An Autocorrelation-Based r-Stability Condition With Application in the Design of IIR Filters

Ensuring the stability of an infinite impulse response (IIR) digital filter is a major problem in the design and implementation of the filter. This letter derives for the IIR filter a new necessary and sufficient
r
-stability condition that is formulated in terms of the autocorrelation (AC) coefficients of the impulse responses of the second-order denominator factors of the filter. Since the magnitude square response of a filter can also be formulated as a function of its AC coefficients, it is convenient to incorporate the new
r
-stability condition into the magnitude response design of the
r
-stable IIR filter. A minimax design algorithm for IIR filters with a prescribed maximum pole radius is presented. Design examples are provided to illustrate the usefulness of the proposed AC-based
r
-stability condition in stable IIR filter design.