The Algebraic Approach to the Discrete Cosine and Sine Transforms and Their Fast Algorithms

The Algebraic Approach to the Discrete Cosine and Sine Transforms and Their Fast Algorithms

It is known that the discrete Fourier transform (DFT) used in digital signal processing can be characterized in the framework of representation theory of algebras, namely as the decomposition matrix for the regular module C[Zn] = C[x]/(x − 1). This characterization provides deep insight on the DFT and can be used to derive and understand the structure of its fast algorithms. In this paper we pr...

A Polynomial Approach to Fast Algorithms for Discrete Fourier-cosine and Fourier-sine Transforms

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 polynomi...

Discrete Cosine and Sine Transforms

The discrete fractional cosine and sine transforms

This paper is concerned with the definitions of the discrete fractional cosine transform (DFRCT) and the discrete fractional sine transform (DFRST). The definitions of DFRCT and DFRST are based on the eigen decomposition of DCT and DST kernels. This is the same idea as that of the discrete fractional Fourier transform (DFRFT); the eigenvalue and eigenvector relationships between the DFRCT, DFRS...

Discrete cosine and sine transforms - regular algorithms and pipeline architectures

In this paper, regular fast algorithms for discrete cosine transform (DCT) and discrete sine transform (DST) of types II–IV are proposed and mapped onto pipeline architectures. The algorithms are based on the factorization of transform matrices described earlier by Wang. The regular structures of the algorithms are advantageous when mapping them onto hardware although such algorithms do not rea...