Factorized all-pass IIR adaptive notch filters

A new family of IIR adaptive notch filters is presented. The family is based on a second-order factorization of the all-pass transfer function that forms the multiple notch filter. These realizations represent an extension of a previous ad-hoc scheme for adaptive notch filtering that avoids a high-order polynomial root finding in order to obtain the unknown frequencies of interest. An interesting aspect related to these novel algorithms is the fact that they introduce a different compromise between bias and SNR if compared with previous realizations available in the literature. Specifically, lower bias than in other approaches for low SNR can be achieved using the new realizations. This property is particularly attractive for multiple sinusoids estimation and tracking. In addition to the algorithm presentation, a discussion of the different properties and characteristics (stationary points, convergence) is included. Also, computer simulations are presented to illustrate the expected performance of the proposed adaptive filters.