Design of optimal minimum-phase digital FIR filters using discrete Hilbert transforms

We present a robust noniterative algorithm to design optimal minimum-phase digital FIR filters with real or complex coefficients. We derive: (1) the discrete Hilbert transform (DHT) of the complex cepstrum of a causal complex minimum-phase sequence and (2) the minimum fast Fourier transform length for computing the DHT to achieve a desired coefficient accuracy.