On the Influence of Low Frequency Components in the Weight Behaviour of the LMS Algorithm

Abstract

The Least Mean Square (LMS) algorithm is a very important tool in the estimation and filtering of biomedical signals. Amongst these signals are the periodic and quasiperiodic. For example, the LMS algorithm was used to estimate the coefficients of the Fourier series at a given frequency or even in a spectral analysis. In this paper we study the behavior of the weights of the LMS algorithm when the signal to be estimated acts at very low frequencies. We prove theoretically that lower frequency noise affects the estimation of the weights at higher frequencies. We carried out simulations and showed that experimental findings are in agreement with the theoretical results. Moreover, we exemplify the problem with electrocardiogram signals (ECG).