Moment-based fast discrete sine transforms

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...

Fast Discrete Curvelet Transforms

This paper describes two digital implementations of a new mathematical transform, namely, the second generation curvelet transform [12, 10] in two and three dimensions. The first digital transformation is based on unequally-spaced fast Fourier transforms (USFFT) while the second is based on the wrapping of specially selected Fourier samples. The two implementations essentially differ by the cho...

Fast Factorizations of Discrete Sine Transforms of Types Vi and Vii

Discrete Sine Transforms of types VI and VII (DST-VI/VII) have recently received considerable interest in video coding. In particular, it was shown that DST-VII offers good approximation for KLT of residual signals produced by spatial (Intra) prediction process. In this paper, we offer an additional argument for use of such transforms by showing that they allow fast computation. Specifically, w...

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...