Designing FIR perfect reconstruction systems given several of the analysis and synthesis filters

This paper deals with the problem of designing an N-band maximally-decimated FIR analysis/synthesis system with the perfect-reconstruction property, when K of the filters in both the analysis and synthesis banks are selected beforehand. An algorithm for computing the N-K unknown analysis and synthesis filters is given and the solution set is completely parametrized. The parametrization leads to a ladder-type realization of the system, whose robustness in coefficient quantization and roundoff-error effects has been verified in the past. The linear-phase case is also discussed and conditions that the given synthesis filters must satisfy are stated. An example is provided to illustrate the theory.