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提出了一种利用循环卷积 (Cyclic convolution)和扭循环卷积 (Skew cyclic convolution)实现计算奇素长度离散余弦变换 (DCT)的快速新算法。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 ,本文定义了一种新的下标变换算子 ,利用该算子进行下标变换 ,将偶下标 DCT系数的计算转化为一个循环卷积 ,根据不同长度 ,奇下标 DCT系数的计算被转化为循环卷积或扭循环卷积。利用循环卷积和扭循环卷积的高效率和规则的算法 ,构造具有简单、规则的结构和较低的运算复杂性的奇素长度 DCT快速算法。
A new and fast algorithm for computing odd-prime discrete cosine transform (DCT) is proposed by using Cyclic convolution and Skew cyclic convolution. The algorithm divides the DCT coefficients into three parts: DC component, even subscript component and odd subscript component. According to the theory of number theory, a new subscript transformation operator is defined. By using this operator, subscripted DCT coefficients are transformed into a circular convolution. According to different length, odd subscript DCT coefficients The calculations are converted into circular convolution or twisted circular convolution. Using the high efficiency and regular algorithm of convolution and twiddle circle convolution, we construct the fast algorithm of singular prime DCT with simple and regular structure and low computational complexity.