Abstract
For tonal noise generated by periodic noise sources like rotating machines, the so-called anti-noise by a set of adaptive weights is used to cancel the noise. In this paper, we consider a complex LMS algorithm that can be used to train a set of adaptive weights to counter an arbitrary number of periodic noise sources. The proposed method is based on the eigen decomposition of the correlation matrix of the input vector whose elements are complex sinusoids. A necessary and sufficient condition on the step size for the LMS algorithm to converge is given. Also, an expression of the excess mean square error is derived when the observation noise is present.
