A derivation of ARMA coefficients using a digital lattice filter

Abstract

AbstractA shaping filter for a stationary stochastic process can be viewed as the open‐circuit voltage transfer function of a resistance‐terminated reactance 2‐port. Further, Levinson's theory regarding spectral analysis (AR analysis) based on the autoregression model of a stationary stochastic process is equivalent to Ricca's theorem in network theory. Using these facts, from the digital lattice filter which is developed from the AR analysis, we can determine the impulse response of the inverse of the reflection coefficient at the output of the resistance‐terminated reactance 2‐port corresponding to the stationary stochastic process which is analyzed. In this paper we present a technique in which an AR analysis is performed on an autoregressive, moving average process (ARMA process), the impulse response is approximated by a rational function as described above and, by determining the open‐circuit voltage transfer function, the ARMA coefficients are derived. Also, we present two different regression methods for determining the rational function approximations to the impulse response. In general, there is no guarantee that the rational function approximations determined by these methods will be physically realizable transfer functions, but it has been verified by modeling tests that, for an ARMA process of finite degree, by this technique we can determine ARMA coefficients which are better than those obtained by AR analysis to approximate the power spectrum.