Journal ArticleDOI
A General Class of Split-Radix FFT Algorithms for the Computation of the DFT of Length- $2^{m}$
TLDR
A general class of split-radix fast Fourier transform (FFT) algorithms for computing the length-2m DFT is proposed by introducing a new recursive approach coupled with an efficient method for combining the twiddle factors and it is shown that the number of arithmetic operations required is independent of s and is (2m-3)2m+1+8.Abstract:
In this paper, a general class of split-radix fast Fourier transform (FFT) algorithms for computing the length-2m DFT is proposed by introducing a new recursive approach coupled with an efficient method for combining the twiddle factors. This enables the development of higher split-radix FFT algorithms from lower split-radix FFT algorithms without any increase in the arithmetic complexity. Specifically, an arbitrary radix-2/2s FFT algorithm for any value of s, 4les sles m, is proposed and its arithmetic complexity analyzed. It is shown that the number of arithmetic operations (multiplications plus additions) required by the proposed radix-2/2s FFT algorithm is independent of s and is (2m-3)2m+1+8 regardless of whether a complex multiplication is carried out using four multiplications and two additions or three multiplications and three additions. This paper thus provides a variety of choices and ways for computing the length-2m DFT with the same arithmetic complexity.read more
Citations
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Journal ArticleDOI
Binary Discrete Cosine and Hartley Transforms
TL;DR: A systematic method for developing a binary version of a given transform by using the Walsh-Hadamard transform (WHT) is proposed and it is shown that the resulting BDCT corresponds to the well-known sequency-ordered WHT, whereas the BDHT can be considered as a new Hartley-ordering WHT.
Journal ArticleDOI
New Parametric Discrete Fourier and Hartley Transforms, and Algorithms for Fast Computation
TL;DR: A new reciprocal-orthogonal parametric discrete Fourier transform (DFT) is proposed by appropriately replacing some specific twiddle factors in the kernel of the classical DFT by independent parameters that can be chosen arbitrarily from the complex plane.
A Fast Fourier Transform Algorithm Using Base 8 Iterations
TL;DR: This collection of papers is the result of a desire to make available reprints of articles on digital signal processing for use in a graduate course offered at MIT, and to present reprints in an easily accessible form.
Journal ArticleDOI
Design of a mixed prime factor FFT for portable digital radio mondiale receiver
TL;DR: A mixed radix-2n and prime factor FFT algorithm for portable DRM receivers is proposed that can reduce the processing time and energy consumption compared to conventional digital signal processor (DSP) based DRM receivers.
Journal ArticleDOI
A Fast Algorithm With Less Operations for Length- $N=q\times 2^{m}$ DFTs
Kenli Li,Weihua Zheng,Keqin Li +2 more
TL;DR: This paper presents a fast Fourier transform (FFT) algorithm for computing length-q×2m DFTs, and the proposed algorithm achieves reduction of arithmetic complexity over the related algorithms.
References
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Journal ArticleDOI
An algorithm for the machine calculation of complex Fourier series
J.W. Cooley,John W. Tukey +1 more
TL;DR: Good generalized these methods and gave elegant algorithms for which one class of applications is the calculation of Fourier series, applicable to certain problems in which one must multiply an N-vector by an N X N matrix which can be factored into m sparse matrices.
Journal ArticleDOI
`Split radix' FFT algorithm
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.
Journal ArticleDOI
Simple FFT and DCT algorithms with reduced number of operations
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.
Journal ArticleDOI
Implementation of "Split-radix" FFT algorithms for complex, real, and real-symmetric data
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.
Journal ArticleDOI
On computing the split-radix FFT
TL;DR: This paper presents an efficient Fortran program that computes the Duhamel-Hollmann split-radix FFT, which seems to require the least total arithmetic of any power-of-two DFT algorithm.