Some new results in the design of Mth-band FIR filters

In this paper, the design of Mth-band FIR filters via semidefinite programming (SDP) is investigated. Some of the frequency response properties of a general nonlinear-phase Mth-band filter are first examined, yielding a few constraints for the amplitude and phase responses of the Mth-band filter. An SDP-based optimization problem is formulated for the least-square and minimax design of Mth-band filters. Although the formulation is established for a nonlinear phase filter, the design result shows that an exactly linear phase can be obtained when the desired phase/delay characteristic is properly specified.