A new detecting method for periodic weak signals based on fractional order stopping oscillation system

Abstract

In this paper, a new detecting method for weak periodic signals with unknown periods and unknown forms, the so-called fractional stopping oscillation method, is presented. This new detecting method, which is based on the research of some dissipative system of single degree of freedom, is sensitive to periodic signal—even with unknown period and unknown form—and insensitive to noise. Compared with the known chaotic detections in which a built-in signal must be pre-set with the same frequency and the same form as the detected periodic signal, the fractional stopping oscillation method can not only be used even at lower SNR than chaotic detection, but also has some other notable advantages as follows: (1) it need not get the period and the form of detected signal before hand or pre-estimate them; (2) it need not pre-calculate the chaotic threshold value; (3) the existence of periodic signal in system input can be reliably and quantitatively judged by volatility index function, designed in this paper, for stopping oscillation method; (4) a more sensitive detection method can be achieved by the fractionalization of the detection system, especially, the detection threshold can reach -182 dB when the background noise is colored Gaussian noise.