Type II, III, and IV Linear-Phase FIR Structures Based on Cardinal Filters

Novel structures of type II, III, and IV linear-phase finite impulse response (FIR) systems are proposed. It is constituted of a linear combination of basic sub-filters, called cardinal filters, with weighting coefficients equal to the derivatives of the system amplitude response at a prescribed frequency. Since the cardinal filters can be synthesized via recursive closed-form expressions, regardless of the desired system amplitude response, the proposed structure provides a universal design for arbitrary derivative-constrained linear-phase FIR filters. Design examples of maximally flat filters show that further improvement by combining derivative constraints with the least squared error optimization technique can be obtained.