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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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01 Sep 1991
TL;DR: The Bluestein FFT may be the algorithm of choice on multiprocessors, particularly those with the hypercube architecture because of its minimal communication requirements and for most values of N it is also shown to be superior to another alternative, namely parallel multiplication.
Abstract: The original Cooley-Tukey FFT was published in 1965 and presented for sequences with length N equal to a power of two. However, in the same paper they noted that their algorithm could be generalized to composite N in which the length of the sequence was a product of small primes. In 1967, Bergland presented an algorithm for composite N and variants of his mixed radix FFT are currently in wide use. In 1968, Bluestein presented an FFT for arbitrary N including large primes. However, for composite N, Bluestein's FFT was not competitive with Bergland's FFT. Since it is usually possible to select a composite N, Bluestein's FFT did not receive much attention. Nevertheless because of its minimal communication requirements, the Bluestein FFT may be the algorithm of choice on multiprocessors, particularly those with the hypercube architecture. In contrast to the mixed radix FFT, the communication pattern of the Bluestein FFT maps quite well onto the hypercube. With P = 2^d processors, an ordered Bluestein FFT requires 2d communication cycles with packet length N/2P which is comparable to the requirements of a power of two FFT. For fine-grain computations, the Bluestein FFT requires 20log"2N computational cycles. Although this is double that required for a mixed radix FFT, the Bluestein FFT may nevertheless be preferred because of its lower communication costs. For most values of N it is also shown to be superior to another alternative, namely parallel multiplication.
22 citations
TL;DR: In this article, a method for bootstrapping stationary Gaussian sequences is studied, where the FFT is applied to the original data, randomized in the frequency domain, and the inverse FFT was applied.
Abstract: A method for bootstrapping stationary Gaussian sequences is studied. The FFT is applied to the original data, randomized in the frequency domain, and the inverse FFT is applied. The result is a sequence whose second order properties are similar to those of the original sequence. Conditions under which the method is valid are given.
22 citations
21 Aug 2000
TL;DR: A new and efficient algorithm for the computation of filter banks that performs the filtering in frequency domain to utilize the advantage of FFT by combining FFT with decimation filter.
Abstract: This paper proposes a new and efficient algorithm for the computation of filter banks. The algorithm performs the filtering in frequency domain to utilize the advantage of FFT. By combining FFT with decimation filter, more than 80% computation power can be saved.
22 citations
14 Apr 1991
TL;DR: The authors introduce the pruned short-time FFT, a novel computational structure for efficiently computing the STFT with dense temporal sampling that achieves the same computational savings as the Goertzel algorithm, but is unconditionally stable.
Abstract: Although most applications which use the short-time Fourier transform (STFT) temporally downsample the output, some applications exploit a dense temporal sampling of the STFT. One example, coded-division multiple-beam sonar, is discussed. Given a need for the densely sampled STFT, the complexity of the computation can be reduced from O(N log N) for the general short-time FFT structure to O(N) using the Goertzel algorithm. The authors introduce the pruned short-time FFT, a novel computational structure for efficiently computing the STFT with dense temporal sampling. The pruned FFT achieves the same computational savings as the Goertzel algorithm, but is unconditionally stable. >
22 citations
TL;DR: Korn and Lambiotte as mentioned in this paper showed that trigonometric tables can lead to more than three times faster execution times compared to the traditional Pease algorithm for large transforms on the CDC STAR-100 vector computer.
Abstract: A recent article in this journal by D. G. Korn and J. J. Lambiotte, Jr. discusses implementations of the FFT algorithm on the CDC STAR-100 vector computer. The 'Pease'-algorithm is recommended in cases when only a few transforms can be performed simultaneously. We show how the use of a different algorithm and of trigonometric tables will lead to more than three times faster execution times. The times for large transforms increase only about 39% if the tables are eliminated in order to save storage.
22 citations