Designing N-band biorthogonal FIR systems given several of the analysis and synthesis filters

The problem of designing an N-band biorthogonal FIR analysis/synthesis system, given K of its analysis and synthesis filters, is addressed in this paper. A necessary and sufficient condition on the K filters, that guides their selection, is derived. The solution set is completely parameterized via ladder-type structures that guarantee the perfect reconstruction property under both coefficient quantization and roundoff errors. Both nonlinear- and linear-phase systems are considered. A design example is included to illustrate the theory.