Mean-sense behavior of filtered-X LMS algorithm in the presence of frequency mismatch

Narrowband active noise control (ANC) systems are promising in suppressing sinusoidal noises, especially the lower frequency portion generated by rotating machines. In real-life applications, when a non-acoustic sensor is used to acquire the synchronization signal from which the primary noise frequencies are identified, the frequencies of reference sinusoids generated by the cosine wave generator usually contain errors due to sensor aging, fatigue accumulation, etc. That is frequency mismatch (FM) may exist between the reference signal and the primary noise. This paper analyzes performance degradation of the typical filtered-X LMS (FXLMS)-based narrowband ANC system in the presence of FM by investigating convergence of the system in the mean sense. The obtained analytical results enrich our understanding of influence of the FM on system performance. Computer simulations are conducted to verify the analysis results.