Bounding Adaptive Filter Poles Using Kharitonov's Theorem

A method of bounding the coefficients of ARMA filters is presented and shown to guarantee strict sense stability (poles remain inside the unit circle). The method is general and can be used to stabilize any filter which has a proper rational transfer function. Application of Kharitonov's theorem[1] with additional constraints[2] yields optimal coefficient bounds which can be computed off-line. The precomputed bounds are applied at run-time requiring either O(N) or O(N/sup 2/) arithmetic operations per iteration. In contrast to previous bounding approaches, this method applies to filters of arbitrary order. Also, poles can be restricted to fie within any specified radius of the z-plane origin. Significant improvements in convergence behavior and stability are noted.