Matrix Theory for Filter Bank Analysis and Design

Abstract

Recent developments in both multirate systems theory and microelectronic technology have led to widespread interest in using analysis/synthesis systems based on filter banks for an ever increasing number of applications. Typically the performance of such application-specific systems is affected significantly by both the properties of the individual analysis and synthesis filters as well as by the structure and quality of the overall analysis/synthesis system. The properties of interest associated with the individual filters include the passband deviations, the transition bandwidths and behavior, the stopband deviations, the phase characteristics, the filter type (i.e., finite impulse response, FIR, or infinite impulse response, IIR), the order of the filters, and the computational efficiency of the implementation. Structural properties include the number of frequency bands, the bandwidths of the filters, and the overall frequency coverage. The quality of the overall analysis/synthesis system is mainly a function of its ability to reconstruct the input signal at the output. Sometimes a small loss in reconstruction accuracy can be traded for gains elsewhere, such as in computational complexity. The design phase for application-specific systems based on filter banks should address all of these separate issues simultaneously in a single design context.