STRUCTURES FOR M-CHANNEL PERFECT-RECONSTRUCTION FIR QMF BANKS WHICH YIELD LINEAR-PHASE ANALYSIS FILTERS

In this paper, we develop structures for FIR perfect-reconstruction QMF banks which cover a subclass of systems that yield linear-phase analysis filters for arbitrary M. The parameters of these structures can be optimized in order to design analysis filters with minimum stopband energy which at the same time have linear-phase and satisfy the perfect-reconstruction property. If there are M subbands, then depending upon whether the coefficients hk{n) of each analysis filter is symmetric or antisymmetric, several combinations of filter banks are possible. Some of these permit perfect-reconstruction and some do not. For a given M, we develop a formula for the number of combinations for a subclass of linear-phase perfect-reconstruction structures. As an example, we elaborate on a perfect-reconstruction linear-phase lattice structure for three channels and develop a lattice structure for this case. The lattice structure is such that, regardless of the parameter values, the QMF bank enjoys perfect-reconstruction property while at the same time the analysis filters have linear phase. These parameters can therefore be optimized to obtain analysis filters with good magnitude response, without losing the above two features. A design example, based on optimization of the parameters in the lattice structure, is presented, along with tables of impulse response coefficients. © 1990 IEEE