Constrained FIR Filter Design by the Method of Vector Space Projections

A new technique for designing linear and arbitraryphase finite-impulse response (FIR) filters with various types of constraints is proposed. The approach is based on the method of vector space projections. We describe the constraint sets and their associated projections that capture the properties of the desired filters. In filter design, as in many other engineering problems, one is primarily interested in meeting design constraints, i.e., finding a feasible solution, not necessarily an optimum one. Vector space projection methods are well-suited for this purpose. We furnish numerous examples of FIR filter design by vector space projections, including the important and difficult arbitrary phase/magnitude problem. Examples that demonstrate the advantages and flexibility of this method over other known methods are furnished.