Fast Algorithm for Modulated Complex Lapped Transform

摘要

A new algorithm for the modulated complex lapped transform (MCLT) with a sine windowing function is presented. It is shown that by merging the windowing operation with the main computation, both the real and the imaginary parts of the MCLT with $2N$ inputs can be obtained from two $N$-point discrete cosine transforms of type II (DCTs-II) of appropriate inputs. The resulting algorithm is computationally very efficient. In general, the value of $N$ is an even number. When $N$ is a power of 2, the proposed algorithm uses only $N log N + 2$ real multiplications (including the scaling factors in the DCT computation), with none of those being outside the DCT blocks.