Stability-guaranteed odd-order variable-bandwidth filters using stabilized odd-order transfer function

This paper describes a 2-stage tactic for achieving an odd-order variable-bandwidth (OO-VBW) filter with absolutely guaranteed stability. The design methodology aims to minimize the p-norm amplitude-response error while maintaining the OO-VBW-filter's stability. In order to tune OO-VBW filter's amplitude response, we utilize a kind of functions of the bandwidth (BW)-tuning parameter to express the filter's coefficients. Because those functions have changeable function values, the designed OO-VBW-filter's amplitude response possesses variability. Another important concern in this paper is the stability issue. When the filter coefficient values expressed as function values are changed, the OO-VBW filter that has feedback structures may become unstable. This necessitates that the OO-VBW-filter's stability must always be preserved during real-time tuning. In order to stabilize such an OO-VBW filter that has feedback structures, a coefficient-conversion (CC) algorithm is adopted, and it is incorporated into the 2-stage methodology for obtaining the OO-VBW filter. To illustrate both the stability and high approximation accuracy, the design of an OO-VBW bandpass filter is simulated. The simulation details verify that both stability and high accuracy can be successfully achieved.