**56. The Discrete Cosine Transform over Finite Prime
Fields
**

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.

** **