The Discrete Cosine Transform over Prime Finite Fields
Discrete Mathematics
2020-05-21 v1 Data Structures and Algorithms
Signal Processing
Abstract
This paper examines finite field trigonometry as a tool to construct trigonometric digital transforms. In particular, by using properties of the k-cosine function over GF(p), the Finite Field Discrete Cosine Transform (FFDCT) is introduced. The FFDCT pair in GF(p) is defined, having blocklengths that are divisors of (p+1)/2. A special case is the Mersenne FFDCT, defined when p is a Mersenne prime. In this instance blocklengths that are powers of two are possible and radix-2 fast algorithms can be used to compute the transform.
Keywords
Cite
@article{arxiv.1503.03763,
title = {The Discrete Cosine Transform over Prime Finite Fields},
author = {M. M. Campello de Souza and H. M. de Oliveira and R. M. Campello de Souza and M. M. Vasconcelos},
journal= {arXiv preprint arXiv:1503.03763},
year = {2020}
}
Comments
5 pages, 1 table, Lecture Notes in Computer Science, LNCS 3124, Heidelberg: Springer Verlag, 2004, vol.1, pp.482-487, 2004