Optimal design of real and complex minimum phase digital FIR filters

We present a generalized optimal minimum phase digital FIR filter design algorithm that supports (1) arbitrary magnitude response specifications, (2) high coefficient accuracy, and (3) real and complex filters. 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 (1970). We extend the transform pair to the complex case and show that the algorithm gives arbitrary coefficient accuracy. We present design examples that exceed the coefficient accuracy of the optimal real minimum phase filters reported by Chen and Parks (1986) and reduce the length of the optimal complex linear phase filters designed by Karam and McClellan (1995).