The Discrete Cosine Transform over Prime Finite Fields

March 12, 2015 · The Ethereal · 🏛 International Conference on Telecommunications

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Authors M. M. Campello de Souza, H. M. de Oliveira, R. M. Campello de Souza, M. M. Vasconcelos arXiv ID 1503.03763 Category cs.DM: Discrete Mathematics Cross-listed cs.DS, eess.SP Citations 17 Venue International Conference on Telecommunications Last Checked 2 months ago
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.
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