Design and Stability Guarantee of Variable Center-Frequency Bandpass Filters

A variable digital filter has the tunability to freely alter its frequency-domain properties, and its applicability meets the need for rapid frequency-domain characteristic tuning. This paper describes a useful scheme for designing a bandpass digital filter and shows how to guarantee the filter's stability. The bandpass filter has a passband whose center-frequency (CF) is variable, while the width of its passband remains fixed. The CF of a passband is adjusted by a single parameter referred to as CF parameter. This implies that changing the CF parameter value is capable of varying the passband CF. This variable center-frequency (VCF) bandpass filter has a recursive transfer function, and all its coefficients are parameterized as the polynomials in the CF parameter. To get a stable VCF bandpass filter, the coefficients of the transfer function's denominator are mapped to other new parameters before carrying out the nonlinear-optimization design. This trick transforms the stability-constrained design problem (nonlinear optimization problem) into an unconstrained nonlinear optimization problem, and guarantees the stability of the attained VCF filter. This transformation-based methodology particularly works for variable filter designs because varying filter parameters may compromise the stability of the filter.