Generalised strategy for stabilising minimax-type variable bandpass filter

Abstract

ABSTRACT This paper first develops a novel transformation-based strategy for guaranteeing the stability of recursive-type variable digital filters, and then presents a new type of functions called less-than-unity (LTU) functions required in performing stability-guaranteed parameter transformations (LTU transformations). The LTU transformations can be viewed as the generalised existing one. Based on the LTU transformations, a recursive bandpass filter with variable passband-width (PBW) is attained using the minimax criterion so that the stability is ensured. The recursive bandpass filter has continuously PBW and fixed passband centre frequency. To meet the stability condition of the recursive variable PBW bandpass filter (variable-PBW filter), the LTU parameter transformations are incorporated into the minimisation of the maximum amplitude-response error. It can be proved that incorporating the LTU transformations into the design process definitely produces a recursive variable-PBW filter whose stability is absolutely guaranteed. For verifying the ensured stability and demonstrating the high design accuracy, detailed computer simulations are included. The illustrative example verifies that the obtained variable-PBW filter not only has definitely ensured stability, but also its approximation accuracy is extremely high.