Normal-form state-space realization of single frequency IIR notch filters and its application to adaptive notch filters

Abstract

This paper deals with the normal-form state-space realization of second-order IIR notch filters. A method for approximately realizing a normal-form state-space model from the transfer function of a single frequency notch filter is developed. The pole and zero sensitivity of the normal-form state-space model is then analyzed, and it is shown that the normal-form state-space notch filter has minimum pole sensitivity. In addition, a single frequency adaptive notch filter is constructed by applying the normal-form state-space model. In this connection, a method for generating gradients required to adjust the coefficients of a normal-form state-space adaptive notch filter is explored. A numerical example is presented to demonstrate the validity and effectiveness of the proposed adaptive notch filter.