Problem dimensionality reduction in design of optimal IIR filters

A typical design of a digital IIR filter that is optimal in the sense of the weighted least squares criterion is performed by using a numerical optimisation procedure capable of searching for local minima of highly non-linear functions of vector arguments. Normally such a search is carried out inside a multidimensional space of filter parameters or, if constraints are imposed, inside a subset of the space. The dimensionality of the space is therefore equal to the number of tuneable parameters of the filter. In this article we show that this approach to designing WLS optimal filters can be effectively changed in such a way that the number of dimensions of the search space is significantly smaller than the number of tuneable coefficients. The proposed modification not only reduces the dimensionality of the filter design problem. It can also improve robustness of the design procedure and reduce errors by delivering more accurate approximations of the local minima.