Magnitude squared design of recursive filters with the chebyshev norm using a constrained rational Remez algorithm

We describe a Remez type exchange algorithm for the design of stable recursive filters for which the Chebyshev norm of H(ω) - F(ω) is minimized, where H(ω) and F(ω) are the realized and desired magnitude squared frequency responses. The number of poles and zeros can be chosen arbitrarily and the zeros do not have to lie on the unit circle. The algorithm allows us to design filters with non-conventional frequency responses with arbitrary weighting functions. It also gives optimal minimum phase FIR filters and Elliptic recursive filters as special cases. We discuss three main difficulties in the use of the Remez algorithm for recursive filter design and give ways to overcome them.