A Study on Least Mean p-th Adaptive Notch Filter

Abstract

In this paper we propose a least mean p-th adaptive notch filter that has a cost function of E[e^p(n)], where e(n) is the estimation error. The structure of the adaptive filter is a tandem connection of the second-order adaptive notch filter with an allpass filter. In general, the bandwidth of the notch filter is preferable to be extremely small for the theoretical and practical viewpoint. However, the convergence speed of the weight becomes slow if the bandwidth is reduced. The transfer function of the notch filter has a following special characteristic, that is zero in the center frequency and unity in other frequency. The equivalent broad bandwidth can be obtained when the cost function is chosen as E[e^p(n)]. The higher convergence speed and the excellent stationary performance are obtained by the use of combination of E[e^p(n)]. Finally, the convergence performance of the estimation accuracy is verified by the computer simulation.