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.

An analysis for the realization of an in-place and in-order prime factor algorithm

Abstract: It is shown that the prime factor algorithm (PFA) has an intrinsic property that allows it to be easily realized in an in-place and in-order form. In contrast to other approaches that use two equations for loading data from and returning the results to the memory, respectively, it is shown formally that in many cases only one equation is enough for both operations. Thus a truly in-place and in-order computation is obtained. Nevertheless, the sequence length of the PFA computation must be carefully selected. The conditions under which a particular sequence length is possible for in-place and in-order PFA computation are analyzed. >

Fast Fourier Transform Multilevel Fast Multipole Algorithm in Rough Ocean Surface Scattering

Abstract: In this article, the microwave backscattering from 3-D rough sea surfaces has been numerically studied. Due to the advantages of the memory and CPU savings of the rigorous multilevel fast multipole algorithm, it was employed to calculate the radar cross-section of the sea surface at large incident angles. Usually, the sea surface can be regarded as a planar scatterer comparing the roughness height with the domain; therefore, an algorithm, called the fast Fourier transform multilevel fast multipole algorithm, was applied in the calculation of this case for a nearly planar scatterer. The difference of the fast Fourier transform multilevel fast multipole algorithm is the use of fast Fourier transform for the translation operator, which can further reduce the computational memory and the CPU time compared with the common multilevel fast multipole algorithm. In the calculation, the Thorsos window and Gaussian window were used in the azimuthal and range direction, respectively, to suppress the edge eff...

Digital signals, processors and noise

Abstract: Part 1 Introduction: background sampling and analog-to-digital conversion time-domain analysis - describing signals and processors, digital convolution Fourier analysis - the discrete Fourier series, the Fourier transform the z-transform - definition and properties, z-plane poles and zeros. Part 2 Digital filter design: non-recursive filters - introduction, the Fourier transform method, window functions, equiripple filters recursive filters - introduction, the bilinear transformation, impulse-invariant filters. Part 3 The discrete and fast Fourier transforms: the discrete Fourier transform the fast Fourier transform (FFT) - basis of the FFT, index mapping, twiddle factors and FFT butterflies, decimation-in-time algorithms, decimation-in-frequency algorithms, FFT processing, fast convolution. Part 4 Describing random sequences: introduction basis measures of random sequences - amplitude distribution, mean, mean-square and variance, ensemble averages and time averages, autocorrelation, power spectrum, cross-correlation, cross-spectrum. Part 5 Processing random sequences: response of linear processors white noise through a filter system identification by cross-correlation signals in noise - introduction, signal recovery, matched filter detection, signal averaging appendix A - computer programs - list of programs and introductory notes basic programs PASCL programs appendix B - tables of Fourier and z-transforms - the discrete Fourier series - properties the Fourier transform of speriodic digital signals - properties and pairs the unilateral z-transform - pairs the unilateral z-transform - properties the discrete Fourier transform - properties.

Fast discrete cosine transform algorithm for systolic arrays

Abstract: A fast algorithm for an N-point discrete cosine transform (DCT) is derived from a 4N-point Winograd Fourier transform algorithm (WFTA). This algorithm, which has the same form as Winograd's Fourier transform and convolution algorithms, is suitable for a high-speed implementation using one-bit systolic arrays.