Design of FIR Paraunitary Approximations to Principal Component Filter Banks

In this paper, we present two new algorithms for designing finite impulse response (FIR) paraunitary (PU) filter banks that are optimal approximations to ideal principal component filter banks (PCFBs). The first algorithm is optimal in the sense that it minimizes the mean square error between the desired response and the approximation. The second algorithm is optimal in the sense that it minimizes the maximum error. Both algorithms utilize a complete parameterization of FIR PU filter banks in terms of Givens rotation building blocks, and jointly optimize all the filters in the filter bank.