Paraunitary Filter Bank Design using Derivative Constraints

In this paper two new algorithms are presented for designing finite impulse response (FIR) paraunitary (PU) filter banks. Each algorithm minimizes the mean square error between the desired response and the FIR PU approximation subject to constraints on either the derivative of the complex frequency response or the power response of individual channel filters. The derivative constraints are useful for shaping the response of a channel filter at particular frequencies of interest. An example illustrating the utility of derivative constraints is presented whereby a FIR PU approximation is derived for an ideal principal component filter bank (PCFB).