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Another discrete Fourier transform computation with small multiplications via the Walsh transform

Yukihiro Tadokoro, T. Higuchi

Open publisher page 5 citations

Abstract

This paper describes another computational algorithm for the discrete Fourier transform(DFT) via the discrete Walsh transform(DWT). The number of multiplications required by this algorithm is approximately NL/9 where N is the number of data points and L is the number of Fourier coefficients desired. This number shows a 33 % decrease against NL/6 in the previous algorithm published by us. The proposed algorithm can be derived by using conventional sampling points in the DFT. The DFT computation via the DWT is superior to the fast Fourier transform(FFT) approach in applications where L is relatively small compared with N and where the Walsh and Fourier coefficients are both desired.

About this research paper

What this paper is about

This paper describes another computational algorithm for the discrete Fourier transform(DFT) via the discrete Walsh transform(DWT). The number of multiplications required by this algorithm is approximately NL/9 where N is the number of data points and L is the number of Fourier coefficients desired. This number shows a 33 % decrease against NL/6 in the previous algorithm published by us. The proposed algorithm can be derived by using conventional sampling points in the DFT. The DFT computation via the DWT is superior to the fast Fourier transform(FFT) approach in applications where L is relatively small compared with N and where the Walsh and Fourier coefficients are both desired.

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OpenAlex reports 5 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

This paper describes another computational algorithm for the discrete Fourier transform(DFT) via the discrete Walsh transform(DWT). The number of multiplications required by this algorithm is approximately NL/9 where N is the number of data points and L is the number of Fourier coefficients desired. This number shows a 33 % decrease against NL/6 in the previous algorithm published by us. The proposed algorithm can be derived by using conventional sampling points in the DFT. The DFT computation via the DWT is superior to the fast Fourier transform(FFT) approach in applications where L is relatively small compared with N and where the Walsh and Fourier coefficients are both desired.

Key concepts: Discrete Fourier transform (general), Split-radix FFT algorithm, Prime-factor FFT algorithm, Discrete sine transform, Non-uniform discrete Fourier transform, Fast Fourier transform, Discrete Hartley transform, Discrete-time Fourier transform

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