素有限域上的离散余弦变换
The Discrete Cosine Transform over Prime Finite Fields
摘要：
本文探讨了有限域三角函数作为一种工具来构建三角数字变换。特别地，利用GF（p）上的k-余弦函数的性质，引入了有限域离散余弦变换（FFDCT）。定义GF（p）中的FFDCT对，其具有作为（p+1）/2的约数的块长度。一个特殊的例子是梅森FFDCT，当p是梅森素数时定义。在这种情况下，块长度是2的幂是可能的，并且基数2快速算法可以用于计算变换。
英文摘要：
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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