一种用循环卷积实现的素长度DCT新快速算法

提出了一种利用循环卷积（Cyclic convolution)和扭循环卷积（Skew cyclic convolution)实现的计算奇素长度离散余弦变换（DCT）快速新算法,算法将DCT系数分成三部分：DC分量,偶下标分量和奇下标分量,根据数论理论,定义了一种新的下标变换算子,利用该算子被转化为循环卷积或扭循环积,由于循环卷积和扭循环卷积具有非常高的效率和规则,因此,本算法具有简单,规则的结构和较纸的运算复杂性。

A New Fast Algorithm for Computing Prime-length DCT Through Cyclic Convolutions

This paper proposes a new algorithm for the computation of Discrete Cosine Transform (DCT) with odd prime length using cyclic or skew cyclic convolutions. The algorithm separates DCT coefficients into three parts: DC coefficients, even-and odd-indexed DCT coefficients. According to the number theory a new index-mapping operation is defined. By means of the index-mapping operation,the even-indexed part is converted to a cyclic convolution, and the odd-indexed part is converted to a cyclic or skew cyclic convolution depending on its length. Since efficient and fast cyclic convolution algorithms are available in the literature, the algorithm has low computational complexity, simple and regular structure.