Equiripple Design Of Real And Complex Filter Banks

A simple methodology is presented for mapping minimax-optimal, equiripple unconstrained filters such as those produced by the Parks-McClellan algorithm to design equiripple perfect-reconstruction filter banks. The method is applied both to the design of standard low- and high-pass filters for perfect reconstruction, and to the design of critically sampled complex filters. For the case of real filter-bank design, our method produces equiripple low- and high-pass filters optimizing standard minimax filter design criteria while meeting the constraints of perfect reconstruction. For the case of complex filter-bank design, our method generates a critically-sampled, envelop/phase representation of a resonating signal while allowing perfect reconstruction. The magnitude response of the complex filter is an equiripple approximation to an ideal positive frequency passband, and the phase response is an equiripple approximation of pure linear phase