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The Discrete Cosine Transform over Prime Finite Fields (1503.03763v1)
Published 12 Mar 2015 in cs.DM, cs.DS, and eess.SP
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.