Unsupervised detection and parameter estimation of multi-component sinusoidal signals in noise

Abstract

Detection and parameter estimation of multi-component sinusoidal signals in noise is an important problem which finds its application in diverse areas. Conventional DFT-based techniques experience difficulties in detecting a weak peak in the presence of other strong peaks and high noise levels. In this paper, we present a simple recursive scheme which overcomes these difficulties. Specifically, we compute the ratio between the maximum and median values of the DFT magnitudes. If the ratio exceeds a certain threshold, a sinusoidal component is detected, estimated, and subsequently removed. This procedure is repeated until no more peaks are found. Our technique is automated in the sense that once a threshold is selected, the algorithm operates in an unsupervised fashion. Examples are provided to illustrate the effectiveness of the proposed algorithm.