the developing test bed to quantify modulation and coding concepts.
Erbert, G
2009-09-01
The Amplitude Modulator Chassis (AMC) is the final component in the MOR system and connects directly to the PAM input through a 100-meter fiber. The 48 AMCs temporally shape the 48 outputs of the MOR using an arbitrary waveform generator coupled to an amplitude modulator. The amplitude modulation element is a two stage, Lithium Niobate waveguide device, where the intensity of the light passing through the device is a function of the electrical drive applied. The first stage of the modulator is connected to a programmable high performance Arbitrary Waveform Generator (AWG) consisting of 140 impulse generators space 250 ps apart. An arbitrary waveform is generated by independently varying the amplitude of each impulse generator and then summing the impulses together. In addition to the AWG a short pulse generator is also connected to the first stage of the modulator to provide a sub 100-ps pulse used for timing experiments. The second stage of the modulator is connect to a square pulse generator used to further attenuate any pre or post pulse light passing through the first stage of the modulator. The fast rise and fall time of the square pulse generator is also used to produce fast rise and fall times of the AWG by clipping the AWG pulse. For maximum extinction, a pulse bias voltage is applied to each stage of the modulator. A pulse voltage is applied as opposed to a DC voltage to prevent charge buildup on the modulator. Each bias voltage is adjustable to provide a minimum of 50-dB extinction. The AMC is controlled through ICCS to generate the desired temporal pulse shape. This process involves a closed-loop control algorithm, which compares the desired temporal waveform to the produced optical pulse, and iterates the programming of the AWG until the two waveforms agree within an allowable tolerance.
NASA Astrophysics Data System (ADS)
Hearn, T. M.
2014-12-01
Modern data from the China Bulletin and temporary network deployments has been used to update amplitude tomography using ML and MS seismic amplitudes. This work builds on the results of Hearn et al., 2008. ML attenuation estimates are much better resolved due to the inclusion of subnet data. We find that the trade-off between geometrical spreading and attenuation estimates are well constrained; however, both of these parameters have significant trade-off with the frequency dependence of attenuation. Maps of attenuation using the ML amplitudes are similar to those of Lg attenuation found by other authors suggesting that ML attenuation estimates form a suitable proxy for Lg attenuation estimates. We are now able to associate high attenuation directly with the Longmen Shan and the Qilian Shan mountains and also, where resolved, with the Kunlun Shan, Altyn Tag, and Tian Shan mountains. Grabens around the Ordos Platform also show high attenuation. Basins, however, do not in general show high attenuation. The main exception to this is the Bohai Basin. We conclude that the ML waveforms, like the Lg waveforms, interrogate the entire crustal column and are most sensitive to tectonically active structures and rapid changes in crustal structure. Data from MS data do not include subnet readings and do not have the resolution that was obtained with the ML data. Nonetheless, features are similar with the exception that basins appear more highly attenuative.
Gray, G.W.; Jensen, A.S.
1957-10-22
A pulse-height analyzer system of improved design for sorting and counting a series of pulses, such as provided by a scintillation detector in nuclear radiation measurements, is described. The analyzer comprises a main transmission line, a cathode-ray tube for each section of the line with its deflection plates acting as the line capacitance; means to bias the respective cathode ray tubes so that the beam strikes a target only when a prearranged pulse amplitude is applied, with each tube progressively biased to respond to smaller amplitudes; pulse generating and counting means associated with each tube to respond when the beam is deflected; a control transmission line having the same time constant as the first line per section with pulse generating means for each tube for initiating a pulse on the second transmission line when a pulse triggers the tube of corresponding amplitude response, the former pulse acting to prevent successive tubes from responding to the pulse under test. This arrangement permits greater deflection sensitivity in the cathode ray tube and overcomes many of the disadvantages of prior art pulse-height analyzer circuits.
Extended Gaussian quadratures for functions with an end-point singularity of logarithmic type
NASA Astrophysics Data System (ADS)
Pachucki, K.; Puchalski, M.; Yerokhin, V. A.
2014-11-01
The extended Gaussian quadrature rules are shown to be an efficient tool for numerical integration of wide class of functions with singularities of logarithmic type. The quadratures are exact for the functions pol1n-1(x)+lnx pol2n-1(x), where pol1n-1(x) and pol2n-1(x) are two arbitrary polynomials of degree n-1 and n is the order of the quadrature formula. We present an implementation of numerical algorithm that calculates the nodes and the weights of the quadrature formulas, provide a Fortran code for numerical integration, and test the performance of different kinds of Gaussian quadratures for functions with logarithmic singularities. Catalogue identifier: AETP_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AETP_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 2535 No. of bytes in distributed program, including test data, etc.: 39 963 Distribution format: tar.gz Programming language: Mathematica, Fortran. Computer: PCs or higher performance computers. Operating system: Linux, Windows, MacOS. RAM: Kilobytes. Classification: 4.11. Nature of problem: Quadrature formulas for numerical integration, effective for a wide class of functions with end-point singularities of logarithmic type. Solution method: The method of solution is based on the algorithm developed in Ref. [1] with some modifications. Running time: Milliseconds to minutes. J. Ma, V. Rokhlin, S. Wandzura, Generalized Gaussian quadrature rules for systems of arbitrary functions, Soc. Indust. Appl. Math. J. Numer. Anal. 33 (3) (1996) 971-996.
NASA Astrophysics Data System (ADS)
Čársky, Petr
2010-09-01
The UGU term was used as a model of the UGT term, and its evaluation by numerical quadrature was examined systematically with a training set of eight molecules. Minimum numbers of points have been determined for radial Gauss-Legendre and angular Lebedev quadratures that preserve the accuracy needed for practical applications. These quadratures are recommended for efficient calculation of electron scattering by polyatomic molecules.
The generation of arbitrary order, non-classical, Gauss-type quadrature for transport applications
Spence, Peter J.
2015-09-01
A method is presented, based upon the Stieltjes method (1884), for the determination of non-classical Gauss-type quadrature rules, and the associated sets of abscissae and weights. The method is then used to generate a number of quadrature sets, to arbitrary order, which are primarily aimed at deterministic transport calculations. The quadrature rules and sets detailed include arbitrary order reproductions of those presented by Abu-Shumays in [4,8] (known as the QR sets, but labelled QRA here), in addition to a number of new rules and associated sets; these are generated in a similar way, and we label them the QRS quadrature sets. The method presented here shifts the inherent difficulty (encountered by Abu-Shumays) associated with solving the non-linear moment equations, particular to the required quadrature rule, to one of the determination of non-classical weight functions and the subsequent calculation of various associated inner products. Once a quadrature rule has been written in a standard form, with an associated weight function having been identified, the calculation of the required inner products is achieved using specific variable transformations, in addition to the use of rapid, highly accurate quadrature suited to this purpose. The associated non-classical Gauss quadrature sets can then be determined, and this can be done to any order very rapidly. In this paper, instead of listing weights and abscissae for the different quadrature sets detailed (of which there are a number), the MATLAB code written to generate them is included as Appendix D. The accuracy and efficacy (in a transport setting) of the quadrature sets presented is not tested in this paper (although the accuracy of the QRA quadrature sets has been studied in [12,13]), but comparisons to tabulated results listed in [8] are made. When comparisons are made with one of the azimuthal QRA sets detailed in [8], the inherent difficulty in the method of generation, used there, becomes apparent
Schuyler, Adam D; Maciejewski, Mark W; Stern, Alan S; Hoch, Jeffrey C
2015-01-01
Nonuniform sampling (NUS) in multidimensional NMR permits the exploration of higher dimensional experiments and longer evolution times than the Nyquist Theorem practically allows for uniformly sampled experiments. However, the spectra of NUS data include sampling-induced artifacts and may be subject to distortions imposed by sparse data reconstruction techniques, issues not encountered with the discrete Fourier transform (DFT) applied to uniformly sampled data. The characterization of these NUS-induced artifacts allows for more informed sample schedule design and improved spectral quality. The DFT–Convolution Theorem, via the point-spread function (PSF) for a given sampling scheme, provides a useful framework for exploring the nature of NUS sampling artifacts. In this work, we analyze the PSFs for a set of specially constructed NUS schemes to quantify the interplay between randomization and dimensionality for reducing artifacts relative to uniformly undersampled controls. In particular, we find a synergistic relationship between the indirect time dimensions and the “quadrature phase dimension” (i.e. the hypercomplex components collected for quadrature detection). The quadrature phase dimension provides additional degrees of freedom that enable partial-component NUS (collecting a subset of quadrature components) to further reduce sampling-induced aliases relative to traditional full-component NUS (collecting all quadrature components). The efficacy of artifact reduction is exponentially related to the dimensionality of the sample space. Our results quantify the utility of partial-component NUS as an additional means for introducing decoherence into sampling schemes and reducing sampling artifacts in high dimensional experiments. PMID:25899289
Design and Application of Quadrature Compensation Patterns in Bulk Silicon Micro-Gyroscopes
Ni, Yunfang; Li, Hongsheng; Huang, Libin
2014-01-01
This paper focuses on the detailed design issues of a peculiar quadrature reduction method named system stiffness matrix diagonalization, whose key technology is the design and application of quadrature compensation patterns. For bulk silicon micro-gyroscopes, a complete design and application case was presented. The compensation principle was described first. In the mechanical design, four types of basic structure units were presented to obtain the basic compensation function. A novel layout design was proposed to eliminate the additional disturbing static forces and torques. Parameter optimization was carried out to maximize the available compensation capability in a limited layout area. Two types of voltage loading methods were presented. Their influences on the sense mode dynamics were analyzed. The proposed design was applied on a dual-mass silicon micro-gyroscope developed in our laboratory. The theoretical compensation capability of a quadrature equivalent angular rate no more than 412 °/s was designed. In experiments, an actual quadrature equivalent angular rate of 357 °/s was compensated successfully. The actual compensation voltages were a little larger than the theoretical ones. The correctness of the design and the theoretical analyses was verified. They can be commonly used in planar linear vibratory silicon micro-gyroscopes for quadrature compensation purpose. PMID:25356646
On the Computation of High Order Rys Quadrature Weights and Nodes
NASA Technical Reports Server (NTRS)
Schwenke, David W.
2014-01-01
Since its introduction in 1976, the Rys Quadrature method has proven a very attractive method for evaluating electron repulsion integrals for calculations using Gaussian type orbitals. Since then, there have been considerable refinements of the method, but at it's core, Gaussian weights and nodes are used to exactly evaluate using a numerical approach to the transform integral. One of the powers of the Rys Quadrature method is the relative ease in evaluating integrals involving functions of high angular momentum. In this work we report on the complete resolution of these numerical difficulties, and we have easily computed accurate quadrature weights and nodes up to order 101. All calculations were carried out using 128-bit precision.
Řeháček, Jaroslav; Teo, Yong Siah; Hradil, Zdeněk; Wallentowitz, Sascha
2015-01-01
We reveal that quadrature squeezing can result in significantly better quantum-estimation performance with quantum heterodyne detection (of H. P. Yuen and J. H. Shapiro) as compared to quantum homodyne detection for Gaussian states, which touches an important aspect in the foundational understanding of these two schemes. Taking single-mode Gaussian states as examples, we show analytically that the competition between the errors incurred during tomogram processing in homodyne detection and the Arthurs-Kelly uncertainties arising from simultaneous incompatible quadrature measurements in heterodyne detection can often lead to the latter giving more accurate estimates. This observation is also partly a manifestation of a fundamental relationship between the respective data uncertainties for the two schemes. In this sense, quadrature squeezing can be used to overcome intrinsic quantum-measurement uncertainties in heterodyne detection. PMID:26195198
Quadrature rules for finite element approximations of 1D nonlocal problems
NASA Astrophysics Data System (ADS)
Zhang, Xiaoping; Gunzburger, Max; Ju, Lili
2016-04-01
It is well known that calculations of the entries of the stiffness matrix in the finite element approximations of nonlocal diffusion and mechanics models are often very time-consuming due to the double integration process over the domain and the singularities of the nonlocal kernel functions. In this paper, we propose some effective and accurate quadrature rules for computing these double integrals for one-dimensional nonlocal problems; in particular, for problems with highly singular kernels, the corresponding inner integrals can be first evaluated exactly in our method, and the outer one then will be approximated by some popular quadrature rules. With these quadrature rules, the assembly of the stiffness matrix in the finite element method for the nonlocal problems becomes similar to that for the classical partial differential equations and is thus quite efficient.
Phase measurement device using inphase and quadrature components for phase estimation
NASA Technical Reports Server (NTRS)
Halverson, Peter G. (Inventor); Ware, Brent (Inventor); Shaddock, Daniel A. (Inventor); Spero, Robert E. (Inventor)
2009-01-01
A phasemeter for estimating the phase of a signal. For multi-tone signals, multiple phase estimates may be provided. An embodiment includes components operating in the digital domain, where a sampled input signal is multiplied by cosine and sine terms to provide estimates of the inphase and quadrature components. The quadrature component provides an error signal that is provided to a feedback loop, the feedback loop providing a model phase that tends to track the phase of a tone in the input signal. The cosine and sine terms are generated from the model phase. The inphase and quadrature components are used to form a residual phase, which is added to the model phase to provide an estimate of the phase of the input signal. Other embodiments are described and claimed.
Low-Latitude Solar Wind During the Fall 1998 SOHO-Ulysses Quadrature
NASA Technical Reports Server (NTRS)
Poletto, G.; Suess, S. T.; Biesecker, D. A.; Esser, R.; Gloeckler, G.; Ko, Y.-K.; Zurbuchen, T. H.
2002-01-01
Solar and Heliospheric Observatory (SOH0)-Ulysses quadratures occur when the SOHO-Sun-Ulysses-included angle is 90 deg. These offer the opportunity to directly compare properties of plasma parcels, observed by SOHO [Dorningo et al.] in the low corona, with properties of the same parcels measured, in due time, in situ, by Ulysses [ Wenzel et al]. We refer the reader to Suess et al. for an extended discussion of SOHO-Ulysses quadrature geometry. Here it suffices to recall that there are two quadratures per year, as SOHO makes its one-year revolution around the Sun. This, because SOHO is at the L1 Lagrangian point, in essentially the same place as the Earth, while Ulysses is in a near-polar -5-year solar orbit with a perihelion of 1.34 AU and aphelion of 5.4 AU.
Parrish, Robert M; Hohenstein, Edward G; Martínez, Todd J; Sherrill, C David
2013-05-21
We investigate the application of molecular quadratures obtained from either standard Becke-type grids or discrete variable representation (DVR) techniques to the recently developed least-squares tensor hypercontraction (LS-THC) representation of the electron repulsion integral (ERI) tensor. LS-THC uses least-squares fitting to renormalize a two-sided pseudospectral decomposition of the ERI, over a physical-space quadrature grid. While this procedure is technically applicable with any choice of grid, the best efficiency is obtained when the quadrature is tuned to accurately reproduce the overlap metric for quadratic products of the primary orbital basis. Properly selected Becke DFT grids can roughly attain this property. Additionally, we provide algorithms for adopting the DVR techniques of the dynamics community to produce two different classes of grids which approximately attain this property. The simplest algorithm is radial discrete variable representation (R-DVR), which diagonalizes the finite auxiliary-basis representation of the radial coordinate for each atom, and then combines Lebedev-Laikov spherical quadratures and Becke atomic partitioning to produce the full molecular quadrature grid. The other algorithm is full discrete variable representation (F-DVR), which uses approximate simultaneous diagonalization of the finite auxiliary-basis representation of the full position operator to produce non-direct-product quadrature grids. The qualitative features of all three grid classes are discussed, and then the relative efficiencies of these grids are compared in the context of LS-THC-DF-MP2. Coarse Becke grids are found to give essentially the same accuracy and efficiency as R-DVR grids; however, the latter are built from explicit knowledge of the basis set and may guide future development of atom-centered grids. F-DVR is found to provide reasonable accuracy with markedly fewer points than either Becke or R-DVR schemes. PMID:23697409
NASA Astrophysics Data System (ADS)
Parrish, Robert M.; Hohenstein, Edward G.; Martínez, Todd J.; Sherrill, C. David
2013-05-01
We investigate the application of molecular quadratures obtained from either standard Becke-type grids or discrete variable representation (DVR) techniques to the recently developed least-squares tensor hypercontraction (LS-THC) representation of the electron repulsion integral (ERI) tensor. LS-THC uses least-squares fitting to renormalize a two-sided pseudospectral decomposition of the ERI, over a physical-space quadrature grid. While this procedure is technically applicable with any choice of grid, the best efficiency is obtained when the quadrature is tuned to accurately reproduce the overlap metric for quadratic products of the primary orbital basis. Properly selected Becke DFT grids can roughly attain this property. Additionally, we provide algorithms for adopting the DVR techniques of the dynamics community to produce two different classes of grids which approximately attain this property. The simplest algorithm is radial discrete variable representation (R-DVR), which diagonalizes the finite auxiliary-basis representation of the radial coordinate for each atom, and then combines Lebedev-Laikov spherical quadratures and Becke atomic partitioning to produce the full molecular quadrature grid. The other algorithm is full discrete variable representation (F-DVR), which uses approximate simultaneous diagonalization of the finite auxiliary-basis representation of the full position operator to produce non-direct-product quadrature grids. The qualitative features of all three grid classes are discussed, and then the relative efficiencies of these grids are compared in the context of LS-THC-DF-MP2. Coarse Becke grids are found to give essentially the same accuracy and efficiency as R-DVR grids; however, the latter are built from explicit knowledge of the basis set and may guide future development of atom-centered grids. F-DVR is found to provide reasonable accuracy with markedly fewer points than either Becke or R-DVR schemes.
Extended Kalman filtering for joint mitigation of phase and amplitude noise in coherent QAM systems.
Pakala, Lalitha; Schmauss, Bernhard
2016-03-21
We numerically investigate our proposed carrier phase and amplitude noise estimation (CPANE) algorithm using extend Kalman filter (EKF) for joint mitigation of linear and non-linear phase noise as well as amplitude noise on 4, 16 and 64 polarization multiplexed (PM) quadrature amplitude modulation (QAM) 224 Gb/s systems. The results are compared to decision directed (DD) carrier phase estimation (CPE), DD phase locked loop (PLL) and universal CPE (U-CPE) algorithms. Besides eliminating the necessity of phase unwrapping function, EKF-CPANE shows improved performance for both back-to-back (BTB) and transmission scenarios compared to the aforementioned algorithms. We further propose a weighted innovation approach (WIA) of the EKF-CPANE which gives an improvement of 0.3 dB in the Q-factor, compared to the original algorithm. PMID:27136830
On the remainder term of Gauss-Radau quadratures for analytic functions
NASA Astrophysics Data System (ADS)
Milovanovic, Gradimir V.; Spalevic, Miodrag M.; Pranic, Miroslav S.
2008-09-01
For analytic functions the remainder term of Gauss-Radau quadrature formulae can be represented as a contour integral with a complex kernel. We study the kernel on elliptic contours with foci at the points ±1 and a sum of semi-axes [varrho]>1 for the Chebyshev weight function of the second kind. Starting from explicit expressions of the corresponding kernels the location of their maximum modulus on ellipses is determined. The corresponding Gautschi's conjecture from [On the remainder term for analytic functions of Gauss-Lobatto and Gauss-Radau quadratures, Rocky Mountain J. Math. 21 (1991), 209-226] is proved.
Quadrature formulas on the unit circle with prescribed nodes and maximal domain of validity
NASA Astrophysics Data System (ADS)
Bultheel, Adhemar; Daruis, Leyla; González-Vera, Pablo
2009-09-01
In this paper we investigate the Szego-Radau and Szego-Lobatto quadrature formulas on the unit circle. These are (n+m)-point formulas for which m nodes are fixed in advance, with m=1 and m=2 respectively, and which have a maximal domain of validity in the space of Laurent polynomials. This means that the free parameters (free nodes and positive weights) are chosen such that the quadrature formula is exact for all powers zj, -p<=j<=p, with p=p(n,m) as large as possible.
An evaluation of Clenshaw-Curtis quadrature rule for integration w.r.t. singular measures
NASA Astrophysics Data System (ADS)
Calabrò, F.; Corbo Esposito, A.
2009-07-01
This work is devoted to the study of quadrature rules for integration with respect to (w.r.t.) general probability measures with known moments. Automatic calculation of the Clenshaw-Curtis rules is considered and analyzed. It is shown that it is possible to construct these rules in a stable manner for quadrature w.r.t. balanced measures. In order to make a comparison Gauss rules and their stable implementation for integration w.r.t. balanced measures are recalled. Convergence rates are tested in the case of binomial measures.
NASA Astrophysics Data System (ADS)
Amin, Najam Muhammad; Zhigong, Wang; Zhiqun, Li
2015-05-01
A down-conversion in-phase/quadrature (I/Q) mixer employing a folded-type topology, integrated with a passive differential quadrature all-pass filter (D-QAF), in order to realize the final down-conversion stage of a 60 GHz receiver architecture is presented in this work. Instead of employing conventional quadrature generation techniques such as a polyphase filter or a frequency divider for the local oscillator (LO) of the mixer, a passive D-QAF structure is employed. Fabricated in a 65 nm CMOS process, the mixer exhibits a voltage gain of 7-8 dB in an intermediate frequency (IF) band ranging from 10 MHz-1.75 GHz. A fixed LO frequency of 12 GHz is used to down-convert a radio frequency (RF) band of 10.25-13.75 GHz. The mixer displays a third order input referred intercept point (IIP3) ranging from -8.75 to -7.37 dBm for a fixed IF frequency of 10 MHz and a minimum single-sideband noise figure (SSB-NF) of 11.3 dB. The mixer draws a current of 6 mA from a 1.2 V supply voltage dissipating a power of 7.2 mW. Project supported by the National High Technology Research and Development Program of China (No. 2011AA010200).
Oder, J.M.
1997-12-01
Several new quadrature sets for use in the discrete ordinates method of solving the Boltzmann neutral particle transport equation are derived. These symmetric quadratures extend the traditional symmetric quadratures by allowing ordinates perpendicular to one or two of the coordinate axes. Comparable accuracy with fewer required ordinates is obtained. Quadratures up to seventh order are presented. The validity and efficiency of the quadratures is then tested and compared with the Sn level symmetric quadratures relative to a Monte Carlo benchmark solution. The criteria for comparison include current through the surface, scalar flux at the surface, volume average scalar flux, and time required for convergence. Appreciable computational cost was saved when used in an unstructured tetrahedral cell code using highly accurate characteristic methods. However, no appreciable savings in computation time was found using the new quadratures compared with traditional Sn methods on a regular Cartesian mesh using the standard diamond difference method. These quadratures are recommended for use in three-dimensional calculations on an unstructured mesh.
PULSE AMPLITUDE DISTRIBUTION RECORDER
Cowper, G.
1958-08-12
A device is described for automatica1ly recording pulse annplitude distribution received from a counter. The novelty of the device consists of the over-all arrangement of conventional circuit elements to provide an easy to read permanent record of the pulse amplitude distribution during a certain time period. In the device a pulse analyzer separates the pulses according to annplitude into several channels. A scaler in each channel counts the pulses and operates a pen marker positioned over a drivable recorder sheet. Since the scalers in each channel have the sanne capacity, the control circuitry permits counting of the incoming pulses until one scaler reaches capacity, whereupon the input is removed and an internal oscillator supplies the necessary pulses to fill up the other scalers. Movement of the chart sheet is initiated wben the first scaler reaches capacity to thereby give a series of marks at spacings proportional to the time required to fill the remaining scalers, and accessory equipment marks calibration points on the recorder sheet to facilitate direct reading of the number of external pulses supplied to each scaler.
Numerical Quadrature and Operator Splitting in Finite Element Methods for Cardiac Electrophysiology
Krishnamoorthi, Shankarjee; Sarkar, Mainak; Klug, William S.
2015-01-01
SUMMARY We examine carefully the numerical accuracy and computational efficiency of alternative formulations of the finite-element solution procedure for the mono-domain equations of cardiac electrophysiology (EP), focusing on the interaction of spatial quadrature implementations with operator splitting, examining both nodal and Gauss quadrature methods, and implementations that mix nodal storage of state variables with Gauss quadrature. We evaluate the performance of all possible combinations of “lumped” approximations of consistent capacitance and mass matrices. Most generally we find that quadrature schemes and lumped approximations that produce decoupled nodal ionic equations allow for the greatest computational efficiency, this being afforded through the use of asynchronous adaptive time-stepping of the ionic state-variable ODEs. We identify two lumped approximation schemes that exhibit superior accuracy, rivaling that of the most expensive variationally consistent implementations. Finally we illustrate some of the physiological consequences of discretization error in EP simulation relevant to cardiac arrhythmia and fibrillation. These results suggest caution with the use of semi-automated free-form tetrahedral and hexahedral meshing algorithms available in most commercially available meshing software, which produce non-uniform meshes having a large distribution of element sizes. PMID:23873868
Serbes, G; Aydin, N
2011-01-01
Dual-tree complex wavelet transform (DTCWT), which is a shift invariant transform with limited redundancy, is an improved version of discrete wavelet transform. Complex quadrature signals are dual channel signals obtained from the systems employing quadrature demodulation. An example of such signals is quadrature Doppler signal obtained from blood flow analysis systems. Prior to processing Doppler signals using the DTCWT, directional flow signals must be obtained and then two separate DTCWT applied, increasing the computational complexity. In this study, in order to decrease computational complexity, a symmetrical modified DTCWT algorithm is proposed (SMDTCWT). A comparison between the new transform and the symmetrical phasing-filter technique is presented. Additionally denoising performance of SMDTCWT is compared with the DWT and the DTCWT using simulated signals. The results show that the proposed method gives the same output as the symmetrical phasing-filter method, the computational complexity for processing quadrature signals using DTCWT is greatly reduced and finally the SMDTCWT based denoising outperforms conventional DWT with same computational complexity. PMID:22255416
Saturation dependence of the quadrature conductivity of oil-bearing sands
NASA Astrophysics Data System (ADS)
Schmutz, M.; Blondel, A.; Revil, A.
2012-02-01
We have investigated the complex conductivity of oil-bearing sands with six distinct oil types including sunflower oil, silicone oil, gum rosin, paraffin, engine oil, and an industrial oil of complex composition. In all these experiments, the oil was the non-wetting phase. The in-phase (real) conductivity follows a power law relationship with the saturation (also known as the second Archie's law) but with a saturation exponent n raging from 1.1 to 3.1. In most experiments, the quadrature conductivity follows also a power law relationship with the water saturation but with a power law exponent p can be either positive or negative. For some samples, the quadrature conductivity first increases with saturation and then decreases indicating that two processes compete in controlling the quadrature conductivity. One is related to the insulating nature of the oil phase and a second could be associated with the surface area of the oil / water interface. The quadrature conductivity seems to be influenced not only by the value of the saturation exponent n (according to the Vinegar and Waxman model, p = n - 1), but also by the surface area between the oil phase and the water phase especially for very water-repellent oil having a fractal oil-water interface.
A multivariate quadrature based moment method for LES based modeling of supersonic combustion
NASA Astrophysics Data System (ADS)
Donde, Pratik; Koo, Heeseok; Raman, Venkat
2012-07-01
The transported probability density function (PDF) approach is a powerful technique for large eddy simulation (LES) based modeling of scramjet combustors. In this approach, a high-dimensional transport equation for the joint composition-enthalpy PDF needs to be solved. Quadrature based approaches provide deterministic Eulerian methods for solving the joint-PDF transport equation. In this work, it is first demonstrated that the numerical errors associated with LES require special care in the development of PDF solution algorithms. The direct quadrature method of moments (DQMOM) is one quadrature-based approach developed for supersonic combustion modeling. This approach is shown to generate inconsistent evolution of the scalar moments. Further, gradient-based source terms that appear in the DQMOM transport equations are severely underpredicted in LES leading to artificial mixing of fuel and oxidizer. To overcome these numerical issues, a semi-discrete quadrature method of moments (SeQMOM) is formulated. The performance of the new technique is compared with the DQMOM approach in canonical flow configurations as well as a three-dimensional supersonic cavity stabilized flame configuration. The SeQMOM approach is shown to predict subfilter statistics accurately compared to the DQMOM approach.
NUMERICAL APPROXIMATION OF SEMI-INTEGRALS AND SEMIDERIVATIVES BY PRODUCT QUADRATURE RULES
This paper is concerned with the numerical calculation of the semi-integral and semiderivative of a function f, whose values f (xj) are known on a discrete set of abscissas 0 = x(1) < x(2) < ... < x(n). A family of product quadrature rules is developed to approximate the semi-int...
Exact Integrations of Polynomials and Symmetric Quadrature Formulas over Arbitrary Polyhedral Grids
NASA Technical Reports Server (NTRS)
Liu, Yen; Vinokur, Marcel
1997-01-01
This paper is concerned with two important elements in the high-order accurate spatial discretization of finite volume equations over arbitrary grids. One element is the integration of basis functions over arbitrary domains, which is used in expressing various spatial integrals in terms of discrete unknowns. The other consists of quadrature approximations to those integrals. Only polynomial basis functions applied to polyhedral and polygonal grids are treated here. Non-triangular polygonal faces are subdivided into a union of planar triangular facets, and the resulting triangulated polyhedron is subdivided into a union of tetrahedra. The straight line segment, triangle, and tetrahedron are thus the fundamental shapes that are the building blocks for all integrations and quadrature approximations. Integrals of products up to the fifth order are derived in a unified manner for the three fundamental shapes in terms of the position vectors of vertices. Results are given both in terms of tensor products and products of Cartesian coordinates. The exact polynomial integrals are used to obtain symmetric quadrature approximations of any degree of precision up to five for arbitrary integrals over the three fundamental domains. Using a coordinate-free formulation, simple and rational procedures are developed to derive virtually all quadrature formulas, including some previously unpublished. Four symmetry groups of quadrature points are introduced to derive Gauss formulas, while their limiting forms are used to derive Lobatto formulas. Representative Gauss and Lobatto formulas are tabulated. The relative efficiency of their application to polyhedral and polygonal grids is detailed. The extension to higher degrees of precision is discussed.
NASA Astrophysics Data System (ADS)
Cao, Zhang; Song, Wei; Peng, Zhicong; Xu, Lijun
2014-11-01
There exist a number of algorithms to map the phase to amplitude in direct digital synthesis (DDS). For DDS with more than 14 output bits, the Coordinate Rotation Digital Computer (CORDIC) algorithm is well known for its high precision. Also, it is effective in solutions where there is the need of in-phase and quadrature components simultaneously because the algorithm calculates both. In this paper, a Taylor expansion based method was proposed to calculate both in-phase and quadrature at the same time. Numerical simulations for different data format, e.g., double and finite bits, were carried out in Matlab and Quartus, which were followed by the hardware implementation in Field Programmable Gate Array. The results demonstrated that the proposed method possessed higher precision and exhausted less logic elements than the CORDIC algorithm.
Cao, Zhang; Song, Wei; Peng, Zhicong; Xu, Lijun
2014-11-01
There exist a number of algorithms to map the phase to amplitude in direct digital synthesis (DDS). For DDS with more than 14 output bits, the Coordinate Rotation Digital Computer (CORDIC) algorithm is well known for its high precision. Also, it is effective in solutions where there is the need of in-phase and quadrature components simultaneously because the algorithm calculates both. In this paper, a Taylor expansion based method was proposed to calculate both in-phase and quadrature at the same time. Numerical simulations for different data format, e.g., double and finite bits, were carried out in Matlab and Quartus, which were followed by the hardware implementation in Field Programmable Gate Array. The results demonstrated that the proposed method possessed higher precision and exhausted less logic elements than the CORDIC algorithm. PMID:25430130
622-Mbps Orthogonal Frequency Division Multiplexing Modulator Developed
NASA Technical Reports Server (NTRS)
Nguyen, Na T.
1999-01-01
The Communications Technology Division at the NASA Lewis Research Center is developing advanced electronic technologies for the space communications and remote sensing systems of tomorrow. As part of the continuing effort to advance the state-of-the art in satellite communications and remote sensing systems, Lewis is developing a programmable Orthogonal Frequency Division Multiplexing (OFDM) modulator card for high-data-rate communication links. The OFDM modulator is particularly suited to high data-rate downlinks to ground terminals or direct data downlinks from near-Earth science platforms. It can support data rates up to 622 megabits per second (Mbps) and high-order modulation schemes such as 16-ary quadrature amplitude modulation (16-ary QAM) or 8- phase shift keying (8PSK). High order modulations can obtain the bandwidth efficiency over the traditional binary phase shift keying (BPSK) or quadrature phase shift keying (QPSK) modulator schemes. The OFDM modulator architecture can also be precompensated for channel disturbances and alleviate amplitude degradations caused by nonlinear transponder characteristics.
On the Period-Amplitude and Amplitude-Period Relationships
NASA Technical Reports Server (NTRS)
Wilson, Robert M.; Hathaway, David H.
2008-01-01
Examined are Period-Amplitude and Amplitude-Period relationships based on the cyclic behavior of the 12-month moving averages of monthly mean sunspot numbers for cycles 0.23, both in terms of Fisher's exact tests for 2x2 contingency tables and linear regression analyses. Concerning the Period-Amplitude relationship (same cycle), because cycle 23's maximum amplitude is known to be 120.8, the inferred regressions (90-percent prediction intervals) suggest that its period will be 131 +/- 24 months (using all cycles) or 131 +/- 18 months (ignoring cycles 2 and 4, which have the extremes of period, 108 and 164 months, respectively). Because cycle 23 has already persisted for 142 months (May 1996 through February 2008), based on the latter prediction, it should end before September 2008. Concerning the Amplitude-Period relationship (following cycle maximum amplitude versus preceding cycle period), because cycle 23's period is known to be at least 142 months, the inferred regressions (90-percent prediction intervals) suggest that cycle 24's maximum amplitude will be about less than or equal to 96.1 +/- 55.0 (using all cycle pairs) or less than or equal to 91.0 +/- 36.7 (ignoring statistical outlier cycle pairs). Hence, cycle 24's maximum amplitude is expected to be less than 151, perhaps even less than 128, unless cycle pair 23/24 proves to be a statistical outlier.
Pang, Yong; Yu, Baiying; Vigneron, Daniel B; Zhang, Xiaoliang
2014-02-01
Quadrature coils are often desired in MR applications because they can improve MR sensitivity and also reduce excitation power. In this work, we propose, for the first time, a quadrature array design strategy for parallel transmission at 298 MHz using single-feed circularly polarized (CP) patch antenna technique. Each array element is a nearly square ring microstrip antenna and is fed at a point on the diagonal of the antenna to generate quadrature magnetic fields. Compared with conventional quadrature coils, the single-feed structure is much simple and compact, making the quadrature coil array design practical. Numerical simulations demonstrate that the decoupling between elements is better than -35 dB for all the elements and the RF fields are homogeneous with deep penetration and quadrature behavior in the area of interest. Bloch equation simulation is also performed to simulate the excitation procedure by using an 8-element quadrature planar patch array to demonstrate its feasibility in parallel transmission at the ultrahigh field of 7 Tesla. PMID:24649430
Pang, Yong; Yu, Baiying; Vigneron, Daniel B.
2014-01-01
Quadrature coils are often desired in MR applications because they can improve MR sensitivity and also reduce excitation power. In this work, we propose, for the first time, a quadrature array design strategy for parallel transmission at 298 MHz using single-feed circularly polarized (CP) patch antenna technique. Each array element is a nearly square ring microstrip antenna and is fed at a point on the diagonal of the antenna to generate quadrature magnetic fields. Compared with conventional quadrature coils, the single-feed structure is much simple and compact, making the quadrature coil array design practical. Numerical simulations demonstrate that the decoupling between elements is better than –35 dB for all the elements and the RF fields are homogeneous with deep penetration and quadrature behavior in the area of interest. Bloch equation simulation is also performed to simulate the excitation procedure by using an 8-element quadrature planar patch array to demonstrate its feasibility in parallel transmission at the ultrahigh field of 7 Tesla. PMID:24649430
NASA Technical Reports Server (NTRS)
Sidi, A.; Israeli, M.
1986-01-01
High accuracy numerical quadrature methods for integrals of singular periodic functions are proposed. These methods are based on the appropriate Euler-Maclaurin expansions of trapezoidal rule approximations and their extrapolations. They are used to obtain accurate quadrature methods for the solution of singular and weakly singular Fredholm integral equations. Such periodic equations are used in the solution of planar elliptic boundary value problems, elasticity, potential theory, conformal mapping, boundary element methods, free surface flows, etc. The use of the quadrature methods is demonstrated with numerical examples.
Pilot-symbols-aided cycle slip mitigation for DP-16QAM optical communication systems.
Cheng, Haiquan; Li, Yan; Zhang, Fangzheng; Wu, Jian; Lu, Jianxin; Zhang, Guoyi; Xu, Jian; Lin, Jintong
2013-09-23
A pilot-symbols-aided phase unwrapping (PAPU), which utilizes the time-division multiplexed pilot symbols that are transmitted with data, is proposed to do cycle slip detection and correction with the carrier phase estimation (CPE). Numerical simulations for 10 Gbaud dual-polarization 16-ary quadrature amplitude modulation (DP-16QAM) systems show that the block averaging quadrature phase-shift keying (QPSK) partitioning with PAPU greatly eliminates the performance degradation caused by cycle slips, maintains a low CS probability with less influence of filter length, and achieves a bit-error-rate (BER) performance below soft-decision forward error correction (FEC) limit 2 × 10⁻² at 15 dB optical signal-to-noise ratio with only 1.56% overhead and 6 MHz combined laser linewidth. PMID:24104108
Transmission and reception of PDM dual-subcarrier coherent 16QAM-OFDM signals
NASA Astrophysics Data System (ADS)
Li, Fan; Zhang, Junwen; Yu, Jianjun; Li, Xinying
2015-12-01
In this paper, 16-Gbaud polarization-division-multiplexed (PDM) dual-subcarrier coherent optical orthogonal frequency division multiplexing (CO-OFDM) transmission and reception are successfully demonstrated without overhead. The in-phase and quadrature (I/Q) components of dual-subcarrier 16-ary quadrature amplitude modulation (QAM) OFDM signal are both seven-level signals in time domain, and thus can be equalized like a 49 QAM signal in time domain with cascaded multi-modulus algorithm (CMMA) equalization method. The experimental results show that there is no power penalty observed between optical back to back (OBTB) and after 80-km single-mode fiber-28 (SMF-28) with time domain CMMA equalization method. A 0.4 dB optical signal to noise ratio (OSNR) penalty in OBTB is observed when the bandwidth of channel is set at 26 GHz at the BER of 2.0 × 10-2.
High spectral density transmission emulation using amplified spontaneous emission noise.
Elson, Daniel J; Galdino, Lidia; Maher, Robert; Killey, Robert I; Thomsen, Benn C; Bayvel, Polina
2016-01-01
We demonstrate the use of spectrally shaped amplified spontaneous emission (SS-ASE) noise for wideband channel loading in the investigation of nonlinear transmission limits in wavelength-division multiplexing transmission experiments using Nyquist-spaced channels. The validity of this approach is explored through statistical analysis and experimental transmission of Nyquist-spaced 10 GBaud polarization-division multiplexing (PDM) quadrature phase-shift keying and PDM-16-ary quadrature amplitude modulation (QAM) channels, co-propagated with SS-ASE over single mode fiber. It is shown that this technique, which is simpler to implement than a fully modulated comb of channels, is valid for distances exceeding 240 km for PDM-16QAM with dispersion of 16 ps/nm/km, yields a good agreement with theory, and provides a conservative measure of system performance. PMID:26696160
Substorm statistics: Occurrences and amplitudes
Borovsky, J.E.; Nemzek, R.J.
1994-05-01
The occurrences and amplitudes of substorms are statistically investigated with the use of three data sets: the AL index, the Los Alamos 3-satellite geosynchronous energetic-electron measurements, and the GOES-5 and -6 geosynchronous magnetic-field measurements. The investigation utilizes {approximately} 13,800 substorms in AL, {approximately} 1400 substorms in the energetic-electron flux, and {approximately} 100 substorms in the magnetic field. The rate of occurrence of substorms is determined as a function of the time of day, the time of year, the amount of magnetotail bending, the orientation of the geomagnetic dipole, the toward/away configuration of the IMF, and the parameters of the solar wind. The relative roles of dayside reconnection and viscous coupling in the production of substorms are assessed. Three amplitudes are defined for a substorms: the jump in the AL index, the peak of the >30-keV integral electron flux at geosynchronous orbit near midnight, and the angle of rotation of the geosynchronous magnetic field near midnight. The substorm amplitudes are statistically analyzed, the amplitude measurements are cross correlated with each other, and the substorm amplitudes are determined as functions of the solar-wind parameters. Periodically occurring and randomly occurring substorms are analyzed separately. The energetic-particle-flux amplitudes are consistent with unloading and the AL amplitudes are consistent with direct driving plus unloading.
CHY formula and MHV amplitudes
NASA Astrophysics Data System (ADS)
Du, Yi-Jian; Teng, Fei; Wu, Yong-Shi
2016-05-01
In this paper, we study the relation between the Cachazo-He-Yuan (CHY) formula and the maximal-helicity-violating (MHV) amplitudes of Yang-Mills and gravity in four dimensions. We prove that only one special rational solution of the scattering equations found by Weinzierl supports the MHV amplitudes. Namely, localized at this solution, the integrated CHY formula produces the Parke-Taylor formula for MHV Yang-Mills amplitudes as well as the Hodges formula for MHV gravitational amplitudes, with an arbitrary number of external gluons/gravitons. This is achieved by developing techniques, in a manifestly Möbius covariant formalism, to explicitly compute relevant reduced Pfaffians/determinants. We observe and prove two interesting properties (or identities), which facilitate the computations. We also check that all the other ( n - 3)! - 1 solutions to the scattering equations do not support the MHV amplitudes, and prove analytically that this is indeed true for the other special rational solution proposed by Weinzierl, that actually supports the anti-MHV amplitudes. Our results reveal a mysterious feature of the CHY formalism that in Yang-Mills and gravity theory, solutions of scattering equations, involving only external momenta, somehow know about the configuration of external polarizations of the scattering amplitudes.
A PWM quadrature-booster phase shifter for ac power transmission
Lopes, L.A.C.; Joos, G.; Ooi, B.T.
1997-01-01
The conventional structures used for phase shifters employ quadrature voltage injection controlled by means of on-load tap changers that require considerable maintenance. Line-commutated thyristor structures have been proposed to replace tap changers, but problems related to filter requirements or the number of switches have limited their utilization. This paper proposes a pulse width modulation (PWM) quadrature-booster phase shifter based on a force-commutated ac controller. It offers features such as fast dynamic response, continuous variation of the phase angle with low harmonic injection, and it requires a simple power structure and can be controlled by adjusting the duty cycle of the switches. The operating principles of the proposed phase shifter are analyzed and their feasibility is demonstrated through digital simulation and experimental implementation.
Solution of stochastic media transport problems using a numerical quadrature-based method
Pautz, S. D.; Franke, B. C.; Prinja, A. K.; Olson, A. J.
2013-07-01
We present a new conceptual framework for analyzing transport problems in random media. We decompose such problems into stratified subproblems according to the number of material pseudo-interfaces within realizations. For a given subproblem we assign pseudo-interface locations in each realization according to product quadrature rules, which allows us to deterministically generate a fixed number of realizations. Quadrature integration of the solutions of these realizations thus approximately solves each subproblem; the weighted superposition of solutions of the subproblems approximately solves the general stochastic media transport problem. We revisit some benchmark problems to determine the accuracy and efficiency of this approach in comparison to randomly generated realizations. We find that this method is very accurate and fast when the number of pseudo-interfaces in a problem is generally low, but that these advantages quickly degrade as the number of pseudo-interfaces increases. (authors)
NASA Astrophysics Data System (ADS)
Pierré, J.-E.; Passieux, J.-C.; Périé, J.-N.; Bugarin, F.; Robert, L.
2016-02-01
Like subset-based methods, the very first finite element versions of digital image correlation were closely related to the regular structure of images, as they were based on regular quadrilateral elements corresponding to an integer number of pixels. The use of unstructured meshes, to exploit the full potential of FE-DIC in structural mechanics, is now widespread. Most of the time, the formulation, the quadrature and the definition of the region of interest still rely on the pixels grid. In this paper, a formulation in the physical coordinate system and not in the image frame is proposed for 2D digital image correlation. In addition to a more precise definition of the region of interest, it allows the use of a more accurate quadrature rule. It is also shown that lens distortions can be successfully taken into account directly with such a formalism.
Adams, M.L. ); Wareing, T.A. )
1993-01-01
We study diffusion-synthetic acceleration (DSA) for within-group scattering iterations in discrete ordinates calculations. We consider analytic (not spatially discretized) equations in Cartesian coordinates with linearly anisotropic scattering. We place no restrictions on the discrete ordinates quadrature set. We assume an infinite homogeneous medium. Our main results are as follows: 1. DSA is unstable in two dimensions (2D) and three dimensions (3D), given forward-peaked scattering. It can be stabilized by taking extra transport sweeps each iteration. 2. Standard DSA is unstable, given any quadrature set that does not correctly integrate linear functions of angle. 3. Relative to one dimension (ID), DSA's performance is degraded in 2D and 3D.
A note on the bounds of the error of Gauss-Turan-type quadratures
NASA Astrophysics Data System (ADS)
Milovanovic, Gradimir V.; Spalevic, Miodrag M.
2007-03-01
This note is concerned with estimates for the remainder term of the Gauss-Turan quadrature formula,where is the Gori-Michelli weight function, with Un-1(t) denoting the (n-1)th degree Chebyshev polynomial of the second kind, and f is a function analytic in the interior of and continuous on the boundary of an ellipse with foci at the points +/-1 and sum of semiaxes [varrho]>1. The present paper generalizes the results in [G.V. Milovanovic, M.M. Spalevic, Bounds of the error of Gauss-Turan-type quadratures, J. Comput. Appl. Math. 178 (2005) 333-346], which is concerned with the same problem when s=1.
NASA Astrophysics Data System (ADS)
Zhen, Shenglai; Chen, Bo; Yuan, Liang; Li, Min; Liang, Jing; Yu, Benli
2010-03-01
In-phase and quadrature-phase (I/Q) signals often need to be formed in the laser interferometric vibration measurement technique. To avoid the disadvantages of traditional I/Q signals forming methods such as effect of piezoelectric ceramic (PZT) for generating high frequency carrier, or optical configuration with complicated structure, a novel interferometric vibration measurement sensor with quadrature detection is proposed. The sensor utilizes simple optical configuration which contains 1/8 wave plate to generate two I/Q signals, then the signals were processed by arctangent algorithm which is compiled by Labview software through data acquisition card. Theoretical analysis and experimental Lissajous figures synthesis prove the phase orthogonality of the two signals. The experimental results indicate that the system can measure the vibration displacement accurately.
An accurate quadrature technique for the contact boundary in 3D finite element computations
NASA Astrophysics Data System (ADS)
Duong, Thang X.; Sauer, Roger A.
2015-01-01
This paper presents a new numerical integration technique for 3D contact finite element implementations, focusing on a remedy for the inaccurate integration due to discontinuities at the boundary of contact surfaces. The method is based on the adaptive refinement of the integration domain along the boundary of the contact surface, and is accordingly denoted RBQ for refined boundary quadrature. It can be used for common element types of any order, e.g. Lagrange, NURBS, or T-Spline elements. In terms of both computational speed and accuracy, RBQ exhibits great advantages over a naive increase of the number of quadrature points. Also, the RBQ method is shown to remain accurate for large deformations. Furthermore, since the sharp boundary of the contact surface is determined, it can be used for various purposes like the accurate post-processing of the contact pressure. Several examples are presented to illustrate the new technique.
Quadrature algorithms to the luminosity distance with a time-dependent dark energy model
Yue, Nan-Nan; Liu, De-Zi; Pei, Xiao-Xing; Zhang, Tong-Jie; Yang, Zhi-Liang; Zhu, Fang-Fang E-mail: bingzi@mail.bnu.edu.cn E-mail: fiona-90@live.cn E-mail: zlyang@bnu.edu.cn
2011-11-01
In our previous work [1], we have proposed two methods for computing the luminosity distance d{sub L}{sup Λ} in ΛCDM model. In this paper, two effective quadrature algorithms, known as Romberg Integration and composite Gaussian Quadrature, are presented to calculate the luminosity distance d{sub L}{sup CPL} in the Chevallier-Polarski-Linder parametrization(CPL) model. By comparing both the efficiency and accuracy of the two algorithms, we find that the second is more promising. Moreover, we develop another strategy adapted for approximating d{sub L}{sup Λ} in flat ΛCDM universe. To some extent, our methods can make contributions to the recent numerical stimulation for the investigation of dark energy cosmology.
New Adaptive Method for IQ Imbalance Compensation of Quadrature Modulators in Predistortion Systems
NASA Astrophysics Data System (ADS)
Zareian, Hassan; Vakili, Vahid Tabataba
2009-12-01
Imperfections in quadrature modulators (QMs), such as inphase and quadrature (IQ) imbalance, can severely impact the performance of power amplifier (PA) linearization systems, in particular in adaptive digital predistorters (PDs). In this paper, we first analyze the effect of IQ imbalance on the performance of a memory orthogonal polynomials predistorter (MOP PD), and then we propose a new adaptive algorithm to estimate and compensate the unknown IQ imbalance in QM. Unlike previous compensation techniques, the proposed method was capable of online IQ imbalance compensation with faster convergence, and no special calibration or training signals were needed. The effectiveness of the proposed IQ imbalance compensator was validated by simulations. The results clearly show the performance of the MOP PD to be enhanced significantly by adding the proposed IQ imbalance compensator.
Analysis of V-cycle multigrid algorithms for forms defined by numerical quadrature
Bramble, J.H. . Dept. of Mathematics); Goldstein, C.I.; Pasciak, J.E. . Applied Mathematics Dept.)
1994-05-01
The authors describe and analyze certain V-cycle multigrid algorithms with forms defined by numerical quadrature applied to the approximation of symmetric second-order elliptic boundary value problems. This approach can be used for the efficient solution of finite element systems resulting from numerical quadrature as well as systems arising from finite difference discretizations. The results are based on a regularity free theory and hence apply to meshes with local grid refinement as well as the quasi-uniform case. It is shown that uniform (independent of the number of levels) convergence rates often hold for appropriately defined V-cycle algorithms with as few as one smoothing per grid. These results hold even on applications without full elliptic regularity, e.g., a domain in R[sup 2] with a crack.
NASA Astrophysics Data System (ADS)
Lam, C. S.; Yao, York-Peng
2016-06-01
The Cachazo-He-Yuan (CHY) formula for on-shell scattering amplitudes is extended off-shell. The off-shell amplitudes (amputated Green's functions) are Möbius invariant, and have the same momentum poles as the on-shell amplitudes. The working principles which drive the modifications to the scattering equations are mainly Möbius covariance and energy momentum conservation in off-shell kinematics. The same technique is also used to obtain off-shell massive scalars. A simple off-shell extension of the CHY gauge formula which is Möbius invariant is proposed, but its true nature awaits further study.
Rational Gauss-Chebyshev quadrature formulas for complex poles outside [-1,1
NASA Astrophysics Data System (ADS)
Deckers, Karl; van Deun, Joris; Bultheel, Adhemar
2008-06-01
In this paper we provide an extension of the Chebyshev orthogonal rational functions with arbitrary real poles outside [-1,1] to arbitrary complex poles outside [-1,1] . The zeros of these orthogonal rational functions are not necessarily real anymore. By using the related para-orthogonal functions, however, we obtain an expression for the nodes and weights for rational Gauss-Chebyshev quadrature formulas integrating exactly in spaces of rational functions with arbitrary complex poles outside [-1,1] .
Variable transformations and Gauss-Legendre quadrature for integrals with endpoint singularities
NASA Astrophysics Data System (ADS)
Sidi, Avram
2009-09-01
Gauss-Legendre quadrature formulas have excellent convergence properties when applied to integrals int^1_0f(x) dx with fin C^infty[0,1] . However, their performance deteriorates when the integrands f(x) are in C^infty(0,1) but are singular at x=0 and/or x=1 . One way of improving the performance of Gauss-Legendre quadrature in such cases is by combining it with a suitable variable transformation such that the transformed integrand has weaker singularities than those of f(x) . Thus, if x=psi(t) is a variable transformation that maps [0,1] onto itself, we apply Gauss-Legendre quadrature to the transformed integral int^1_{0}f(psi(t))psi'(t) dt , whose singularities at t=0 and/or t=1 are weaker than those of f(x) at x=0 and/or x=1 . In this work, we first define a new class of variable transformations we denote widetilde{mathcal{S}}_{p,q} , where p and q are two positive parameters that characterize it. We also give a simple and easily computable representative of this class. Next, by invoking some recent results by the author concerning asymptotic expansions of Gauss-Legendre quadrature approximations as the number of abscissas tends to infinity, we present a thorough study of convergence of the combined approximation procedure, with variable transformations from widetilde{mathcal{S}}_{p,q} . We show how optimal results can be obtained by adjusting the parameters p and q of the variable transformation in an appropriate fashion. We also give numerical examples that confirm the theoretical results.
Hayward, Thomas J; Oba, Roger M
2013-07-01
Numerical methods are presented for approximating the probability density functions (pdf's) of acoustic fields and receiver-array responses induced by a given joint pdf of a set of acoustic environmental parameters. An approximation to the characteristic function of the random acoustic field (the inverse Fourier transform of the field pdf) is first obtained either by construction of the empirical characteristic function (ECF) from a random sample of the acoustic parameters, or by application of generalized Gaussian quadrature to approximate the integral defining the characteristic function. The Fourier transform is then applied to obtain an approximation of the pdf by a continuous function of the field variables. Application of both the ECF and generalized Gaussian quadrature is demonstrated in an example of a shallow-water ocean waveguide with two-dimensional uncertainty of sound speed and attenuation coefficient in the ocean bottom. Both approximations lead to a smoother estimate of the field pdf than that provided by a histogram, with generalized Gaussian quadrature providing a smoother estimate at the tails of the pdf. Potential applications to acoustic system performance quantification and to nonparametric acoustic signal processing are discussed. PMID:23862782
A Gaussian quadrature method for total energy analysis in electronic state calculations
NASA Astrophysics Data System (ADS)
Fukushima, Kimichika
This article reports studies by Fukushima and coworkers since 1980 concerning their highly accurate numerical integral method using Gaussian quadratures to evaluate the total energy in electronic state calculations. Gauss-Legendre and Gauss-Laguerre quadratures were used for integrals in the finite and infinite regions, respectively. Our previous article showed that, for diatomic molecules such as CO and FeO, elliptic coordinates efficiently achieved high numerical integral accuracy even with a numerical basis set including transition metal atomic orbitals. This article will generalize straightforward details for multiatomic systems with direct integrals in each decomposed elliptic coordinate determined from the nuclear positions of picked-up atom pairs. Sample calculations were performed for the molecules O3 and H2O. This article will also try to present, in another coordinate, a numerical integral by partially using the Becke's decomposition published in 1988, but without the Becke's fuzzy cell generated by the polynomials of internuclear distance between the pair atoms. Instead, simple nuclear weights comprising exponential functions around nuclei are used. The one-center integral is performed with a Gaussian quadrature pack in a spherical coordinate, included in the author's original program in around 1980. As for this decomposition into one-center integrals, sample calculations are carried out for Li2.
Positive amplitudes in the amplituhedron
NASA Astrophysics Data System (ADS)
Arkani-Hamed, Nima; Hodges, Andrew; Trnka, Jaroslav
2015-08-01
The all-loop integrand for scattering amplitudes in planar SYM is determined by an "amplitude form" with logarithmic singularities on the boundary of the amplituhedron. In this note we provide strong evidence for a new striking property of the superamplitude, which we conjecture to be true to all loop orders: the amplitude form is positive when evaluated inside the amplituhedron. The statement is sensibly formulated thanks to the natural "bosonization" of the superamplitude associated with the amplituhedron geometry. However this positivity is not manifest in any of the current approaches to scattering amplitudes, and in particular not in the cellulations of the amplituhedron related to on-shell diagrams and the positive grassmannian. The surprising positivity of the form suggests the existence of a "dual amplituhedron" formulation where this feature would be made obvious. We also suggest that the positivity is associated with an extended picture of amplituhedron geometry, with the amplituhedron sitting inside a co-dimension one surface separating "legal" and "illegal" local singularities of the amplitude. We illustrate this in several simple examples, obtaining new expressions for amplitudes not associated with any triangulations, but following in a more invariant manner from a global view of the positive geometry.
Shape of Pion Distribution Amplitude
Radyushkin, Anatoly
2009-11-01
A scenario is investigated in which the leading-twist pion distribution amplitude $\\varphi_\\pi (x)$ is approximated by the pion decay constant $f_\\pi$ for all essential values of the light-cone fraction $x$. A model for the light-front wave function $\\Psi (x, k_\\perp)$ is proposed that produces such a distribution amplitude and has a rapidly decreasing (exponential for definiteness) dependence on the light-front energy combination $ k_\\perp^2/x(1-x)$. It is shown that this model easily reproduces the fit of recent large-$Q^2$ BaBar data on the photon-pion transition form factor. Some aspects of scenario with flat pion distribution amplitude are discussed.
OPE for all helicity amplitudes
NASA Astrophysics Data System (ADS)
Basso, Benjamin; Caetano, João; Córdova, Lucía; Sever, Amit; Vieira, Pedro
2015-08-01
We extend the Operator Product Expansion (OPE) for scattering amplitudes in planar SYM to account for all possible helicities of the external states. This is done by constructing a simple map between helicity configurations and so-called charged pentagon transitions. These OPE building blocks are generalizations of the bosonic pentagons entering MHV amplitudes and they can be bootstrapped at finite coupling from the integrable dynamics of the color flux tube. A byproduct of our map is a simple realization of parity in the super Wilson loop picture.
Toward complete pion nucleon amplitudes
NASA Astrophysics Data System (ADS)
Mathieu, V.; Danilkin, I. V.; Fernández-Ramírez, C.; Pennington, M. R.; Schott, D.; Szczepaniak, Adam P.; Fox, G.
2015-10-01
We compare the low-energy partial-wave analyses of π N scattering with high-energy data via finite-energy sum rules. We construct a new set of amplitudes by matching the imaginary part from the low-energy analysis with the high-energy, Regge parametrization and reconstruct the real parts using dispersion relations.
Toward complete pion nucleon amplitudes
Mathieu, Vincent; Danilkin, Igor V.; Fernández-Ramírez, Cesar; Pennington, Michael R.; Schott, Diane M.; Szczepaniak, Adam P.; Fox, G.
2015-10-05
We compare the low-energy partial wave analyses πN scattering with a high-energy data via finite energy sum rules. We also construct a new set of amplitudes by matching the imaginary part from the low-energy analysis with the high-energy, Regge parametrization and then reconstruct the real parts using dispersion relations.
Large amplitude drop shape oscillations
NASA Technical Reports Server (NTRS)
Trinh, E. H.; Wang, T. G.
1982-01-01
An experimental study of large amplitude drop shape oscillation was conducted in immiscible liquids systems and with levitated free liquid drops in air. In liquid-liquid systems the results indicate the existence of familiar characteristics of nonlinear phenomena. The resonance frequency of the fundamental quadrupole mode of stationary, low viscosity Silicone oil drops acoustically levitated in water falls to noticeably low values as the amplitude of oscillation is increased. A typical, experimentally determined relative frequency decrease of a 0.5 cubic centimeters drop would be about 10% when the maximum deformed shape is characterized by a major to minor axial ratio of 1.9. On the other hand, no change in the fundamental mode frequency could be detected for 1 mm drops levitated in air. The experimental data for the decay constant of the quadrupole mode of drops immersed in a liquid host indicate a slight increase for larger oscillation amplitudes. A qualitative investigation of the internal fluid flows for such drops revealed the existence of steady internal circulation within drops oscillating in the fundamental and higher modes. The flow field configuration in the outer host liquid is also significantly altered when the drop oscillation amplitude becomes large.
Employing helicity amplitudes for resummation
NASA Astrophysics Data System (ADS)
Moult, Ian; Stewart, Iain W.; Tackmann, Frank J.; Waalewijn, Wouter J.
2016-05-01
Many state-of-the-art QCD calculations for multileg processes use helicity amplitudes as their fundamental ingredients. We construct a simple and easy-to-use helicity operator basis in soft-collinear effective theory (SCET), for which the hard Wilson coefficients from matching QCD onto SCET are directly given in terms of color-ordered helicity amplitudes. Using this basis allows one to seamlessly combine fixed-order helicity amplitudes at any order they are known with a resummation of higher-order logarithmic corrections. In particular, the virtual loop amplitudes can be employed in factorization theorems to make predictions for exclusive jet cross sections without the use of numerical subtraction schemes to handle real-virtual infrared cancellations. We also discuss matching onto SCET in renormalization schemes with helicities in 4- and d -dimensions. To demonstrate that our helicity operator basis is easy to use, we provide an explicit construction of the operator basis, as well as results for the hard matching coefficients, for p p →H +0 , 1, 2 jets, p p →W /Z /γ +0 , 1, 2 jets, and p p →2 , 3 jets. These operator bases are completely crossing symmetric, so the results can easily be applied to processes with e+e- and e-p collisions.
Mandelstam, S.
1986-06-01
Work on the derivation of an explicit perturbation series for string and superstring amplitudes is reviewed. The light-cone approach is emphasized, but some work on the Polyakov approach is also mentioned, and the two methods are compared. The calculation of the measure factor is outlined in the interacting-string picture. (LEW)
Positivity of spin foam amplitudes
NASA Astrophysics Data System (ADS)
Baez, John C.; Christensen, J. Daniel
2002-04-01
The amplitude for a spin foam in the Barrett-Crane model of Riemannian quantum gravity is given as a product over its vertices, edges and faces, with one factor of the Riemannian 10j symbols appearing for each vertex, and simpler factors for the edges and faces. We prove that these amplitudes are always nonnegative for closed spin foams. As a corollary, all open spin foams going between a fixed pair of spin networks have real amplitudes of the same sign. This means one can use the Metropolis algorithm to compute expectation values of observables in the Riemannian Barrett-Crane model, as in statistical mechanics, even though this theory is based on a real-time (eiS) rather than imaginary-time e-S path integral. Our proof uses the fact that when the Riemannian 10j symbols are nonzero, their sign is positive or negative depending on whether the sum of the ten spins is an integer or half-integer. For the product of 10j symbols appearing in the amplitude for a closed spin foam, these signs cancel. We conclude with some numerical evidence suggesting that the Lorentzian 10j symbols are always nonnegative, which would imply similar results for the Lorentzian Barrett-Crane model.
Constant-amplitude RC oscillator
NASA Technical Reports Server (NTRS)
Kerwin, W. J.; Westbrook, R. M.
1970-01-01
Sinusoidal oscillator has a frequency determined by resistance-capacitance /RC/ values of two charge control devices and a constant-amplitude voltage independent of frequency and RC values. RC elements provide either voltage-control, resistance-control, or capacitance-control of the frequency.
Wu, S.H.; Wu, C.Y.; Hsu, P.
1996-12-31
This work considers radiative heat transfer in a three-dimensional, rectangular, scattering medium exposed to diffuse radiation. Applying the quadrature method with singularity subtraction to the exact integral equations in terms of the moments of intensity can generate highly accurate solutions, and so the method is adopted in this work. The example solutions provided are for radiative equilibrium in homogeneous absorbing-emitting media, and for radiative transfer in nonhomogeneous absorbing-scattering (isotropic and linearly anisotropic) media with non-reflecting surfaces. To validate the solutions, the present results are compared with the solutions obtained by the YIX method and other methods.
A Synthetic Quadrature Phase Detector/Demodulator for Fourier Transform Transform Spectrometers
NASA Technical Reports Server (NTRS)
Campbell, Joel
2008-01-01
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.
Mathews, K.A.; Brennan, C.R.
1995-12-31
The exponential characteristic method is one of a family of nonlinear spatial quadratures which are positive and at least second order accurate. The authors initially developed the method in slab geometry, where it gave accurate results for deep penetration problems using coarse meshes. Characteristic methods are restricted to Cartesian geometries, so they next tested it with rectangular cells, where it was again a strong performer. Here the authors extend the method to unstructured grids of arbitrarily shaped and oriented triangles and report on its performance.
Optimization of quadrature signal processing for laser interferometers for demanding applications
NASA Astrophysics Data System (ADS)
PodŻorny, Tomasz; Budzyń, Grzegorz; Tkaczyk, Jakub
2016-06-01
Presented paper performs an analysis of quadrature signal processing algorithms for high demanding laser interferometry applications. Careful signal processing is required to minimize nonlinearities which come from optical path and components' imperfections, and reduce overall instrumental error. Paper focuses on algebraic fits, because implementation for real time systems was a main requirement. The most demanding applications are stationary measurements where the position slightly fluctuates in the range below one fringe period. Therefore, analysis was performed for samples that were spread along a few milliradians of a full circle.
Nodal systems with maximal domain of exactness for Gaussian quadrature formulas
NASA Astrophysics Data System (ADS)
Berriochoa, E.; Cachafeiro, A.
2008-03-01
The aim of this work is to study quadrature formulas for measures on the complex plane. The novelty of our contribution is to consider the exactness on subspaces of polynomials on the variables z and . Using this approach we characterize, in a unified way, the classical nodal systems for measures on the real line and the nodal systems for measures on the unit circle, which are based on para-orthogonal polynomials. We also characterize the nodal systems on the unit circle, which are not based on para-orthogonal polynomials (only for the case of nodal systems with 1 or 2 points).
Extremal states for photon number and quadratures as gauges for nonclassicality
NASA Astrophysics Data System (ADS)
Hradil, Z.; Řeháček, J.; de la Hoz, P.; Leuchs, G.; Sánchez-Soto, L. L.
2015-04-01
Rotated quadratures carry the phase-dependent information of the electromagnetic field, so they are somehow conjugate to the photon number. We analyze this noncanonical pair, finding an exact uncertainty relation, as well as a couple of weaker inequalities obtained by relaxing some restrictions of the problem. We also find the intelligent states saturating that relation and complete their characterization by considering extra constraints on the second-order moments of the variables involved. Using these moments, we construct performance measures tailored to diagnose photon-added and Schrödinger-cat-like states, among others.
On bi-orthogonal systems of trigonometric functions and quadrature formulas for periodic integrands
NASA Astrophysics Data System (ADS)
Cruz-Barroso, Ruymán; González-Vera, Pablo; Njåstad, Olav
2007-04-01
In this paper, quadrature formulas with an arbitrary number of nodes and exactly integrating trigonometric polynomials up to degree as high as possible are constructed in order to approximate 2?-periodic weighted integralsE For this purpose, certain bi-orthogonal systems of trigonometric functions are introduced and their most relevant properties studied. Some illustrative numerical examples are also given. The paper completes the results previously given by Szeg? in Magy Tud Akad Mat Kut Intez K?zl 8:255?273, 1963 and by some of the authors in Annales Mathematicae et Informaticae 32:5?44, 2005.
Automatic IQ Imbalance Compensation Technique for Quadrature Modulator by Single-Tone Testing
NASA Astrophysics Data System (ADS)
Kim, Minseok; Konishi, Yohei; Takada, Jun-Ichi; Gao, Boxin
This letter proposes an automatic IQ imbalance compensation technique for quadrature modulators by means of spectrum measurement of RF signal using a spectrum analyzer. The analyzer feeds back only magnitude information of the frequency spectrum of the signal. To realize IQ imbalance compensation, the conventional method of steepest descent is modified; the descent direction is empirically determined and a variable step-size is introduced for accelerating convergence. The experimental results for a four-channel transmitter operating at 11GHz are presented for verification.
Vibration analysis of shear deformable circular arches by the differential quadrature method
NASA Astrophysics Data System (ADS)
Kang, K.; Bert, C. W.; Striz, A. G.
1995-06-01
The differential quadrature method is applied in the computation of the eigenvalues of the equations of motion governing in-plane and out-of-plane vibration of circular arches, based on the Bresse-Timoshenko beam theory in which both rotatory inertia and shear deformation are taken into account. Fundamental frequencies are calculated for arches of rectangular and circular cross sections under clamped-clamped end conditions and the results are compared with numerical solutions by another method. The present method gives good accuracy with only a limited number of grid points.
True amplitude prestack depth migration
NASA Astrophysics Data System (ADS)
Deng, Feng
Reliable analysis of amplitude variation with offset (or with angle) requires accurate amplitudes from prestack migration. In routine seismic data processing, amplitude balancing and automatic gain control are often used to reduce amplitude lateral variations. However, these methods are empirical and lack a solid physical basis; thus, there are uncertainties that might produce erroneous conclusions, and hence cause economic loss. During wavefield propagation, geometrical spreading, intrinsic attenuation, transmission losses and the energy conversion significantly distort the wavefield amplitude. Most current true-amplitude migrations usually compensate only for geometrical spreading. A new prestack depth migration based on the framework of reverse-time migration in the time-space domain was developed in this dissertation with the aim of compensating all of the propagation effects in one integrated algorithm. Geometrical spreading is automatically included because of the use of full two-way wave extrapolation. Viscoelastic wave equations are solved to handle the intrinsic attenuation with a priori quality factor. Transmission losses for both up- and down-going waves are compensated using a two-pass, recursive procedure based on extracting the angle-dependent reflection/transmission coefficients from prestack migration. The losses caused by the conversion of energy from one elastic model to another are accounted for through elastic wave extrapolation; the influence of the S wave velocity contrast on the P wave reflection coefficient is implicitly included by using the Zoeppritz equations to describe the reflection and transmission at an elastic interface. Only smooth background models are assumed to be known. The contrasts/ratios of the model parameters can be estimated by fitting the compensated angle-dependent reflection coefficients obtained from data for multiple sources. This is one useful by-product of the algorithm. Numerical tests on both 2D and 3D scalar
Application of Quadrature Methods for Re-Weighting in Lattice QCD
Abdou Abdel-Rehim, William Detmold, Kostas Orginos
2011-12-01
Re-weighting is a useful tool that has been employed in Lattice QCD in different contexts including, tuning the strange quark mass, approaching the light quark mass regime, and simulating electromagnetic fields on top of QCD gauge configurations. In case of re-weighting the sea quark mass, the re-weighting factor is given by the ratio of the determinants of two Dirac operators D{sub a} and D{sub b}. A popular approach for computing this ratio is to use a pseudofermion representation of the determinant of the composite operator {Omega} = D{sub a}(D{sub b}{sup {dagger}}D{sub b}){sup -1} D{sub a}{sup {dagger}}. Here, we study using quadrature methods together with noise vectors to compute the ratio of determinants. We show that, with quadrature methods each determinant can be computed separately using the operators {Omega}{sub a} = D{sub a}{sup {dagger}}D{sub a} and {Omega}{sub b} = D{sub b}{sup {dagger}} D{sub b}. We also discuss using bootstrap re-sampling to remove the bias from the determinant estimator.
Shilyagin, P A; Gelikonov, G V; Gelikonov, V M; Moiseev, A A; Terpelov, D A
2014-07-31
We have thoroughly investigated the method of simultaneous reception of spectral components with the achromatised quadrature phase shift between two portions of a reference wave, designed for the effective suppression of the 'mirror' artefact in the resulting image obtained by means of spectral domain optical coherence tomography (SD OCT). We have developed and experimentally tested a phase-shifting element consisting of a beam divider, which splits the reference optical beam into the two beams, and of delay lines being individual for each beam, which create a mutual phase difference of π/2 in the double pass of the reference beam. The phase shift achromatism over a wide spectral range is achieved by using in the delay lines the individual elements with different dispersion characteristics. The ranges of admissible adjustment parameters of the achromatised delay line are estimated for exact and inexact conformity of the geometric characteristics of its components to those calculated. A possibility of simultaneous recording of the close-to-quadrature spectral components with a single linear photodetector element is experimentally confirmed. The suppression of the artefact mirror peak in the OCT-signal by an additional 9 dB relative to the level of its suppression is experimentally achieved when the air delay line is used. Two-dimensional images of the surface positioned at an angle to the axis of the probe beam are obtained with the correction of the 'mirror' artefact while maintaining the dynamic range of the image. (laser biophotonics)
Selcuk, N.; Kayakol, N.
1996-11-01
Effects of order of approximation (S{sub 2} and S{sub 4}), angular quadrature (S{sub n} and S{sub n}{prime}) and spatial differencing (diamond and variable-weight) schemes, on the predictive accuracy of discrete ordinates method were investigated by predicting the distributions of radiative flux density and source term of a rectangular enclosure problem and comparing the results with exact solutions produced previously. The enclosure problem is based on data reported earlier on a large-scale experimental furnace with steep temperature gradients. It is a black-walled enclosure containing an absorbing-emitting medium of constant properties. Comparisons show that better agreement is obtained in radiative energy source terms than in flux densities and that the order of approximation plays a more significant role than angular quadrature and spatial differencing schemes in the accuracy of predicted radiative flux densities and radiative energy source terms. Only slight improvements are obtained when S{sub n} and variable-weight differencing schemes are employed.
Mathews, K.; Sjoden, G.; Minor, B. )
1994-09-01
The exponential characteristic spatial quadrature for discrete ordinates neutral particle transport in slab geometry is derived and compared with current methods. It is similar to the linear characteristic (or, in slab geometry, the linear nodal) quadrature but differs by assuming an exponential distribution of the scattering source within each cell, S(x) = a exp(bx), whose parameters are root-solved to match the known (from the previous iteration) average and first moment of the source over the cell. Like the linear adaptive method, the exponential characteristic method is positive and nonlinear but more accurate and more readily extended to other cell shapes. The nonlinearity has not interfered with convergence. The authors introduce the exponential moment functions,'' a generalization of the functions used by Walters in the linear nodal method, and use them to avoid numerical ill-conditioning. The method exhibits O([Delta]x[sup 4]) truncation error on fine enough meshes; the error is insensitive to mesh size for coarse meshes. In a shielding problem, it is accurate to 10% using 16-mfp-thick cells; conventional methods err by 8 to 15 orders of magnitude. The exponential characteristic method is computationally more costly per cell than current methods but can be accurate with very thick cells, leading to increased computational efficiency on appropriate problems.
Maximum of the modulus of kernels in Gauss-Turan quadratures
NASA Astrophysics Data System (ADS)
Milovanovic, Gradimir V.; Spalevic, Miodrag M.; Pranic, Miroslav S.
2008-06-01
We study the kernels K_{n,s}(z) in the remainder terms R_{n,s}(f) of the Gauss-Turan quadrature formulae for analytic functions on elliptical contours with foci at pm 1 , when the weight omega is a generalized Chebyshev weight function. For the generalized Chebyshev weight of the first (third) kind, it is shown that the modulus of the kernel \\vert K_{n,s}(z)\\vert attains its maximum on the real axis (positive real semi-axis) for each ngeq n_0, n_0Dn_0(rho,s) . It was stated as a conjecture in [Mathematics of Computation 72 (2003), 1855-1872]. For the generalized Chebyshev weight of the second kind, in the case when the number of the nodes n in the corresponding Gauss-Turan quadrature formula is even, it is shown that the modulus of the kernel attains its maximum on the imaginary axis for each ngeq n_0, n_0Dn_0(rho,s) . Numerical examples are included. Retrieve articles in all Journals with MSC (1991): [41]41A55, [42]65D30, [43]65D32
Methods to Prescribe Particle Motion to Minimize Quadrature Error in Meshfree Methods
NASA Astrophysics Data System (ADS)
Templeton, Jeremy; Erickson, Lindsay; Morris, Karla; Poliakoff, David
2015-11-01
Meshfree methods are an attractive approach for simulating material systems undergoing large-scale deformation, such as spray break up, free surface flows, and droplets. Particles, which can be easily moved, are used as nodes and/or quadrature points rather than a relying on a fixed mesh. Most methods move particles according to the local fluid velocity that allows for the convection terms in the Navier-Stokes equations to be easily accounted for. However, this is a trade-off against numerical accuracy as the flow can often move particles to configurations with high quadrature error, and artificial compressibility is often required to prevent particles from forming undesirable regions of high and low concentrations. In this work, we consider the other side of the trade-off: moving particles based on reducing numerical error. Methods derived from molecular dynamics show that particles can be moved to minimize a surrogate for the solution error, resulting in substantially more accurate simulations at a fixed cost. Sandia National Laboratories is a multiprogram laboratory operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
A dual-band quadrature VCO with gain proportional to oscillation frequency
NASA Astrophysics Data System (ADS)
Wenrui, Zhu; Haigang, Yang; Tongqiang, Gao; Hui, Zhang
2013-08-01
This paper presents a novel dual-band quadrature voltage controlled oscillator (VCO) with the gain proportional to the oscillation frequency. Frequency synthesizers with this VCO can reduce the bandwidth fluctuation over all the frequency ranges without compensation or calibration. Besides the original switched capacitor array, an extra switched varactor array is adopted for the implementation of the proposed VCO. The tuning technique of changing the values of the capacitor and varactor at the same ratio is also derived. For verification purposes, a 2.5 G/3.5 G dual-band quadrature VCO is fabricated in a 0.13 μm CMOS process for WiMAX applications. Measurement results show that the VCO gain is closely proportional to the oscillation frequency with ±16% variation over the entire frequency range. The phase noise is -138.15 dBc/Hz at 10 MHz from the 2.5 GHz carrier and -137.44 dBc/Hz at 10 MHz from the 3.5 GHz carrier.
A multivariate quadrature based approach for LES based supersonic combustion modeling
NASA Astrophysics Data System (ADS)
Donde, Pratik; Koo, Heeseok; Raman, Venkat
2010-11-01
The direct quadrature method of moments (DQMOM) was developed to solve high-dimensional probability density function (PDF) equations that arise in the description of turbulent combustion. This method is particularly useful in shock-containing supersonic internal flows such as those encountered in scramjet engines. In the DQMOM approach, the PDF is described in terms of a finite number of weighted delta functions whose weights and locations in composition space are obtained by solving specific transport equations. Since this approach is fully Eulerian in nature, it is advantageous compared to conventional Lagrangian methods used for solving the PDF transport equation. However, implementation of this formulation in the context of the large eddy simulation (LES) methodology leads to large numerical errors. For instance, the high-resolution numerical schemes used in LES lead to non-realizable and diffusive evolution of the DQMOM equations. Here, we propose a novel semi-discrete quadrature method of moments (SeQMOM) that overcomes this problem. A decoupling procedure is used to extend this method to multivariate PDF descriptions. The numerical implementation in LES as well as validation exercises will be presented.
Low-Latitude Solar Wind During the Fall 1998 SOHO-Ulysses Quadrature
NASA Technical Reports Server (NTRS)
Poletto, G.; Suess, Steven T.; Biesecker, D.; Esser, R.; Gloeckler, G.; Zurbuchen, T.; Whitaker, Ann F. (Technical Monitor)
2001-01-01
The Fall 1998 SOlar-Heliospheric Observatory (SOHO) - Ulysses quadrature occurred when Ulysses was at 5.2 AU, 17.4 deg South of the equator, and off the West line of the Sun. SOHO coronal observations, at heliocentric distances of a few solar radii, showed that the line through the solar center and Ulysses crossed, over the first days of observations, a dark, weakly emitting area and through the northern edge of a streamer complex during the second half of the quadrature campaign. Ulysses in situ observations showed this transition to correspond to a decrease from higher speed wind typical of coronal hole flow to low speed wind. Physical parameters (density, temperature, flow speed) of the low latitude coronal plasma sampled over the campaign are determined using constraints from what is the same plasma measured later in situ and simulating the intensities of the Hydrogen Lyman-alpha and OVI 1032 and 1037 Angstrom lines, measured by the Ultra Violet Coronagraph Spectrometer (UVCS) on SOHO. The densities, temperatures and outflow speed are compared with the same characteristic flow parameters for high-latitude fast wind streams and typical slow solar wind.
A quadrature based method of moments for nonlinear Fokker-Planck equations
NASA Astrophysics Data System (ADS)
Otten, Dustin L.; Vedula, Prakash
2011-09-01
Fokker-Planck equations which are nonlinear with respect to their probability densities and occur in many nonequilibrium systems relevant to mean field interaction models, plasmas, fermions and bosons can be challenging to solve numerically. To address some underlying challenges, we propose the application of the direct quadrature based method of moments (DQMOM) for efficient and accurate determination of transient (and stationary) solutions of nonlinear Fokker-Planck equations (NLFPEs). In DQMOM, probability density (or other distribution) functions are represented using a finite collection of Dirac delta functions, characterized by quadrature weights and locations (or abscissas) that are determined based on constraints due to evolution of generalized moments. Three particular examples of nonlinear Fokker-Planck equations considered in this paper include descriptions of: (i) the Shimizu-Yamada model, (ii) the Desai-Zwanzig model (both of which have been developed as models of muscular contraction) and (iii) fermions and bosons. Results based on DQMOM, for the transient and stationary solutions of the nonlinear Fokker-Planck equations, have been found to be in good agreement with other available analytical and numerical approaches. It is also shown that approximate reconstruction of the underlying probability density function from moments obtained from DQMOM can be satisfactorily achieved using a maximum entropy method.
Suppressing the mechanical quadrature error of a quartz double-H gyroscope through laser trimming
NASA Astrophysics Data System (ADS)
Zhao, Ke; Feng, Li-Hui; Wang, Qian-Qian; Liu, Ming-Zhi; Wang, Ben-Guo; Cui, Fang; Sun, Yu-Nan
2013-11-01
In this paper, we introduce a z-axis quartz gyroscope using a double-H tuning fork, which has a high sensitivity. However, it also causes a large mechanical quadrature error. The laser trimming method is used to suppress this error at quartz level. The trimming law is obtained through the finite element method (FEM). A femtosecond laser processing system is used to trim the gold balancing masses on the beams, and experimental results are basically consistent with the simulated ones. The mechanical quadrature error is suppressed by 96%, from 26.3° s-1 to 1.1° s-1. Nonlinearity changes from 1.48% to 0.30%, angular random walk (ARW) is reduced from 2.19° h-1/2 to 1.42° h-1/2, and bias instability is improved by a factor of 7.7, from 197.6° h-1 to 25.4° h-1.
Patsourakos, Spiros; Vourlidas, Angelos E-mail: vourlidas@nrl.navy.mil
2009-08-01
The nature of coronal mass ejection (CME)-associated low corona propagating disturbances, 'extreme ultraviolet (EUV) waves', has been controversial since their discovery by EIT on SOHO. The low-cadence, single-viewpoint EUV images and the lack of simultaneous inner corona white-light observations have hindered the resolution of the debate on whether they are true waves or just projections of the expanding CME. The operation of the twin EUV imagers and inner corona coronagraphs aboard STEREO has improved the situation dramatically. During early 2009, the STEREO Ahead (STA) and Behind (STB) spacecrafts observed the Sun in quadrature having a {approx}90 deg. angular separation. An EUV wave and CME erupted from active region 11012, on February 13, when the region was exactly at the limb for STA and hence at disk center for STB. The STEREO observations capture the development of a CME and its accompanying EUV wave not only with high cadence but also in quadrature. The resulting unprecedented data set allowed us to separate the CME structures from the EUV wave signatures and to determine without doubt the true nature of the wave. It is a fast-mode MHD wave after all.
Randomized gap and amplitude estimation
NASA Astrophysics Data System (ADS)
Zintchenko, Ilia; Wiebe, Nathan
2016-06-01
We provide a method for estimating spectral gaps in low-dimensional systems. Unlike traditional phase estimation, our approach does not require ancillary qubits nor does it require well-characterized gates. Instead, it only requires the ability to perform approximate Haar random unitary operations, applying the unitary whose eigenspectrum is sought and performing measurements in the computational basis. We discuss application of these ideas to in-place amplitude estimation and quantum device calibration.
Genus dependence of superstring amplitudes
Davis, Simon
2006-11-15
The problem of the consistency of the finiteness of the supermoduli space integral in the limit of vanishing super-fixed point distance and the genus-dependence of the integral over the super-Schottky coordinates in the fundamental region containing a neighborhood of |K{sub n}|=0 is resolved. Given a choice of the categories of isometric circles representing the integration region, the exponential form of bounds for superstring amplitudes is derived.
Pulse amplitude modulated chlorophyll fluorometer
Greenbaum, Elias; Wu, Jie
2015-12-29
Chlorophyll fluorometry may be used for detecting toxins in a sample because of changes in micro algae. A portable lab on a chip ("LOAC") based chlorophyll fluorometer may be used for toxin detection and environmental monitoring. In particular, the system may include a microfluidic pulse amplitude modulated ("PAM") chlorophyll fluorometer. The LOAC PAM chlorophyll fluorometer may analyze microalgae and cyanobacteria that grow naturally in source drinking water.
Phase variation of hadronic amplitudes
Dedonder, J.-P.; Gibbs, W. R.; Nuseirat, Mutazz
2008-04-15
The phase variation with angle of hadronic amplitudes is studied with a view to understanding the underlying physical quantities that control it and how well it can be determined in free space. We find that unitarity forces a moderately accurate determination of the phase in standard amplitude analyses but that the nucleon-nucleon analyses done to date do not give the phase variation needed to achieve a good representation of the data in multiple scattering calculations. Models are examined that suggest its behavior near forward angles is related to the radii of the real and absorptive parts of the interaction. The dependence of this phase on model parameters is such that if these radii are modified in the nuclear medium (in combination with the change due to the shift in energy of the effective amplitude in the medium) then the larger magnitudes of the phase needed to fit the data might be attainable but only for negative values of the phase variation parameter.
NASA Astrophysics Data System (ADS)
Hasegawa, Takemitsu; Hibino, Susumu; Hosoda, Yohsuke; Ninomiya, Ichizo
2007-08-01
An improvement is made to an automatic quadrature due to Ninomiya (J. Inf. Process. 3:162?170, 1980) of adaptive type based on the Newton?Cotes rule by incorporating a doubly-adaptive algorithm due to Favati, Lotti and Romani (ACM Trans. Math. Softw. 17:207?217, 1991; ACM Trans. Math. Softw. 17:218?232, 1991). We compare the present method in performance with some others by using various test problems including Kahaner?s ones (Computation of numerical quadrature formulas. In: Rice, J.R. (ed.) Mathematical Software, 229?259. Academic, Orlando, FL, 1971).
NASA Astrophysics Data System (ADS)
Ogawa, Hisashi; Ohdan, Hideaki; Miyata, Kazunori; Taguchi, Masahiro; Makino, Kenzo; Yonezawa, Hidehiro; Yoshikawa, Jun-ichi; Furusawa, Akira
2016-06-01
Real-time controls based on quantum measurements are powerful tools for various quantum protocols. However, their experimental realization has been limited by mode mismatch between the temporal mode of quadrature measurement and that heralded by photon detection. Here, we demonstrate real-time quadrature measurement of a single-photon wave packet induced by photon detection by utilizing continuous temporal-mode matching between homodyne detection and an exponentially rising temporal mode. Single photons in exponentially rising modes are also expected to be useful resources for interactions with other quantum systems.