Complexity Comparison of Linear-Phase Mth-Band and General FIR Filters

Linear-phase Mth-band finite-length impulse response (FIR) filters are characterized by every Mth impulse response coefficient being equal to zero, except for the middle tap. This leads to a realization with few multiplications. However, other properties include that the passband ripple is bounded by the stopband ripple and that the transition band is symmetric around pi/M rad. Depending on the filter specifications this may sometimes lead to an overly constrained filter design. In this work we investigate the trade-off between Mth-band and general linear-phase FIR filters. The results are bounds on the filter specification for when the linear-phase Mth-band or general FIR filter is advantageous to use.