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50 Years of fft algorithms and Applications

CIRCUITS SYSTEMS AND SIGNAL PROCESSING 2019年第12期38卷 5665-5698页

作者： Kumar, G. Ganesh Sahoo, Subhendu K. Meher, Pramod Kumar BITS Pilani Dept Elect Engn Hyderabad Campus Hyderabad Telangana India CV Raman Coll Engn Bhubaneswar India

The fast Fourier transform (fft) algorithm was developed by Cooley and Tukey in 1965. It could reduce the computational complexity of discrete Fourier transform significantly from O(N-2) to O(Nlog(2)N). The invention of fft is considered as a landmark development in the field of digital signal processing (DSP), since it could expedite the DSP algorithms significantly such that real-time digital signal processing could be possible. During the past 50 years, many researchers have contributed to the advancements in the fft algorithm to make it faster and more efficient in order to match with the requirements of various applications. In this article, we present a brief overview of the key developments in fft algorithms along with some popular applications in speech and image processing, signal analysis, and communication systems.

关键词： DFT fft algorithms Computational complexity Digital signal processing

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A Modified-fft Algorithm for Determining the Basic Frequency Tone of Latotou Traditional Music Instrument 7

A Modified-FFT Algorithm for Determining the Basic Frequency...

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7th International Conference on Electrical Engineering and Informatics (ICEEI)

作者： Palantei, Elyas Hamid, Helson Dewiani Univ Hasanuddin UNHAS Fac Engn Dept Elect Engn Gowa South Sulawesi Indonesia

ISBN: (纸本)9781728124186

A Latotou traditional music instrument has not have the standardized frequency tone as other music instruments have. There are two main things required in order to be succeed on constructing that traditional instrument i.e. the creator feeling and the accuracy to hearing the frequency tone. Every single process to make Latotou instrument that usually performed by the hobbiest and expert old people, in practical, a very smooth tone variability existed. Every single Latotou instrument was successfully constructed it will not have the same basic frequency during the setting-up and the tone synchronization performed. To tackle those problems, the conventional method applied for many years was altered. The Matlab GUI interface based on a modified fft algorithm was designed and installed into a PC desktop/laptop in order to automatically determine the basic frequency tone while the instrument was played. The similar method was applied by other researchers to determine the basic frequency tone of both Gamelan and Suling traditional musical instruments. The fft based GUI processing exhibited the interesting outcomes in terms of the dissimilarity percentage compared to the tone frequency produced by the referenced Guitar. During the experimental testing by gently hitting each bar/slate element of the constructed Latotou musical instrument, various basic frequency tones were consecutively determined. The whole built in GUI Matlab system applying fast Fourier transform algorithm on detecting the basic tone frequency of Latotou musical instrument has an accuracy with a fairly small error percentage of abruptly 2.5 %.

关键词： Latotou traditional music Voice Processing GUI interface fft algorithms

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algorithms FOR THE REDUCTION OF THE INPUT OUTPUT OPERATIONS IN THE CALCULATION OF THE TWO-DIMENSIONAL DISCRETE FOURIER-TRANSFORM

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SIGNAL PROCESSING 1987年第3期12卷 277-289页

作者： PITAS, I STRINTZIS, MG Department of Electrical Engineering University of Thessaloniki Thessaloniki 54006 Greece

The computation of the Discrete Fourier Transform (DFT) of large two-dimensional sequences requires extraordinary memory commitment. If such memory is not available, the data are stored in peripheral devices and blocks of the records are retrieved sequentially for the calculation of various stages of the DFT. This approach requires a great many input-output operations. The present paper proposes three new algorithms for the reduction of the input-output (I-O) operations. It is proven that the reduction achieved is of a logarithmic order of magnitude. Die Berechnung der diskreten Fouriertransformierten (DFT) großer zweidimensionaler Felder erfordert außerordentlich viel Speicherplatz. Ist dieser im Hauptspeicher nicht vorhanden, so werden die Daten in peripheren Massenspeichern abgelegt, und kleinere Teilbereiche werden blockweise eingelsen und entsprechend den Vorschriften der DFT abgearbeitet. Diese Implementierung erfordert eine große Anzahl von Ein-Ausgabe-Operationen. Der vorliegende Beitrag präsentiert drei neue Algorithmen für die Reduktion der Zahl dieser Ein-Ausgabe-Operationen. Wie gezeigt wird, läßt sich eine Reduktion logarithmischer Größenordnung erreichnen. Le calcul de la transformation de Fourier discrète (TFD) de grandes séquences bidimensionnelles nécessite des mémoires extraordinaires. Si ces mémoires ne sont pas disponibles, les données sont mémorisées sur des dispositifs périfériques et des blocks d'enregistrements sont recherchés séquentiellement pour le calcul des différentes étapes de la TFD. Cette approche nécessite beaucoups d'opérations d'entrée/sortie. Cet article propose trois algorithmes nouveaux pour la réduction des opérations entrée sortie. Il est prouvé que la réduction obtenue est de l'ordre logarithmique.

关键词： Memory reduction optimal memory management fft algorithms

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SEMISYSTOLIC ARRAY IMPLEMENTATION OF CIRCULAR, SKEW CIRCULAR, AND LINEAR CONVOLUTIONS

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IEEE TRANSACTIONS ON COMPUTERS 1985年第2期34卷 190-196页

作者： ERSOY, O Central Institute for Industrial Research Abstract Authors References Cited By Keywords Metrics Similar Download Citation Email Print Request Permissions

Semisystolic array implementation of circular and linear convolutions in one and multidimensions are discussed. The common feature of the various architectures studied is the broadcasting of the input sequence to the cells of the array. In the case of circular convolutions, there is also circular communication between the cells. A circular convolution of period N can be calculated in N time steps whereas the response time for the computation of N outputs of linear convolution with finite weight and data vectors is also N time steps without initial delay.

关键词： Convolution fft algorithms Toeplitz forms VLSI parallel processing semisystolic arrays

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Characterisation of measurement uncertainties due to preamplifier gain variation

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ELECTRONICS LETTERS 2015年第1期51卷 64-U6665页

作者： Song, Jian Guo, Yong Xin Natl Univ Singapore Singapore 117576 Singapore

The measurement uncertainties associated with preamplifier gain variation due to temperature change are investigated. It is shown that when temperature decreases from the room temperature (25 degrees C) to 0 degrees C, the uncertainty of the preamplifier gain variation is found to be as large as 1.277 dB. Further investigation of mismatch uncertainty between the preamplifier and the system due to temperature change has been carried out. It is expected that mismatch uncertainty will be greatly affected if the preamplifier input and output voltage standing wave ratio varies at different operating temperatures.

关键词： discrete Hartley transforms inverse transforms fast Fourier transforms discrete Fourier transforms computational complexity two-band fast Hartley transform inverse discrete Hartley transforms DHTs forward discrete Hartley transforms fast Fourier transform fft algorithms discrete Fourier transform DFT radix-2 fast Hartley transform FHT two-band decomposition input data out data shuffling input data shuffling computational complexity

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SOME RESULTS IN FIXED-POINT FAST FOURIER-TRANSFORM ERROR ANALYSIS

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IEEE TRANSACTIONS ON COMPUTERS 1977年第3期26卷 305-308页

作者： SUNDARAMURTHY, M REDDY, VU SIR GEORGE WILLIAMS UNIV MONTREAL 107QUEBECCANADA INDIAN INST TECHNOL CTR RADAR & COMMUNKHARAGPURW BENGALINDIA

This correspondence presents some results in fixed-point error analysis of fast Fourier transform algorithms. Two kinds of schemes for preventing overflow are considered in the analysis. The results, obtained for the decimation-in-frequency form of the algorithm, are compared with those of decimation-in-time. The results show that the error performance of the decimation-in-frequency algorithm is better than that of decimation-in-time.

关键词： Decimation-in-frequency decimation-in-time fft algorithms roundoff errors signal-to-noise ratio.

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fft-Based Methods for Computational Contact Mechanics

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FRONTIERS IN MECHANICAL ENGINEERING-SWITZERLAND 2020年 6卷

作者： Wang, Q. Jane Sun, Linlin Zhang, Xin Liu, Shuangbiao Zhu, Dong Northwestern Univ Mech Engn Evanston IL 60208 USA Northwestern Univ Ctr Surface Engn & Tribol Evanston IL 60208 USA Northwestern Polytech Univ Sch Mech Engn Xian Peoples R China Tritech Solut Mt Prospect IL USA

Computational contact mechanics seeks for numerical solutions to contact area, pressure, deformation, and stresses, as well as flash temperature, in response to the interaction of two bodies. The materials of the bodies may be homogeneous or inhomogeneous, isotropic or anisotropic, layered or functionally graded, elastic, elastoplastic, or viscoelastic, and the physical interactions may be subjected to a single field or multiple fields. The contact geometry can be cylindrical, point (circular or elliptical), or nominally flat-to-flat. With reasonable simplifications, the mathematical nature of the relationship between a surface excitation and a body response for an elastic contact problem is either in the form of a convolution or correlation, making it possible to formulate and solve the contact problem by means of an efficient Fourier-transform algorithm. Green's function inside such a convolution or correlation form is the fundamental solution to an elementary problem, and if explicitly available, it can be integrated over a region, or an element, to obtain influence coefficients (ICs). Either the problem itself or Green's functions/ICs can be transformed into a space-related frequency domain, via a Fourier transform algorithm, to formulate a frequency-domain solution for contact problems. This approach converts the original tedious integration operation into multiplication accompanied by Fourier and inverse Fourier transforms, and thus a great computational efficiency is achieved. The conversion between ICs and frequency-response functions facilitate the solutions to problems with no explicit space-domain Green's function. This paper summarizes different algorithms involving the fast Fourier transform (fft), developed for different contact problems, error control, as well as solutions to the problems involving different contact geometries, different types of materials, and different physical issues. The related works suggest that (i) a proper fft algorithm should

关键词： contact of materials fast fourier transform fft algorithms contact pressure contact stress tribology

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A Comparison of Computing Spectral Transforms of Logic Functions using Python Frameworks on GPU 57

A Comparison of Computing Spectral Transforms of Logic Funct...

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57th International Scientific Conference on Information, Communication and Energy Systems and Technologies (ICEST)

作者： Radmanovic, Milos M. Fac Elect Engn Aleksandra Medvedeva 14 Nish 18000 Serbia

ISBN: (纸本)9781665485005

The spectral transforms of logic functions have numerous applications in logic synthesis, signal processing, pattern recognition, and in many related areas. It is very important to be able to efficiently compute these transforms. Python frameworks show extremely high computation performance for (Fast Fourier Transform) fft-based algorithms executed on graphics processing units (GPUs). Thus, this paper presents a comparison of computation time for different implementations of spectral transform of logic functions, performed on GPUs using three different Python frameworks. It is used TensorFlow, PyTorch, and CuPy, frameworks. The experiments were performed on Nvidia GeForce RTX 2060 GPU, which belongs to the middle GPU price range. Computational times are compared using randomly-generated truth vectors of size up to 4096. The aim of this paper is to identify the computing platform and Python programming framework which produces the fastest spectral transform of logic functions.

关键词： Logic functions spectral transforms fft algorithms parallel GPU computing Python frameworks

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A FPGA-based implementation of data acquisition and processing for digital protective relays

A FPGA-based implementation of data acquisition and processi...

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4th International Conference on ASIC

作者： Feng, T Zhang, GQ Wang, JH Geng, YS Zhang, H Xi An Jiao Tong Univ Dept Elect Apparatus Xian 710049 Peoples R China

ISBN: (纸本)0780366778

In order to improve the performance of digital protective relay, a data acquisition and processing system based on FPGA is designed in VHDL and implemented in this paper. They are foul parts in system: ADC control, 32-point fft module, frequency counter and power meter. It cans control ADC and multiplexer to sample and convert 16-channel voltage and current signal of power system, process the discrete data with fft algorithms in real time, measure the system frequency and power. So it can supply the processed data for protective relays and measurement All parts can be implemented in an Altera ACEX EP1k100. Using this system, the protective relays will achieve the good characteristic: high reliability and performance, multi-function, small size and cheap cost.

关键词： relay protection power system relaying power system protection field programmable gate arrays fast Fourier transforms data acquisition analogue-digital conversion power meters power engineering computing application specific integrated circuits digital instrumentation FPGA-based implementation data acquisition system data processing system digital protective relay VHDL design ADC control fft module frequency counter power meter multiplexer control fft algorithms real time processing Altera ACEX EP1k100

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Numerical solution of the Dirac equation for an armchair graphene nanoribbon in the presence of a transversally variable potential

Numerical solution of the Dirac equation for an armchair gra...

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14th International Workshop on Computational Electronics (IWCE)

作者： Marconcini, P. Logoteta, D. Fagotti, M. Macucci, M. Univ Pisa Dipartimento Ingn Informaz Via Caruso 16 I-56122 Pisa Italy Univ Pisa Dept Fisica & INFN I-56127 Pisa Italy

ISBN: (纸本)9781424493845

We compute, using a continuum model based on the Dirac equation, the transverse modes and the longitudinal wave vectors in an armchair ribbon, in the presence of a transversally variable external potential. We show that the application of a standard finite difference method to this problem is not effective, since it can lead to the appearance of spurious solutions and to poor precision. We show how an approach based on Fourier analysis allows to overcome this difficulty and to drastically speed up the calculations, using well-established fft algorithms.

关键词： C Dirac equation Dirac equation fft algorithms Fourier analysis Fourier analysis armchair graphene nanoribbon continuum model fast Fourier transforms finite difference methods graphene longitudinal wave vectors nanostructured materials numerical solution standard finite difference method transversally variable external potential transversally variable potential transverse modes

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