Iterative algorithm for the design of optimal FIR analysis/synthesis filters for overdecimated filter banks

Recently, much attention has been given to the design of signal-adapted filter banks, in which the filter banks are designed to optimize a particular objective function, i.e. coding gain or a multiresolution criterion, for a particular class of input signals. If we restrict the analysis/synthesis filters to satisfy an orthonormality or biorthogonality condition, but put no restrictions on filter orders, then often times it is known how to choose the filters optimally for the objectives mentioned above. However, such filters are often unrealizable infinite order filters. In this paper, we consider the design of optimal analysis/synthesis filters in which the only restriction is that they must be finite impulse response (FIR) filters. We focus here on minimizing the mean squared reconstruction error for overdecimated filter banks. An iterative method to alternately design the analysis and synthesis banks is presented in which the error is monotonic nonincreasing for each iteration. Simulation results provided show the merit of the proposed algorithm.