Fourier Algorithm Research Articles

An Improved Fourier-Mellin Algorithm Based on the Image Amplitude Spectrum

This paper proposes an improved amplitude spectrum based Fourier-Mellin algorithm Fourier by studying the nature of the Fourier transform image of the amplitude spectrum and the application of phase spectrum in estimation for image motion vector according to the shortcomings of traditional Fourier-Mellin algorithm when the video image translation, rotation and scaling of the situation exist. Experimental results show that the algorithm can estimate the rotation, translation and other vector parameters of a complicated motion model .The complexity of the algorithm has greatly improved comparing to the traditional Fourier-Mellin algorithm.

Measurement of surface roughness of thin films by a hybrid interference microscope with different phase algorithms.

We propose a hybrid and flexible interference microscope combined with different phase algorithms to measure the surface roughness of thin films. Two phase measurement algorithms of the fast Fourier transform method and the five-step phase-shifting interferometry are used to evaluate the surface contour of aluminum-doped zinc oxide thin films coated using varying radio-frequency sputtering powers. The experimental results show that the proposed approach is feasible in determining the 3D deformation and surface roughness of thin films.

On the formation of noise-like pulses in fiber ring cavity configurations

We give an overview of the current status of fiber-based noise-like pulse (NLP) research conducted over the past decade, together with presenting the newly conducted, systematic study on their temporal, spectral, and coherence characteristics in nonlinear polarization rotation (NPR)-based erbium-doped fiber ring cavity configurations. Firstly, our study includes experimental investigations on the characteristic features of NLPs both in the net anomalous dispersion regime and in the net normal dispersion regime, in comparison with coherent optical pulses that can alternatively be obtained from the same cavity configurations, i.e., with the conventional and dissipative solitons. Secondly, our study includes numerical simulations on the formation of NLPs, utilizing a simplified, scalar-field model based on the characteristic transfer function of the NPR mechanism in conjunction with the split-step Fourier algorithm, which offer a great help in exploring the interrelationship between the NLP formation and various cavity parameters, and eventually present good agreement with the experimental results. We stress that if the cavity operates with excessively high gain, i.e., higher than the levels just required for generating coherent mode-locked pulses, i.e., conventional solitons and dissipative solitons, it may trigger NLPs, depending on the characteristic transfer function of the NPR mechanism induced in the cavity. In particular, the NPR transfer function is characterized by the critical saturation power and the linear loss ratio. Finally, we also report on the applications of the fiber-based NLP sources, including supercontinuum generation in a master-oscillator power amplifier configuration seeded by a fiber-based NLP source, as one typical example. We expect that the NLP-related research area will continue to expand, and that NLP-based sources will also find more applications in the future.

High speed directional relaying algorithm based on the fundamental frequency positive sequence superimposed components

The conventional travelling wave protection is susceptible to the high frequency transient quantities, which can reduce the protection reliability. A directional-relay algorithm based on positive sequence superimposed components is proposed in this study. In microprocessor relays, the extraction of fundamental frequency voltages and currents is, conventionally, provided by phasor estimation methods such as the Fourier algorithm. The common required time for fault detection in these relays is approximately one to two cycles. This study presents a high-speed algorithm for the extraction of fundamental frequency positive sequence voltages and currents superimposed components based on Park transformation. In the meantime, specially designed high speed algorithms to solve the difficult problems that exist in a real system are proposed. Extensive simulations are performed to evaluate the performance of the proposed algorithm. The results show that the algorithm is fast and reliable for power transmission line protections. Also it is immune to fault resistances and system condition.

The evaluation of frequency properties of digital measuring element reacting to increment vector current values

The frequency properties of a digital measuring element can be used as criteria for the selection of operating values of the numerical distance protection starting element of power-swing blocking. The conditions of the selection of the operating values of the starting element of power-swing blocking usually ensure sensitivity to short circuiting. The primary function of the starting element is blocking the distance protection from power swings and out-of-step conditions, based on the fact that the rate of current change and its increment for electromechanical processes are much lower than for a short circuit. Mathematical modeling of the digital measuring element based on filter Fourier and FIR algorithms with confirmation of the results by using a computer-controlled testing system allows criteria to be obtained that reflect the physical nature of the processes that can be used when selecting the settings of the starting element of power-swing blocking. An approach to selection of the settings of a digital measuring element of relay protection that is responsive to the current increment, based on analysis of digital signal processing algorithms, allows one to determine the criteria for the detuning of the emergency operation, taking into account the frequency deviation, the impact of the presence of a transient dc component, and the higher harmonics. The frequency properties of the digital measuring element reacting to increment vector current values can be used to determine the threshold detuning from power swings and out-of-step conditions as additional conditions for selecting settings of the starting element of power-swing blocking, which will increase the sensitivity of the distance protection for short circuits and the reliability of detuning from power swings and out-of-step conditions.

On-Line Detection of the Coal Mine Power Cable Parameters Based on the Method of Low Frequency Signal

The coal mine power supply mainly rely on cable, its insulation level directly affects the coal mine safety production. Has long been lack of perfect insulation parameters online detesting equipment, the traditional detection methods need to stop the normal grid power supply, affect the normal production of coal mine, it is great significance that research a kind of on-line insulation parameters detection equipment. Using three-phase reactor in the neutral point insulation system to make artificial neutral point, from this point inject low-frequency voltage signal, the signal through the cable ontology, cable to ground insulation resistance and capacitance, and to a loop resistor. Measure the voltage and current signals and modulus conversion, using DSP to realize rapid changes of Fourier algorithm, can quickly and accurately calculate the cable to ground insulation parameters. The algorithm is effective to solve the traditional measuring circuit transformer reactance and unbalance current's influence to the accuracy of measurement, measurement process will not affect the normal operation of the electric power system, the insulation parameters can be accurately measure online.

A normalized wavefield separation cross-correlation imaging condition for reverse time migration based on Poynting vector

Prestack reverse time migration (PSTM) is a common imaging method; however low-frequency noises reduce the structural imaging precision. Thus, the suppression of migration noises must be considered. The generation mechanism of low-frequency noises is analyzed and the up-, down-, left-, and right-going waves are separated using the Poynting vector of the acoustic wave equation. The computational complexity and memory capacitance of the proposed method are far smaller than that required when using the conventional separation algorithm of 2D Fourier transform. The normalized wavefield separation crosscorrelation imaging condition is used to suppress low-frequency noises in reverse time migration and improve the imaging precision. Numerical experiments using the Marmousi model are performed and the results show that the up-, down-, left-, and right-going waves are well separated in the continuation of the wavefield using the Poynting vector. We compared the imaging results with the conventional method, Laplacian filtering, and wavefield separation with the 2D Fourier transform. The comparison shows that the migration noises are well suppressed using the normalized wavefield separation cross-correlation imaging condition and higher precision imaging results are obtained.

Study of an efficient real-time monitoring and control system for BUE and cutter breakage for CNC machine tools

If machining abnormalities, such as build-up-edge and cutter breakage, occur during machining, serious damage on the workpiece surface and deterioration of production efficiency will happen, and cause additional energy consumption for rework and increase the manufacturing cost. To minimize the effects, an on-line diagnosis method with use of Fast Fourier Transform and algorithm of shorttime signal variation analysis was developed to analyze the vibration signals to quickly detect the two abnormalities in this study. In addition, the real-time machining information from CNC controller was extracted through a bi-lateral communication module to prevent misdiagnosis. The control commands were automatically generated by the proposed system and directly sent to the CNC controller to stop the machine for cutter replacement. Without complex computation, the system can detect the occurrence of BUE or cutter breakage within 1 second and complete machine control within 3 seconds. The system can instantly transmit and save the real machining information and diagnosis/control results to the remote central monitoring platform for further process improvement. With use of TCP/IP communication protocol the central monitoring platform can remote log into the on-site monitoring computer to directly operate the diagnosis/control system. Experimental results showed the feasibility and effectiveness of the proposed system.

An investigation into the bottom interface treatment in parabolic equation models utilizing split-step Fourier and finite-difference algorithms

Recent analysis of parabolic equation model results computed using split-step Fourier algorithms have shown increasing phase errors at long range in simple, isospeed waveguides. Preliminary results suggest that these errors are due to the treatment of the density discontinuity at the water/bottom interface through the use of smoothing functions. In this work, several different approaches are investigated for improving the phase accuracy of the solution, including hybrid methods employing split-step Fourier and finite-difference algorithms, as well as equivalent bottom characterizations. The results are compared relative to their improvements in accuracy as well as computational efficiency.

DUCTING AND TURBULENCE EFFECTS ON RADIO-WAVE PROPAGATION IN AN ATMOSPHERIC BOUNDARY LAYER

The split-step Fourier (SSF) algorithm is applied to simulate the propagation of radio waves in an atmospheric duct. The refractive-index fluctuation in the ducts is assumed to follow a two- dimensional Kolmogorov power spectrum, which is derived from its three-dimensional counterpart via the Wiener-Khinchin theorem. The measured profiles of temperature, humidity and wind speed in the Gulf area on April 28, 1996, are used to derive the average refractive index and the scaling parameters in order to estimate the outer scale and the structure constant of turbulence in the atmospheric boundary layer (ABL). Simulation results show significant turbulence effects above sea in daytime, under stable conditions, which are attributed to the presence of atmospheric ducts. Weak turbulence effects are observed over lands in daytime, under unstable conditions, in which the high surface temperature prevents the formation of ducts.

Numerical analysis of in-phase supermode selection of seven-core photonic crystal fiber by gain distribution

A model based on propagation-rate equations by considering the multi-transverse mode is constructed to describe the amplifier made from seven-core photonic crystal fibers. The output power of the seven eigenmodes in the amplifier infected by the dopant distribution, coupling coefficient and the pump power is discussed using the split-step Fourier algorithm. Mode selection can be realized by the design of dopant distribution and suitable coupling coefficient without the need of other devices. Mode selection may become more convenient due to this method. Moreover, high pump power can contribute to the improvement of the in-phase supermode. These results are helpful for improving the light quality of the amplifier.

Adaptive Fourier-Galerkin methods

We study the performance of adaptive Fourier-Galerkin methods in a periodic box in R d \mathbb {R}^d with dimension d ≥ 1 d\ge 1 . These methods offer unlimited approximation power only restricted by solution and data regularity. They are of intrinsic interest but are also a first step towards understanding adaptivity for the h p hp -FEM. We examine two nonlinear approximation classes, one classical corresponding to algebraic decay of Fourier coefficients and another associated with exponential decay typical of spectral approximation. We investigate the natural sparsity class for the operator range and find that the exponential class is not preserved, thus in contrast with the algebraic class. This entails a striking different behavior of the feasible residuals that lead to practical algorithms, influencing the overall optimality. The sparsity degradation for the exponential class is partially compensated with coarsening. We present several feasible adaptive Fourier algorithms, prove their contraction properties, and examine the cardinality of the activated sets. The Galerkin approximations at the end of each iteration are quasi-optimal for both classes, but inner loops or intermediate approximations are sub-optimal for the exponential class.

Introduction to the special issue on Low-power circuit techniques

This special issue of ‘‘Low-power circuit techniques’’ in the Springer Journal of Analog Integrated Circuits and Signal Processing is published with six papers, which are selected from presented papers at the 2012 International Conference on Analog VLSI Circuits (AVIC 2012). This conference is believed to be the only conference that bares the key word ‘‘Analog VLSI’’, and have accepted very wide range of papers concerning analog circuits. Among them, we called for papers related to low-power circuit techniques for this special issue. The Research Committee on Electronic Circuits of the Institute of Electrical Engineers of Japan (IEEJ) was sponsoring and cooperating with Analog Devices Inc., the University of Valencia and the Polytechnic University of Valencia to hold the 2012 International Conference on Analog VLSI Circuits in Valencia, Spain, on October 24–26, 2012. This conference is the successor of former International Analog VLSI Workshop, which had been successfully held for 14 years. The purpose of the conference is to exchange information, ideas and recent research results on analog VLSI circuits and their applications. This workshop has formed a long-standing community for various analog VLSI circuit specialists from both industry and academia worldwide, and promoted active brainstorming among them at the site. The first two papers are related to power supply circuits and DC–DC converter circuits. The first paper by Nomura et al. presents photovoltaic cell design, oscillator, and bootstrap charge pump circuit integrated on an 0.18 lm CMOS chip, to provide power generation and voltage boost functions on stand-alone microsystems. Sato et al. present a theoretical analysis of efficiency in charge pumps for LED drivers and describe a novel procedure to minimize power loss by applying adiabatic process to charge pump circuits. The third paper by Tanimoto et al. presents a fullydifferential OTA operating from 1-V power supply. The OTA consists from CMOS cascode inverters to obtain a high voltage gain while maintaining rail-to-rail input common-mode range at 1-V power supply. They also fabricated a test chip by using 0.15 lm CMOS technology and confirmed the design techniques to be useful. The fourth and the fifth papers are concerning to high speed communication signal processing. Nakagawa et al. present a passive complex filter design approach, which is relevant to low power analog signal processing at very high frequency. The concept is exemplified with two complex filters operating at 100 kHz and 10 MHz but maybe extended beyond tens of GHz. The fifth paper by Yazaki et al. presents a design of a 20-Gbps CMOS optical receiver, which does not require inductor to suppress power supply noise by a unique design of power supply noise canceling circuit. The designed chip was fabricated in 90 nm CMOS technology and demonstrated effectiveness of the design. The last paper by Carbajo et al. presents a new version of the well known Goertzel algorithm for discrete Fourier J. Calpe-Maravilla Analog Devices S.L., Edificio 8F, Planta 3, Campus UPV, 46022 Valencia, Spain e-mail: javier.calpe@analog.com

Simulation and Analysis for Current Transformers with DC Bias and Remnant Flux

The transfer characteristics of current transformers (CT) change due to DC bias, which directly impacts the accuracy of measurement and power metering. Based on equivalent circuit models and core magnetizing characteristic, qualitatively analysis current transformer saturation increase errors of CT. Transfer errors under DC bias and remnant flux are also obtained based on J-A model of CT in PSCAD/EMTDC and full-wave Fourier algorithm to show that the ratio error and phase displacement increase with the DC bias. Based on FFT spectrum analysis to identify remnant flux and DC bias provides scientific basis for error compensation of CT.

Methods of Phasor Algorithm Applied on Substation Short-Circuit Impedance Calculation Analysis

Dynamic and real-time monitoring of substation, the analysis of the operating state of the substation through the phasor values of the substation. The phase of accurate measurement is a prerequisite to ensure accurate analysis Substation running state. This paper uses Fourier algorithm, recursive least squares algorithm and Kalman algorithm three methods of phasor calculation solving the acquisition voltage, current from the substation, get the results of calculation and error analysis. Come up with a more accurate method of phasor calculation. Provide a practical method for the accurate analysis of the operating state of the substation.

Research and Improvement of Fourier Algorithm in the Microcomputer Relay Protection

Fourier algorithm can be effective utilized in the Microcomputer relay protection to filter out Harmonic component in the AC signal .but the drawback is that not filter attenuation DC component. it may be affect the computation accuracy of the entire system .and it is also reduce the efficiency of the system. In this paper ,we combined with the actual project ,on the basis of analysis of the full-wave Fourier algorithm ,for the problem of it can not filter decaying a periodic component ,we proposed an improved algorithm, and combined with MATLAB simulation ,the results show that the improved algorithm has the advantages of high accuracy and the algorithm is simple. In the microcomputer relay protection of the power system need to handle all kinds of signals, provide the necessary information for the implementation of protection. however, With the rapid development of computer technology and the continuous research of computer algorithms, a lot of actual power system protection device has been widely used in our life, on the one hand, these devices reduce the complexity of building hardware circuit, on the other hand ,it can make full use of the filter function about some algorithms have itself. The most important is that it can avoid the problem of instability and low efficiency with some filter circuit. But, this characteristic need the algorithms has a high precision [2,3]. The algorithm is set up in the microcomputer protection is a mathematical model for achieve some specific function. and write the corresponding computer applications according to this model. Then do some specific mathematical operations with these digital signals will achieve the purpose of protection. At present, the widely used full wave Fourier algorithm has a function of filtering DC component and harmonic component[4],but it can not filtering the decaying DC component in the system. It will be cause a certain interference and influence to the whole system in the practical application, the result is that led to the precision of the operation drop and lose the meaning of the protecting. In this paper, combined with specific engineering example give an improved calculation method. Through example of simulation has proved that using this algorithm can accurately figure out fundamental component and harmonic component, and it has the advantage of algorithm simple and high accuracy [5].

A new fast discrete S-transform and decision tree for the classification and monitoring of power quality disturbance waveforms

SUMMARY In this paper, a new fast discrete S-transform (ST)-based time-frequency signal analyzer has been proposed for the detection, classification, and monitoring of power quality (PQ) disturbances varying in an electric power system. The proposed algorithm is based on the generalized Fourier algorithm that is used to obtain the time-localized spectral characteristics of the time-varying voltage and current signals belonging to PQ events. The fast ST algorithm is realized with different types of frequency scaling, band pass filtering, and interpolation techniques based on Heisenberg's uncertainty principle resulting in a reduced computation cost. In the conventional ST, the window width decreases at higher frequencies with a reduction in frequency resolution and conversely at low frequencies with wider windows. Therefore, the time-varying PQ disturbance signal is down sampled at low frequencies and cropped at high frequencies resulting in the evaluation of a fewer samples. From the time–frequency matrix output, important features are extracted and used with a binary decision tree for an accurate classification of single and simultaneous PQ events. Further, a unified approach is presented to track the time-varying PQ disturbance waveforms like voltage sag, swell, harmonics, and oscillatory transients and produce estimation of their amplitudes and phase angles. Copyright © 2013 John Wiley & Sons, Ltd.

A novel technique for internal fault detection of power transformers based on moving windows

Power transformer differential relays may incorrectly operate due to inrush condition or transformer external faults lead to current transformer (CT) saturation. In this paper, a new technique is presented to distinguish internal fault current from magnetizing inrush current in power transformers. The proposed technique applies two moving windows which both of them estimate magnitude of transformer differential current using different methods. The first moving window method is based on full-cycle Fourier algorithm (long window) which uses one cycle samples of the current and provides precise estimation. The second one is originated from least error square (LES) method that has five sample point input data (short window). LES method has fast response, but its estimation might not be quite accurate. The proposed technique (which is a combination of two mentioned methods) presents a new criterion for discrimination between internal fault currents and inrush currents using the differences between output values of these two estimators. Meanwhile, obtained results demonstrate precise operation of the proposed algorithm for different conditions such as CT saturation and over-flux condition; therefore, it can be a multi-objective technique for transformer protection. Also, a general scheme is presented in order to improve differential protection. In this paper, a real part of 400/230 kV Iranian national grid is simulated using PSCAD software for evaluating the performance of the proposed algorithm. Also, additional validation of the proposed technique is tested offline using data collected from a three-phase, 5 kVA, 60 Hz, laboratory prototype transformer. Copyright © 2013 John Wiley & Sons, Ltd.

Analysis of Four Aberrometers for Evaluating Lower and Higher Order Aberrations

PurposeTo compare the measurements of lower and higher order aberrations (HOA) of 4 commonly used aberrometers.SettingMassachusetts Eye & Ear Infirmary, Boston, USA.DesignProspective, cross-sectional study, in a controlled, single-blinded fashion.MethodsMultiple readings were obtained in 42 eyes of 21 healthy volunteers, at a single visit, with each of the following aberrometers: Alcon LADARWave®, Visx WaveScan®, B & L Zywave®, and Wavelight Allegro Analyzer®. Results were compared and analyzed in regards to the lower and HOA, to the different wavefront sensing devices and software, Tscherning and Hartmann–Shack and between the Fourier and Zernike algorithms. Statistical analysis included Bland-Altman plots, Intraclass Correlation Coefficient (ICC), multiple comparison tests with Analysis of Variance and Kruskal-Wallis. Significant level was set to p<0.05 and alpha level correction was adjusted under the Bonferroni criteria.ResultsMost measurements of all 4 aberrometers were comparable. However, statistically significant differences were found between the aberrometers in total HOA (tHOA), spherical aberration (SA), horizontal coma and astigmatism (2,2). LADARwave and Wavescan showed significant differences in tHOA (P<0.001, ICC = 0.549, LoA = 0.19±0.5) and in SA (P<0.001, ICC = 0.733, LoA = 0.16±0.37). Wavescan showed a significant difference compared to Zywave (p<0.001, ICC = 0.920, LoA = 0.09±0.13) in SA. Comparisons between Allegro Analyzer and Zywave demonstrated significant differences in both Horizontal Coma (3,1) (p<0.001, ICC = −0.207, LoA = −0.15±0.48) and Astigmatism (2,2) (P = 0.003, ICC = −0.965, LoA = 0.2±2.5). Allegro Analyzer also differed from Wavescan in Horizontal Coma (3,1) (P<0.001, ICC = 0.725, LoA = −0.07±0.25).ConclusionsAlthough some measurements were comparable predominately in the lower order aberrations, significant differences were found in the tHOA, SA, horizontal coma and astigmatism. Our analysis suggests that sensor design contributes to agreement in lower order aberrations, and Fourier and Zernike expansion might disagree in higher order aberrations. Therefore, comparison between aberrometers was generally possible with some exceptions in higher order measurements.

ADAPTIVE SUB-LINEAR TIME FOURIER ALGORITHMS

We present a new deterministic algorithm for the sparse Fourier transform problem, in which we seek to identify k ≪ N significant Fourier coefficients from a signal of bandwidth N. Previous deterministic algorithms exhibit quadratic runtime scaling, while our algorithm scales linearly with k in the average case. Underlying our algorithm are a few simple observations relating the Fourier coefficients of time-shifted samples to unshifted samples of the input function. This allows us to detect when aliasing between two or more frequencies has occurred, as well as to determine the value of unaliased frequencies. We show that empirically our algorithm is orders of magnitude faster than competing algorithms.