Analysis of an LMS adaptive feedforward controller for periodic disturbance rejection: Non-wiener solutions for the LMS algorithm with a noisy reference-revisited

LMS adaptive cancellation has been found to be effective in various applications of active noise control of periodic disturbances. A deterministic periodic waveform can be used for the reference when the period of the disturbance is known a priori. However, the algorithm behavior is determined by so-called Non-Wiener solutions. This paper presents a new vector subspace model for simplifying the analysis of the Non-Wiener behavior. The LMS weights are modelled as a deterministic time-varying mean plus a zero-mean fluctuating part. Each weight component is analyzed separately with the subspace model.