Designing FIR filter with variable stopbands

In this paper, we define filters capable of changing frequency response as variable digital filters (VDFs). In the previous VDF having changed a piecewise large attenuation characteristic in the stopband, it is difficult to decrease the filter degree to two or more, changing noises. We propose a transfer function of FIR filters with changing some large attenuations in the stopband by using spectral parameters and its design method. The number of spectrum parameters used here uses the number of changing stopbands. In this method, the minimization problems are formulated as semidefinite programming (SDP) in the frequency domain. Moreover, we present that the proposed VDF can be implemented using Farrow structure. Finally, we confirm the effectiveness of this method through numerical examples.