A parameterization approach to stable recursive digital filter design

Abstract

Digital filter design is to approximate a desired frequency response with a model of transfer functions that can actually be implemented. Being a very powerful and efficient model, recursive digital filters have been extensively used in digital filter design, in which stability has been considered as one of the crucial issues. Classically, there are two different approaches to stable recursive digital filter design. In the first approach, the design problem is solved using linear/nonlinear optimization techniques with a set of linear stability constraints which ensure that the generated filter is stable. These linear stability constraints are just sufficient in the sense that they only define a sub-space of the stable transfer functions. The second approach, called indirect approach, is based on model reduction techniques such as balanced model reduction. The basic idea is to design an FIR filter of very high order first. An IIR filter of lower order is then obtained using model reduction techniques. It should be pointed out that there are two independent approximation procedures involved in this approach. In order to achieve a satisfactory performance, a very high order FIR filter has to be used.