A design method for complex coefficient FIR filters with variable stopband characteristics

In this paper, we propose a design method for complex coefficients FIR variable digital filter (VDF) with changeable multicomponent in the stopband. The proposed VDF has piecewise high attenuation in the stopband, and the VDF varies some characteristics in the stopband using variable parameters. The complex filter coefficients are composed polynomial expression using variable parameters to vary the filter characteristics. The proposed method, the minimization problem for the complex coefficients FIR VDF with changeable multicomponent are formulated as semidefinite programming (SDP) in the frequency domain. Finally, we demonstrate the effectiveness of the proposed method.