Stability of the linear prediction filter: a set theoretic approach

The authors investigate the application of set-theoretic estimation methods to the design of linear-predictive-coding (LPC) digital filters. The constraints involved in the design are represented by sets in an abstract space. Any member of their intersection satisfies all the design specifications and is called feasible. Two sets are considered: the set of stable filters and the set of filters which minimize the mean-square prediction error in an environment where the statistics of the observed data are unknown. These two sets are described analytically and the problem of obtaining a feasible LPC filter is addressed. Experimental results are also presented