一种有效的MDCT/IMDCT快速算法

提出了一种输入序列长度为N=5×2m的改进型的离散余弦变换（MDCT）的有效算法,可以有效减少数据量,提高计算机储存和运算效率.首先将序列长度为N的MDCT转化为N/2的离散余弦变换IV型（DCT-IV）,然后将后者转化为长度为N/2的离散余弦变换II型（DCT-II）,最后再通过加法和乘法运算实现快速计算过程.同时,分析该算法的算术复杂度.结果表明,较之传统方法,提出的算法能使常用窗型下的MDCT算术复杂度降低20%以上,实现了音频和语音编码领域的运算效率的提高.

An efficient algorithm for computation of MDCT/IMDCT

A novel and efficient algorithm for the computation of modified discrete cosine transform（MDCT）with block size N=5×2m is proposed,which can effectively reduce data volume and therefore improve the efficiency of storage and computing.Firstly,the MDCT with block size N is converted into type-IV discrete cosine transform（DCTIV）which is further transformed into DCT-II with block size N/2.Secondly,a modified window is shown,which is piecewise symmetric.Finally,addition and multiplication operations are conducted for rapidly computing the DCT-II. Analysis of the proposed algorithm in terms of computational complexity is provided.The proposed algorithm achieves at least 20%reduction of arithmetic operations compared to the traditional method,which is meaningful for audio and speech coding.