MCLT新型快速算法

Fast algorithm for Modulated Complex Lapped Transform

提出了一种基本计算单元为DCT-II变换的MCLT快速算法。它将基于任意窗函数的MCLT系数的实部和虚部分别映射为一半输入序列为0的DCT-II变换。对于M点的MCLT变换,该算法只需计算两个一半输入序列为0的M点DCT-II变换和两组蝶形运算。对M点的MCLT,当窗函数为正弦窗时,提出快速算法的运算复杂度为O(MlbM);当窗函数为任意窗时,其运算复杂度为O(MlbM+2M)。实验结果表明:相对于已有的快速算法,由于该算法的中间处理过程中,一半输入序列为0,其实际计算时间减少2%以上。该算法降低了软硬件实现的存储复杂度,更符合实际应用要求。

A novel Discrete Cosine Transform（DCT-II） based algorithm for fast computation of the Modulated Complex Lapped Transform（MCLT） with any windows function is presented.For the MCLT of length-2M input data sequence,the pro- posed algorithm is based on two stages of butterfly operations and two DCT-II of length-M.The proposed algorithm involves M/2 zero points separately,thus it reduces the storage need of the hardware and decreases the computation complexity.For a length-M MCLT,the proposed algorithm requires only O（MlbM） multiplication for Sine window function and O（MlbM＋2M） multiplication for any other window function.Experimental results also show that this method can reduce real computation time by 2% compared with Malvar’s algorithm