A reducing the number of polynomial coefficients method for variable notches FIR filters

In this paper, we propose a design method for finite impulse response (FIR) variable digital filters (VDFs) obtaining quasi-equiripple characteristic even if notch frequencies change. The change in filter coefficients, which depends on the change in notch frequencies, is approximated by a polynomial using variable parameters. In this method, the minimization problem for the polynomial coefficients with variable notches is formulated as semidefinite programming (SDP) in the frequency domain. However, the number of polynomial coefficients increases when variable parameters are plural number. Therefore, we also propose a method for reducing the number of polynomial coefficients. The usefulness of the proposed VDF is demonstrated through examples.