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Twiddle factor

About: Twiddle factor is a research topic. Over the lifetime, 910 publications have been published within this topic receiving 11033 citations.


Papers
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Journal ArticleDOI
TL;DR: A new implementation of the real-valued split-radix FFT is presented, an algorithm that uses fewer operations than any otherreal-valued power-of-2-length FFT.
Abstract: This tutorial paper describes the methods for constructing fast algorithms for the computation of the discrete Fourier transform (DFT) of a real-valued series. The application of these ideas to all the major fast Fourier transform (FFT) algorithms is discussed, and the various algorithms are compared. We present a new implementation of the real-valued split-radix FFT, an algorithm that uses fewer operations than any other real-valued power-of-2-length FFT. We also compare the performance of inherently real-valued transform algorithms such as the fast Hartley transform (FHT) and the fast cosine transform (FCT) to real-valued FFT algorithms for the computation of power spectra and cyclic convolutions. Comparisons of these techniques reveal that the alternative techniques always require more additions than a method based on a real-valued FFT algorithm and result in computer code of equal or greater length and complexity.

489 citations

Journal ArticleDOI
TL;DR: A new N = 2n fast Fourier transform algorithm is presented, which has fewer multiplications and additions than radix 2n, n = 1, 2, 3 algorithms, has the same number of multiplications as the Raderi-Brenner algorithm, but much fewer additions.
Abstract: A new N = 2n fast Fourier transform algorithm is presented, which has fewer multiplications and additions than radix 2n, n = 1, 2, 3 algorithms, has the same number of multiplications as the Raderi-Brenner algorithm, but much fewer additions, and is numerically better conditioned, and is performed ‘in place’ by a repetitive use of a ‘butterfly’-type structure.

412 citations

Proceedings ArticleDOI
15 Apr 1996
TL;DR: A new VLSI architecture for a real-time pipeline FFT processor is proposed, derived by integrating a twiddle factor decomposition technique in the divide-and-conquer approach, which has the same multiplicative complexity as the radix-4 algorithm, but retains the butterfly structure of the Radix-2 algorithm.
Abstract: A new VLSI architecture for a real-time pipeline FFT processor is proposed. A hardware-oriented radix-2/sup 2/ algorithm is derived by integrating a twiddle factor decomposition technique in the divide-and-conquer approach. The radix-2/sup 2/ algorithm has the same multiplicative complexity as the radix-4 algorithm, but retains the butterfly structure of the radix-2 algorithm. The single-path delay-feedback architecture is used to exploit the spatial regularity in the signal flow graph of the algorithm. For length-N DFT computation, the hardware requirement of the proposed architecture is minimal on both dominant components: log/sub 4/N-1 complexity multipliers and N-1 complexity data memory. The validity and efficiency of the architecture have been verified by simulation in the hardware description language VHDL.

410 citations

Journal ArticleDOI
TL;DR: A simple algorithm for the evaluation of discrete Fourier transforms (DFT) and discrete cosine transforms (DCT) is presented, which achieves a substantial decrease in the number of additions when compared to currently used FFT algorithms.

366 citations

Journal ArticleDOI
Pierre Duhamel1
TL;DR: This algorithm belongs to that class of recently proposed 2n-FFT's which present the same arithmetic complexity (the lowest among any previously published one) and can easily be applied to real and real-symmetric data with reduced arithmetic complexity by removing all redundancy in the algorithm.
Abstract: A new algorithm is presented for the fast computation of the discrete Fourier transform. This algorithm belongs to that class of recently proposed 2n-FFT's which present the same arithmetic complexity (the lowest among any previously published one). Moreover, this algorithm has the advantage of being performed "in-place," by repetitive use of a "butterfly"-type structure, without any data reordering inside the algorithm. Furthermore, it can easily be applied to real and real-symmetric data with reduced arithmetic complexity by removing all redundancy in the algorithm.

272 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20235
202217
202113
202025
201922
201831