二维离散余弦变换的一种新的快速算法

A NEW FAST ALGORITHM OF 2-D DISCRETE COSINE TRANSFORM

介绍了二维离散余弦变换的一种新的快速算法，对Ｎ×Ｎ ＤＣＴ（Ｎ＝２＾ｍ），只需用Ｎ个一维ＤＣＴ和若干加法运算，与常规的行－列法相比，所需的乘法运算量减少了一半，也比其它快速算法的乘法运算量要少，而加法支算量基本上是相同的。

A new algorithm for the fast computation of a 2-D discrete cosine transform (DCT)is presented. It is shown that the N×N DCT,where N=2~m, can be computed using only N 1-D DCT's and additions, instead of using 2N 1-D DCT's, as in the conventional row-column approach. Hence the total number of multiplications for the proposed algorithm is only half of that required for the row-column approach, and is also less than that of most of other fast algorithms, while the number of additions is almost comparable to that of others.