Design and evaluation of parallel quadrature mirror filters (PQMF)

Quadrature mirror filters (QMF) have been proposed in /1/, and are now widely used in digital sub-band coding of speech. The standard approach to the QMF splitting/reconstruction of a signal is based on a tree arrangement of half-band QMF filters. In this paper, we show that, assuming a proper design, a parallel implementation of the QMF filter bank (PQMF) is much more efficient than the tree implementation. In the first part of the paper, the basic tree approach is briefly reviewed. Than the parallel filter bank structure is introduced, the equations for alias-free reconstruction are derived and solved. It is shown that the parallel approach can drastically be simplified by truncating the so computed impulse responses. The effects of this truncation have been experimentally evaluated and some rules of thumb have been established for optimum truncation order. An example of design is given to illustrate the proposed method.