Modulated Qmf Filter Banks with Perfect Reconstruction

Quadrature mirror filter (QMF) banks are essential building blocks of a subband/transform coder. Generally, one wants the filter bank to have the perfect reconstruction (PR) property, which means that, in absence of coding, a delayed copy of the original signal is reconstructed exactly in the critically-sampled analysis-synthesis system of Fig. 1. Although there are useful filter banks that are not exactly PR, if a PR filter bank with a fast implementation can be found, it is usually preferable. General conditions for PR have been derived by Vaidyanathan. Modulated filter banks are a class of QMF banks where all the impulse responses hk(n) in Fig. 1 are obtained from modulated versions of a single low-pass filter prototype3−5. Princen and Bradley, and Vetterli and Le Gall have shown that an M -channel PR modulated filter bank can be obtained with FIR analysis and synthesis filters as long as their impulse responses have a length L = 2M . The modulated lapped transform (MLT) is a particular modulated filter bank that has a very fast algorithm. In this letter we will show that PR can be obtained not only when L = 2M , but also when L = 2KM , with K a positive integer. In applications such as transmultiplexing and speech coding, the possibility of using longer filters means less interference among the subband signals, and keeping the modulated structure means a possibility of computationally efficient implementations.