The Necessity and Strategy for Stability-Constrained Recursive Variable Digital Filters

Digital filters are the basic signal processing systems required in widespread fields such as speech processing, image processing, and digital communications. The digital filters possessing tunable frequency properties are named as variable filters. Such filters can be regarded as reconfigurable signal processing systems, which are able to perform online characteristic tuning. When a new characteristic is needed, one can change the coefficients in real time to achieve the required updates. In dealing with variable recursive filters, stability-guarantee is a central and unavoidable issue because the change of the filter's coefficients may incur instability. Basically, designing a variable recursive filter necessitates nonlinear programming, and such a design formulation without stability constraints is most likely to produce an unstable recursive filter. Up to the present, the author has proposed an effective strategy to ensure the stability, which is based on parameter-transformations. This paper aims to reconfirm the rationale for the stability-constrained design formulation via computer simulations. Computer simulations are performed to verify that it is most unlikely to get a stable variable recursive filter if the design is carried out without imposing any stability constraints. This indicates that the results from computer simulations are highly consistent with the stability theory, and the simulation results also reconfirm the necessity of stability-constrained strategy for getting a stability-guaranteed variable filter in recursive structure.