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

Abstract

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