Adaptive Normal-Form State-Space Notch Filters

This paper explores novel adaptive state-space notch filters with novel update laws by applying the normal-form state-space realization of a single frequency second-order IIR notch filter. An adaptive iterative algorithm is obtained by employing a gradient descent method for minimizing the mean-squared output error of an adaptive notch filter. An alternative adaptive iterative algorithm is found to be a simplified form of the above technique. Moreover, the step-size bound characterized by the gradient of the mean update term is deduced in each case. It is noted that the normal-form state-space realization has minimum pole sensitivity. A numerical example is presented to demonstrate the validity and effectiveness of the proposed adaptive state-space notch filters.