Coding gain optimized finite impulse response (FIR) Paraunitary (PU) filter banks

Abstract

Filter bank optimization for coding gain maximization for given input statistics has been well studied before. Principal Component Filter Banks (PCFB) have proven to be optimal whenever the minimization objective is a concave function of the subband variances produced by the filter bank. However PCFBs are known to exist for only three special classes of orthonormal filter banks(FBs): Any class of two channel FBs, the transform coder class and the unconstrained order subband coder class. This paper explores the design of FIR Paraunitary(PU) FBs for special case of uniform 3-band subband coder class, giving a detailed analysis of the design method. This method directly maximizes the coding gain. Results have been compared to the PCFB approximation algorithm by Peter Vouras and Trac D. Tran which uses complete parameterization of FIR PU FBs in terms of Givens rotation building blocks.