56. The Discrete Cosine Transform over Finite Prime
This paper examines finite field trigonometry as a tool to construct digital trigonometric transforms.
In particular, by using properties of k-cosine function over a Galois field,
the finite field discrete cosine transform is introduced. The finite field DCT pair in GF(p) is defined,
having blocklengths that are divisors of (p+1)/2. A special case is the Mersenne finite field DCT,
defined when p is Mersenne prime. In this instance block lengths that are power of two are possible and
radix-two fast algorithms can be used to compute the transform.