A control theory approach to the stability and transient analysis of the filtered-x LMS adaptive notch filter

A method is presented for analyzing the stability and transient response of the filtered-x LMS adaptive notch filter by formulating the problem in the complex weight domain and applying standard control theory. Examples are given for pure delay and second-order low-pass cancellation path transfer functions. The method is also extended to the multichannel case, where the eigenvalues of the equivalent open-loop transfer function matrix characterize the behavior.>