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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.
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12 Apr 1997
TL;DR: The results of this work will serve as a framework for creating an object-oriented, poly-functional FFT implementation which will automatically choose the most efficient algorithm given user-specified constraints.
Abstract: A large number of fast Fourier transform (FFT) algorithms have been developed over the years. Among these, the most promising are the radix-2, radix-4, split-radix, fast Hartley transform (FHT), quick Fourier transform (QFT), and the decimation-in-time-frequency (DITF) algorithms. We present a rigorous analysis of these algorithms that includes the number of mathematical operations, computational time, memory requirements, and object code size. The results of this work will serve as a framework for creating an object-oriented, poly-functional FFT implementation which will automatically choose the most efficient algorithm given user-specified constraints.
11 citations
TL;DR: The proposed algorithm for the determination of the coefficients of an n -dimensional ( n -D) transfer function is theoretically attractive and computationally fast and it is based on the discrete Fourier transform (DFT).
Abstract: A new algorithm is presented for the determination of the coefficients of an n -dimensional ( n -D) transfer function. The n -D state-space system is described by the n -D Fornasini–Marchesini models. The proposed algorithm is theoretically attractive and computationally fast and it is based on the discrete Fourier transform (DFT). A step-by-step example is given to illustrate the application of the proposed algorithm.
11 citations
TL;DR: In this article, the authors derived a duality equation relating the extension functions introduced in the extended function FFT (EF-FFT) method to conventional window functions and showed that signals with high-frequency content only within the observation window are best analyzed with EF-FFT methods and signals with time-distributed spectral components (e.g., speech) are best analysed with conventional FFT methods.
Abstract: The periodicity assumption implicit in fast Fourier transform (FFT) techniques can be utilized through time-domain prealiasing to obtain the spectral components of infinite-duration time-domain reflectometry signals when they can be modeled, outside the observation window, with step and/or exponential functions. The technique is shown to be more accurate than both conventional windowing and the other FFT approaches described in the literature for analysis of steplike signals. The duality equation relating the extension functions introduced in the extended function FFT (EF-FFT) method to conventional window functions is derived. Using this relation, it is shown that signals with high-frequency content only within the observation window are best analyzed with EF-FFT methods and that signals with time-distributed spectral components (e.g., speech) are best analyzed with conventional FFT methods. >
11 citations
TL;DR: In this article, a set of efficient formulas to evaluate the deflections of the vertical on the sphere using gridded data was presented, including the Vening-Meinesz formula, the topographic indirect effect on the vertical as well as the terrain corrections.
Abstract: This paper presents a set of efficient formulas to evaluate the deflections of the vertical on the sphere using gridded data. The Vening-Meinesz formula, the topographic indirect effect on the deflections of the vertical as well as the terrain corrections are expressed as both 2D and 1D convolutions on the sphere, and consequently can be evaluated by the 2D and the 1D fast Fourier transform (FFT). When compared with the results obtained from pointwise integration, the use of the 1D FFT gives identical results, and therefore these results were used as control values in this paper. The use of the spherical 2D FFT improves significantly the computational efficiency with little sacrifice of accuracy (0.6″ rms difference from the 1D FFT results). The planar 2D FFT, which is as efficient as the spherical 2D FFT, gives worse results (1.2″ rms difference from the 1D FFT results) because of the extra approximations.
11 citations
18 Aug 1996
TL;DR: A new class of parallel architectures called unfolded swapped networks (USN) for fast Fourier transform (FFT) and related problems is proposed and can be constructed using small butterfly modules, each built on a chip, and requires fewer pins than a similar-sized butterfly network.
Abstract: We propose a new class of parallel architectures called unfolded swapped networks (USN) for fast Fourier transform (FFT) and related problems. The VLSI area of a suitably constructed N(log/sub 2/ N+o(log N))-node USN is no more than N/sup 2/+o(N/sup 2/), which is smaller than the best known result for a log, N-dimensional butterfly network. USNs can be constructed using small butterfly modules, each built on a chip, and requires fewer pins than a similar-sized butterfly network by a factor of /spl Theta/(log N). N-point FFT can be executed on a USN at a speed comparable to a butterfly network, assuming constant link delay; it can be executed on a USN considerably faster than on a butterfly when link delay increases with length and/or when inter-chip data transfers are much slower than intra-chip ones.
11 citations