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Mathematics of Computation

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A polynomial approach to fast algorithms for discrete Fourier-cosine and Fourier-sine transforms


Authors: G. Steidl and M. Tasche
Journal: Math. Comp. 56 (1991), 281-296
MSC: Primary 65T20; Secondary 94A11
DOI: https://doi.org/10.1090/S0025-5718-1991-1052103-1
MathSciNet review: 1052103
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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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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1991-1052103-1
Keywords: Discrete Fourier-cosine transform, discrete Fourier-sine transform, discrete cosine transform, polynomial arithmetic, Chebyshev polynomials, computational complexity, discrete Fourier transform
Article copyright: © Copyright 1991 American Mathematical Society