Two-Channel FIR Filter Banks Utilizing the FRM Approach

The frequency-response masking (FRM) approach has been introduced as a means of generating narrow transition band linear-phase finite impulse response (FIR) filters with a low arithmetic complexity. This paper proposes an approach for synthesizing two-channel maximally decimated FIR filter banks utilizing the FRM technique. For this purpose, a new class of FRM filters is introduced. Filters belonging to this class are used for synthesizing nonlinear-phase analysis and synthesis filters for two types of two-channel filter banks. For the first type, there exist no phase distortion and aliasing errors, but this type suffers from a small amplitude distortion as for the well-known quadrature mirror filter (QMF) banks. Compared to conventional QMF filter banks, the proposed banks lower significantly the overall arithmetic complexity at the expense of a somewhat increased overall filter bank delay in applications demanding narrow transition bands. For the second type, there are also small aliasing errors, allowing one to reduce the arithmetic complexity even further. Efficient structures are introduced for implementing the proposed filter banks, and algorithms are described for maximizing the stopband attenuations of the analysis and synthesis filters in the minimax sense subject to the given allowable amplitude and/or aliasing errors. Examples are included illustrating the benefits provided by the proposed filter banks.