Stabilizing Functions for Designing Minimax-Type Highpass Tunable Filters

A tunable digital system has the high flexibility to vary its frequency-domain properties in real time. A typical tunable digital system is the signal processing system called tunable filter (TF). In the process of digital filtering, a digital filter may need to change its frequency response on the fly. Such a requirement can be met by utilizing a digital filter that possesses frequency-response tunability. Tuning the frequency response in real time necessitates utilizing a TF. The most prominent feature of a TF is the instant variability of its frequency response. To get an instant variation, one just needs to change TF's coefficients. However, a TF faces the stability issue when its coefficients are renewed. The effective strategy to resolve this issue is to stabilize TF by converting the coefficients in TF's denominator into a special kind of functions such that the functions meet the stability requirement. This paper presents five such functions and employs such a function to design a tunable highpass filter with ensured stability. The simulation results demonstrate both the obtained stability and the accurate highpass response approximations.