Split-radix FFT algorithm

About: Split-radix FFT algorithm is a research topic. Over the lifetime, 1845 publications have been published within this topic receiving 41398 citations.

An improved algorithm for harmonic analysis of power system using fft technique

Abstract: There are difficulties in performing synch-ronized sampling and integral period truncation in the harmonic analysis of power system with the fast Fourier transform (FFT) technique However, not to satisfy these conditions, the results will be disturbed by the frequency leakage Some efforts have been made including the utilization of window functions and interpolation algorithms to correct the measured frequency, phase and amplitude by FFT In order to overcome some shortcomings of existing correction methods, an improved algorithm is present in this paper, with which the amplitudes of harmonics can be estimated from the two neighboring spectral lines The polynomial approximation method is also employed to obtain simple formulas for frequency and amplitude correction By these methods, the disturbance of the frequency leakage and the noise can be reduced and the accuracy of the harmonic analysis can be improved Based on the proposed algorithm, the practical correction formulas for some typical window functions are developed The simulation results have verified the effectiveness and practicability of the algorithm

Comparative performance of various trigonometric unitary transforms for transform image coding

Abstract: The feasibility of discrete sine transform (DST) and discrete sine cosine transform (DSCT) for digital image processing problems are investigated. Discrete sine transform and discrete cosine transform can be computed by using two FFT’s of original data sequence of length N. Discrete sine cosine coefficients are computed by FFT of data sequence of length N while the inverse is obtained by computing two FFT's. The performance of each of the unitary transforms in the trigonometric family is studied in terms of quantitative performance measures such as variance distribution, rate distortion, Wiener filtering and how well a transform decorrelates the data efficiently for possible bandwidth compression of a signal represented by a firstorder Markov process model. Computer simulation results on a monochrome image are presented.

A unified treatment of Cooley-Tukey algorithms for the evaluation of the multidimensional DFT

Abstract: In this paper the Cooley-Tukey fast Fourier transform (FFT) algorithm is generalized to the multidimensional case in a natural way which allows for the evaluation of discrete Fourier transforms of rectangularly or hexagonally sampled signals or of signals which are sampled on an arbitrary periodic grid in either the spatial or Fourier domain. This general algorithm incorporates both the traditional rectangular row-column and vector-radix algorithms as special cases. This FFT algorithm is shown to result from the factorization of an integer matrix; for each factorization of that matrix, a different algorithm can be developed. This paper presents the general algorithm, discusses its computational efficiency, and relates it to existing multi-dimensional FFT algorithms.

On the stability of the hyperbolic cross discrete Fourier transform

Abstract: A straightforward discretisation of problems in high dimensions often leads to an exponential growth in the number of degrees of freedom. Sparse grid approximations allow for a severe decrease in the number of used Fourier coefficients to represent functions with bounded mixed derivatives and the fast Fourier transform (FFT) has been adapted to this thin discretisation. We show that this so called hyperbolic cross FFT suffers from an increase of its condition number for both increasing refinement and increasing spatial dimension.

An FFT-based algorithm for 2D power series expansions

Abstract: An effective numerical algorithm based on inverting a specialized Laplace transform is derived for computing the two-dimensional power-series expansion coefficients of a two-variable function. Due to the special structure of the constructed 2D Laplace transform, the accuracy of the inverted function values can be assured effectively by the generalized Riemann zeta function evaluation and the multiple sets of 2D FFT computation. Therefore, the algorithm is particularly amenable to modern computers having multiprocessors and/or vector processors.