A Polynomial Approach to Fast Algorithms for Discrete Fourier-Cosine and Fourier-Sine Transforms
Gabriele Steidl, Manfred Tasche · Mathematics of Computation · 1991
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.