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The discrete Fourier-cosine transform (cos-DFT), the discrete Fourier-sine transform (sin-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-DFT, the sin-DFT and the DCT, which is based on polynomial arithmetic with Chebyshev polynomials and on the Chinese Remainder Theorem.

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