矢量基二维离散余弦变换

A New Vector-Radix Algorithm for 2D DCT

本文提出一种频率抽取(DIF)矢量基二维离散余弦变换(2D DCT)快速算法。该算法将H.S.HOU的一维离散余弦变换(ID DCT)递归快速算法推广到二维,利用三角恒等式cos(α+β)=2cosαcosβ—cos(α—β),得出数值稳定的二维离散余弦变换快速矢量基算法。其数值稳定性比Haque提出的矢量基2D DCT算法要好,和常用的行列算法相比节省25%乘法运算量。文中给出了算法流图。

In this paper, a fast algorithm for decimation-in-frequency, vector radix, two-dimensional discrte cosine trasform(DIFVR 2D DCT) is presented. Hou's one-dimensional DCT algorithm is extended to the 2D case using trigonometric identity cos(α+β)=2cosacosβ-cos(α-β). This new vector-radix algorithm provides a numerically stable superior to the algorithm of Haque, and reduces a 25% multiplication compared with the traditional row-column method. The signal flowgraph is given.