Autoregression and cepstrum-domain filtering

The cepstrum coefficients of an ARMA process, which may easily be derived as functions of the z-plane poles and zeros, can be used to characterise and manipulate a spectrum. We show how to smooth the spectrum using only the ARMA coefficients and without having to find the poles, zeros or cepstrum. This can be used in the identification of signals whose autocorrelation functions decay over differing time scales. Examples are shown of where this technique may be used to identify sinusoids in coloured noise.