A design method for IIR digital filters with variable stopband using semidefinite programming

Several application in digital signal processing demand variable digital filters with arbitrary variable frequency response. For example, in dynamic gravimetry, the main vibration noise is changed by kinds or size of measurement and spec of conveying means. In this case, if a part of main noise is changed, it is important that changing characteristics of filter at once. FIR digital filter are always stable. However, because FIR digital filter generally needs high order, the delay is increased and it is problem in high speed and high accuracy signal processing. Then this paper describes a design method for IIR digital filters with variable stopbands. Numerator filter coefficients are approximated by polynomials using a variable parameter. We solve its transfer function by semidefinite programming in the frequency domain. Finally, a design example is given to demonstrate the proposed techniques.