Variable Bandpass Filters with Full-Band Tunability and Absolutely Guaranteed Stability
Tian–Bo Deng · 2023
Variable digital filters are reconfigurable signal processing systems that possess tunable frequency responses. Therefore, a variable digital filter can carry out real-time online tuning during filtering operations. To produce a new response in a timely manner, the transfer-function's coefficients of a variable filter must be the functions of the parameter that is adopted for tuning the filter's response. In this way, the coefficients are changeable. This paper considers designing a variable bandpass filter with a full-band tunable center-frequency (CF). Since the CF can be changed by using the CF parameter, one can represent the filter coefficients as the functions of the CF parameter. Another stiff problem that needs to be carefully solved is the stability issue. The reason is that updating the filter coefficients during online tuning may incur instability. This paper deals with this stability issue by locating the filter's coefficients inside the stability triangle through parameter transformations. To this end, we transform the denominator coefficients into other unconstrained parameters that can take any values without causing instability. After the transformations, a nonlinear optimizer can be used for optimizing the new parameters. A set of fixed-coefficient bandpass filters with full-band tunable CFs are designed for illustrating the achieved stability guarantee together with the achieved considerably accurate approximations.