Discrete cosine and sine transforms generalized to honeycomb lattice

Discrete Cosine and Sine Transforms Generalized to Honeycomb Lattice

The discrete cosine and sine transforms are generalized to a triangular fragment of the honeycomb lattice. The two-variable orbit functions of the Weyl group A2, discretized simultaneously on the weight and root lattices, induce the family of the extended Weyl orbit functions. The periodicity and von Neumann and Dirichlet boundary properties of the extended Weyl orbit functions are detailed. Th...

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...

The discrete fractional random cosine and sine transforms

Based on the discrete fractional random transform (DFRNT), we present the discrete fractional random cosine and sine transforms (DFRNCT and DFRNST). We demonstrate that the DFRNCT and DFRNST can be regarded as special kinds of DFRNT and thus their mathematical properties are inherited from the DFRNT. Numeral results of DFRNCT and DFRNST for one and two dimensional functions have been given.