Variable-recursive-filter design with theoretical stability-guarantee

The most important issue in designing a variable-recursive-filter is to guarantee its stability. This is because the stability may be destroyed when the denominator-coefficients of a variable-recursive-filter are changed on-line. Once such an instability occurs, all the filtering operations become meaningless. To solve the instability problem, this paper proposes a novel parameter-transformation method for transforming the original denominator-coefficients of a variable-recursive-filter into a set of new parameters, which can take arbitrary values while theoretically guaranteeing the stability of the designed variable-recursive-filter. After transforming the original denominator-coefficients into a set of new parameters, we also present a two-stage scheme for designing a variable-recursive-filter whose stability is always guaranteed. An example is given for demonstrating the theoretical stability-guarantee and the high-accuracy design.