Fast analytical design algorithms for FIR notch filters

Fast analytical design procedures for finite impulse response (FIR) maximally flat (MF) and optimal equiripple (ER) notch filters are introduced. The closed form solution provides recursive computation of the impulse response coefficients of the filter. The ER FIR filters are optimal in the Chebyshev sense. The relation between the MF and ER notch filter is presented in order to emphasize the superior performance of the ER narrow-band filters over their MF counterparts. The discrete nature of the notch frequency in both filter types is emphasized. Four design examples are included to demonstrate the efficiency of the presented approach.