Parametrized Unity-Bounded Functions and Comparisons for Enhancing Tunable Filter Accuracy and Guaranteeing Stability

Tunable digital filters are required in a broad scope of information technology (IT) areas where a digital filter needs to refresh the frequency response in real time during signal processing operations. When it is necessary to refresh filter’s frequency response, the filter user can obtain the required frequency response on the fly by simply updating the filter coefficients. However, when a recursive filter is in operation, updating the filter coefficients risks filter’s stability. This is because the recursive tunable filter may lose stability when the coefficients are suddenly changed. To resolve this instability issue, this paper reveals a pair of parametrized unity-bounded (UB) functions which are needed for guaranteeing the stability. By utilizing the parametrized UB functions to express filter coefficients as the UB functions involving other new variables, those new variables are allowed to hold unfettered values without hurting the stability. This ensures that using the UB functions to express the original coefficients produces a definitely stable filter. This paper aims to reveal two parametrized UB functions featuring abundant varieties, and then investigates as well as compares their impacts on design performance. To clarify the process that exploits the parametrized UB functions to produce a tunable filter, this paper exemplifies the design of a band-pass filter having a tunable passband center frequency (PCF). Design simulations clearly confirm the ensured stability alongside the performance comparisons of the two parametrized UB functions.