Multi-level IIR digital filters

A procedure for approximating a multiband response with piecewise-constant magnitude at arbitrary levels is described. The design is based on the use of a cascade of two-level IIR filters. Analytic results are presented for the design of two-level filters at levels and for obtaining equiripple or monotone response, similar to classical filter design. The location of the poles and zeros is derived. The general multiband design can be carried out using numerical procedures. The filter can be configured as a parallel connection of all-pass sections. A multiplicative complementary pair of causal, stable two-level filters using this structure is presented. Multilevel approximation using a cascade of these filters is described.