Stability constraints used in computer-aided design of recursive digital filters

Some recent papers on digital filter design have been concerned with the use of unconstrained minimization techniques, such as the Fletcher-Powell algorithm, to optimize the design to a prescribed frequency domain description. This paper looks, in detail, into the use of two variable substitution methods to bound the poles and zeros of the filter for stability and minimum phase considerations. One of the methods is shown to be superior to the other. Extensions of the work are indicated for two-dimensional recursive filter design and more restrictive bounding on the filter configuration than would normally be considered.