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.

Fast Fourier transform, iteration, and least-squares-fit demodulation image processing for analysis of single-carrier fringe pattern

Abstract: Fast Fourier transform (FFT), iteration, and least-squares fit are combined to form an image-processing system for the analysis of a carrier-coded fringe pattern. Only one coded fringe pattern is needed for extracting unambiguous information. The coded fringe pattern is first two-dimensionally FFT filtered to produce an initial coded phase with the carrier phase in it. Several phase iterations are carried out if necessary to improve the coded phase. The least-squares-fit technique is used to obtain a pure carrier phase. Then the carrier is removed by subtracting the pure carrier phase from the coded phase. The algorithm offers an improvement over the Fourier-transform method reported in the literature. A program is designed to execute the algorithm, and the processing is automated by a personal computer with an image board. Theory and applications of speckle interferometry and three-dimensional contouring are presented.

A comparison of the time involved in computing fast Hartley and fast Fourier transforms

Abstract: It is shown that the DFT of a real sequence, formed via the Fast Hartley Transform, can be computed at most only 2 times faster than by using a complex Fast Fourier Transform. However, more sophisticated FFT algorithms exist which give the same speedup factor. A simple FHT subroutine is presented to illustrate the similarity of the FHT and FFT butterflies in their simplest forms.

Performance Analysis of FFT Algorithms on Multiprocessor Systems

Abstract: A decimation-in-time radix-2 fast Fourier transform (FFT) algorithm is considered here for implementation in multiprocessors with shared bus, multistage interconnection network (MIN), and in mesh connected computers. Results are derived for data allocation, interprocessor communication, approximate computation time, and speedup of an N point FFT on any P available processing elements (PE's). Further generalization is obtained for a radix-r FFT algorithm. An N X N point two-dimensional discrete Fourier transform (DFT) implementation is also considered when one or more rows of the input data matrix are allocated to each PE.

A new bit reversal algorithm

Abstract: A new bit reversal permutation algorithm is described. Such algorithms are needed for radix 2 (or radix B) fast Fourier transforms (FFTs) or fast Hartley transforms (FHTs). This algorithm is an alternative to one described by Evans (1987). A BASIC version of this algorithm ran slightly faster than the BASIC version of Evans' algorithm given by Bracewell (1986), with some time savings for odd powers of two. This new algorithm also allows for precomputation of seed tables up to one higher power of two than Evans' algorithm. >

Inter-Harmonic Identification using Group-Harmonic Weighting Approach Based on the FFT

Abstract: The fast Fourier transform (FFT) is still a widely-used tool for analyzing and measuring both stationary and transient signals with power system harmonics in power systems. However, the misapplications of FFT can lead to incorrect results caused by some problems such as aliasing effect, spectral leakage and picket-fence effect. A strategy of group-harmonic weighting distribution is proposed for system-wide inter-harmonic evaluation in power systems. The proposed algorithm can restore the dispersing spectral leakage energy caused by the fast Fourier transform (FFT), and calculate the power distribution proportion around the adjacent frequencies at each harmonic to determine the inter-harmonic frequency. Therefore, not only high-precision in integer harmonic measurement by the FFT can be retained, but also the inter-harmonics can be identified accurately, particularly under system frequency drift. The numerical examples are presented to verify the performance of the proposed algorithm.