Fast Algorithm for the Modulated Complex Lapped Transform

We present a complete derivation for a new algorithm for fast computation of the modulated complex lapped transform (MCLT), which we have previously presented. In particular, we present explicit formulas and flowgraphs not only for the direct transform, but also for the inverse transform. For a length-M MCLT, the direct transform algorithm is based on computing a length-2M fast Fourier transform (FFT) plus M butterfly-like stages, without data shuffling. That reduces the number of operations and memory accesses needed to compute the MCLT when compared to previous algorithms. Compared to the original DCT-IV-based algorithm, a software implementation of the new algorithm running in a personal computer leads to 25% faster execution.