Weighted least-squares design of variable recursive digital filters with guaranteed stability

The stability guarantee is the most important issue in designing variable infinite-impulse-response (IIR) digital filters. This paper presents a new variable substitution method for transforming the denominator coefficients of a variable-IIR-filter into another set of variables such that arbitrary values of the new variables can guarantee the stability of the resulting variable-IIR-filter. That is, the design problem subject to stability guarantee (constrained non-linear design problem) is converted into an unconstrained design problem. As a consequence, the resulting variable-IIR-filters are always guaranteed theoretically. A lowpass variable-IIR-filter design example is given to illustrate the effectiveness of the design formulation.