Optimal design of real and complex minimum phase digital FIR filters

We present a generalized optimal minimum phase digital FIR lter design algorithm that supports (1) arbitrary magnitude response speci cations, (2) high coe cient accuracy, and (3) real and complex lters. The algorithm uses the Discrete Hilbert Transform relationship between the magnitude spectrum of a causal real sequence and its minimum phase delay phase spectrum given by Cizek. We extend the transform pair to the complex case. We show that the algorithm gives arbitrary coe cient accuracy. We present design examples that exceed the coe cient accuracy of the optimal real minimum phase lters reported by Chen and Parks and reduce the length of the optimal complex linear phase lters designed by Karam and McClellan.