THE ANALYSIS AND DESIGN OF MULTIDIMENSIONAL FIR PERFECT RECONSTRUCTION FILTER BANKS FOR ARBITRARY SAMPLING LATTICES

In this paper, we present a general analysis of multidimensional multirate filter banks. The approach is applicable to discrete signal spaces of any dimension, to multirate systems based on arbitrary downsampling and upsampling lattices, and for filter banks with any number of channels. We also present a new numerical design procedure for multidimensional multirate perfect reconstruction filter banks, which is based upon methods of nonlinearly constrained numerical optimization. An error function that depends only on the analysis filter impulse response coefficients is minimized, subject to a set of quadratic equality constraints that involve both the analysis and synthesis filter coefficients. With this design framework, it is possible to design a wide variety of filter banks that have a number of desirable properties. The analysis and synthesis filters that result are FIR and of equal size. In addition, both paraunitary and nonparaunitary filter banks can be designed with this method. Unlike paraunitary filter banks, nonparaunitary filter banks are capable of performing analysis bank functions more general than band-splitting with flat passband filters.