A modified algorithm for constrained least square design of multiband FIR filters without specified transition bands

In a previous paper, we described a constrained least square approach to FIR filter design that does not use “don’t care” regions. In that paper, we described a simple algorithm for the design of lowpass filters according to that approach. In this correspondence, we describe a modification of that algorithm that makes it converge for many multiband filter designs. Although no proof of convergence is given, the modified algorithm remains simple and converges rapidly in many cases. In this approach, the user supplies a lower and upper bound constraint that is exactly satisfied by the local minima and maxima of the frequency response amplitude. Yet, the constraints can be made as tight as desired—the transition band automatically adjusts (widens) to accommodate the constraints.