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

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...

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...

Fast and stable algorithms for discrete spherical Fourier transforms

In this paper, we propose an algorithm for the stable and eecient computation of Fourier expansions of square integrable functions on the unit sphere S R 3 , as well as for the evaluation of these Fourier expansions at special knots. The heart of the algorithm is an eecient realization of discrete Legendre function transforms based on a modiied and stabilized version of the Driscoll{Healy algor...

Integral Transforms of Fourier Cosine and Sine Generalized Convolution Type

Discrete Cosine and Sine Transforms