Topic
Prime-factor FFT algorithm
About: Prime-factor FFT algorithm is a research topic. Over the lifetime, 2346 publications have been published within this topic receiving 65147 citations. The topic is also known as: Prime Factor Algorithm.
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08 Jul 2001
TL;DR: An algorithm that efficiently Fourier transforms sparse spatial data to sparse spectral data with controllable error with applications in electromagnetics, diffraction tomography, synthetic aperture radar imaging, and the computation of far field patterns due to general aperture antennas and antenna arrays is presented.
Abstract: An algorithm that efficiently Fourier transforms sparse spatial data to sparse spectral data with controllable error is presented. Unlike the ordinary nonuniform fast Fourier transform (NUFFT), which becomes O(N/sup 2/) for sparse r-space and sparse k-space data, the sparse data fast Fourier transform (SDFFT) presented herein decreases the cost to O(N log N) while preserving the O(N log N) memory complexity. The algorithm can be readily employed in general signal processing applications where only part of the k-space is to be computed - regardless of whether it is a regular region like an angular section of the Ewald's sphere or it consists completely of arbitrary points. Among its applications in electromagnetics are back-projection tomography, diffraction tomography, synthetic aperture radar imaging, and the computation of far field patterns due to general aperture antennas and antenna arrays.
3 citations
25 May 2012
TL;DR: The Pipelined Streaming butterfly stage of DFT/FFT is designed including CORDIC and complex algorithm to increase the Performance and the efficiency of compute, accuracy and range.
Abstract: In this paper, the Pipelined Streaming butterfly stage of DFT/FFT is designed including CORDIC and complex algorithm to increase the Performance. This butterfly stage is full use of the register of DSP to transform the complex quantity to the simple Pipelined algorithm and the iteration of CORDIC to compute the trigonometric. The butterfly stage not only save the resources, but also increase the accuracy of result. The simulation show that the butterfly stage is highly the efficiency of compute, accuracy and range.
3 citations
01 Jan 2016
TL;DR: The formula for computing discrete frequency is given by analyzing the process of deriving discrete Fourier transform expression by using spectral method to resolve the problem of continuation of gravity field by theoretical model data.
Abstract: Fast Fourier Transform( FFT) algorithm plays an important role in efficient numerical simulation and data processing of geophysical fields, such as gravity, magnetic field and electromagnetic field. FFT is intrinsically a numerical computational method for discrete Fourier transform. Now there are many kinds of FFT algorithms that can carry out discrete Fourier transform with random sampling points. Computation of discrete frequency is a key part in correctly using FFT algorithms to resolve numerical simulation and data processing of geophysical fields. In this study,treating discrete Fourier transform as a numerical approximation of Fourier transform, we give the formula for computing discrete frequency by analyzing the process of deriving discrete Fourier transform expression. We use spectral method to resolve the problem of continuation of gravity field by theoretical model data.Experimental results further verify the correctness of the presented formula for computing discrete frequency.
2 citations
01 May 1978
TL;DR: Efficient algorithms for 11 and 13- point DFT's are presented and a more efficient algorithm, compared to earlier published versions, for the computation of 9-point DFT is also included.
Abstract: : Efficient algorithms for 11 and 13-point DFT's are presented. A more efficient algorithm, compared to earlier published versions, for the computation of 9-point DFT is also included. The effect of arithmetic roundoff in implementing the prime factor and the nested algorithms for computing DFT with fixed point arithmetic is analyzed using a statistical model. Various aspects of the prime factor, the nested and the radix-2 FFT algorithms are compared. A processor-based hardware implementation of the prime factor algorithm is discussed.
2 citations
TL;DR: Radix-4 FFT is introduced to realize limit distortion coding of image and it can reduce the number of data store by conformal symmetry of Fourier transform.
Abstract: Image compression technology has been the research focus in the field of image processing all the time In this paper, Radix-4 FFT is introduced to realize limit distortion coding of image The presented method aims to solve the problems of Fourier transform on existing complexity and long time-consuming, and it can reduce the number of data store by conformal symmetry of Fourier transform Using Radix-4 FFT, the time-consuming can be highly shortened and two different kinds of quantization tables are designed according to image compression ratio and the quality of image
2 citations