A novel design technique of filterbank systems

We present a novel design technique for the cosine-modulated FIR orthogonal filterbank systems (OFBS). Given an initial FIR analysis prototype filter, if it satisfies a condition, then we can design the synthesis prototype filter such that the whole filterbank system has a perfect reconstruction property. This filterbank system is called the biorthogonal filterbank system in the sense that the analysis and synthesis prototype filters are not the same. To design a filterbank system such that the analysis and synthesis prototype filters are the same or related as in the traditional cosine modulated filterbank systems, we average the analysis and synthesis prototype filters for the biorthogonal filterbank system, and then use it as the new initial analysis prototype filter. The corresponding new synthesis prototype filter is also designed via the design technique of the biorthogonal filterbank systems. The algorithm is always convergent at a rate determined by a_m=¼(√(a_m-1)+1/√(a_m-1 ))² converging to 1 and, consequently, the analysis prototype filter converges to the synthesis filter monotonically