Statistical design of nearly linear-phase ARMA filters

This paper proposes a method for statistical design of approximately linear-phase autoregressive-moving average (ARMA) digital filters. The key idea of our method is that a time-delayed ARMA filter is used to approximate a high-order FIR filter that meets the prescribed amplitude spectrum sufficiently well. Computer simulations show that the resulting ARMA low-pass, bandpass, and high-pass filters not only meet the prescribed amplitude response specification well, but yield excellent linear phase with much lower order and smaller delay compared to the associated FIR filters.