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A Polynomial Approach to Fast Algorithms for Discrete Fourier-Cosine and Fourier-Sine Transforms

Gabriele Steidl, Manfred Tasche

Open publisher page 11 citations

Abstract

The discrete Fourier-cosine transform $(\cos {\text {-DFT}})$, the discrete Fourier-sine transform $(\sin {\text {-DFT}})$ and the discrete cosine transform (DCT) are closely related to the discrete Fourier transform (DFT) of real-valued sequences. This paper describes a general method for constructing fast algorithms for the $(\cos {\text {-DFT}})$, the $(\sin {\text {-DFT}})$ and the DCT, which is based on polynomial arithmetic with Chebyshev polynomials and on the Chinese Remainder Theorem.

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What this paper is about

The discrete Fourier-cosine transform $(\cos {\text {-DFT}})$, the discrete Fourier-sine transform $(\sin {\text {-DFT}})$ and the discrete cosine transform (DCT) are closely related to the discrete Fourier transform (DFT) of real-valued sequences. This paper describes a general method for constructing fast algorithms for the $(\cos {\text {-DFT}})$, the $(\sin {\text {-DFT}})$ and the DCT, which is based on polynomial arithmetic with Chebyshev polynomials and on the Chinese Remainder Theorem.

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Available abstract

The discrete Fourier-cosine transform $(\cos {\text {-DFT}})$, the discrete Fourier-sine transform $(\sin {\text {-DFT}})$ and the discrete cosine transform (DCT) are closely related to the discrete Fourier transform (DFT) of real-valued sequences. This paper describes a general method for constructing fast algorithms for the $(\cos {\text {-DFT}})$, the $(\sin {\text {-DFT}})$ and the DCT, which is based on polynomial arithmetic with Chebyshev polynomials and on the Chinese Remainder Theorem.

Key concepts: Discrete Fourier transform (general), Discrete cosine transform, Discrete sine transform, Sine and cosine transforms, Mathematics, Fourier transform, Chebyshev polynomials, Discrete-time Fourier transform

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