Performance analysis of an LMS based Fourier analyzer for sinusoidal signals with time-varying amplitude

The estimation of sinusoidal signals in additive noise finds many engineering applications. Examples are the estimation of harmonics in power systems and the pitch detection in musical transcription and so on. In this article, firstly, it is verified from numerical experiment that a least mean square (LMS) based Fourier analyzer for sinusoidal signals with time-varying amplitude can track each amplitude of cosine and sine signals much faster than the conventional LMS method. The frequency response of the algorithm in the steady state is derived in order to provide filtering insight of the adaptive algorithm in the steady state. Finally, performance analysis of the algorithm for sinusoidal signals with linearly decaying amplitude in noise is described by using the above frequency response, and it is verified that the analysis explains quite well for small step size parameters and the number of sinusoids.