Behavior of the adaptive algorithm for non-stationary noise signal: Difference between theoretical formulation and the practical implementation

The use of filtered reference LMS algorithms in active noise control applications was discussed. The difference between the theoretical formulation and practical implementation of the filtered reference LMS algorithm for artificially modulated signals was also discussed. It was observed that if the noise signal was white noise, behaviors were similar in both the theoretical and the practical conditions. It was found that if the noise signals were colored with a low pass filter, the upper bound of the convergence coefficients for stability was limited to a lower value than the theoretical bound.