Journal ArticleDOI
Optimal design of discrete coefficient DFTs for spectral analysis: extension to multiplierless FFTs
W.A. Perera,P.J.W. Rayner +1 more
- Vol. 133, Iss: 1, pp 8-18
TLDR
In this article, it has been shown that the complex coefficients of a discrete Fourier transform (DFT) used in spectral analysis, can be replaced by an optimum set whose real and imaginary components are constrained to be integer powers of two or the sum of two integer powers-of-two.Abstract:
In a previous paper it has been shown that the complex coefficients of a discrete Fourier transform (DFT) used in spectral analysis, can be replaced by an optimum set whose real and imaginary components are constrained to be integer powers of two or the sum of two integer powers of two thus making multiplication trivial. However, the technique used ruled out any further increase in speed and reduction in hardware cost by factorisation of the DFT. The scheme presented in the paper overcomes this drawback and is applicable to the Cooley-Tukey fast Fourier transform algorithm.read more
Citations
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Journal ArticleDOI
Architectures for multiplierless fast Fourier transform hardware implementation in VLSI
TL;DR: A novel processor for the implementation of multiplierless FFT's in VLSI with the capability of achieving a 40 MHz throughput rate for a 1024-point FFT using 20 processing IC's is presented.
Journal ArticleDOI
Parallel architecture for fast transforms with trigonometric kernel
TL;DR: The efficiency of the partitioned parallel architecture is optimum because there is no cycle loss in the systolic computation of all the butterflies for each of the four transforms.
Journal ArticleDOI
Multiplierless implementation of rotators and FFTs
TL;DR: Methods for designing multiplierless implementations of fixed-point rotators and FFTs, in which multiplications are replaced by additions, subtractions, and shifts, which minimise the adder-cost (the number of additions and subtractions), while achieving a specified level of accuracy.
Proceedings ArticleDOI
Optimal design of multiplierless DFTS and FFTS
W. Perera,P. Rayner +1 more
TL;DR: A Mixed Integer Linear Programming (MILP) technique for the optimal design of windowed FFTs with discrete coefficients is presented, resulting in a multiplierless system with significant savings in time and hardware costs.
References
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Book
Theory and application of digital signal processing
TL;DR: Feyman and Wing as discussed by the authors introduced the simplicity of the invariant imbedding method to tackle various problems of interest to engineers, physicists, applied mathematicians, and numerical analysts.
Book
Fast Fourier transform and convolution algorithms
TL;DR: This book explains the development of the Fast Fourier Transform Algorithm and its applications in Number Theory and Polynomial Algebra, as well as some examples of its application in Quantization Effects.
Journal ArticleDOI