Uniform FIR filterbank optimization with group delay specifications

We characterize the delay properties of uniformly modulated finite impulse response (FIR) filterbanks. Conditions on the permissable delay are developed for this class of filterbanks when the perfect reconstruction condition is relaxed. Accurate linear approximations for the phase and the group delay of the total filterbank are derived. These approximations allow linear phase or group delay constraints to be introduced in the filter optimization problem. A tractable quadratic optimization problem for the design of optimal analysis and synthesis filter prototypes is proposed. The problem involves the minimization of the aliasing distortion while constraining group delay and amplitude distortion. Thus, a new algorithm is presented to solve this optimization problem for the analysis and synthesis filterbanks simultaneously. Numerical examples are presented that confirm the theoretical results and verify that the approximations used are highly accurate.