ARMA digital lattice filter with white gaussian input

Abstract

AbstractThis paper presents a new synthesis method for ARMA digital lattice filters. These filters are obtained by a fast algorithm for estimation of ARMA parameters. Some fast algorithms for such estimation have already been proposed in which approximation models are derived using the input and output signals and can be applied to arbitrary input signals. Among these methods, the Mullis‐Roberts algorithm estimates the parameters by the autocorrelation coefficients and impulse response of observed signals. The method is similar to the parameter estimation using white Gaussian process for the input signals. Though the Mullin‐Roberts algorithm can estimate the parameters with less calculation cost than other algorithms, it is not suitable for designing different orders of the AR and MA parts. The fast algorithm proposed in this paper estimates the parameters with the same calculation cost as in the Mullis‐Roberts algorithm when the input signal is restricted to a white Gaussian process and obtains the ARMA parameters as the AR and MA orders are independently increased.The new ARMA lattice filter is synthesized by three prediction errors defined in the new algorithm and consists of a simpler structure than the usual filters of this type. By processing time series signals using the algorithm and the lattice filter, we show the feasibility of estimating the minimum realization for an ARMA model.