Chirp signal detection using the Duffing oscillator

The chaotic oscillator has become an important tool in the analysis of harmonic signals with low signal to noise ratio. On the other hand, traditionally, frequency modulated (FM) signals have always been studied through conventional techniques of time-frequency analysis. Recently, the Duffing oscillator has shown to be a powerful tool to detect frequencies for periodic signals because of its chaotic properties. It is for this reason that this paper presents a chirp signal analysis in the presence of noise using a Duffing oscillator. The oscillator's chaotic characteristic provides information on how the frequency changes in a signal therefore, for the chirp case it is also convenient to apply time-frequency techniques to obtain the frequency shift for such signals. Here, it is found that is possible to use the Duffing oscillator for the analysis of chirp signals with -15 dB of SNR. The time-frequency techniques used in this paper are the Short Time Fourier Transform, the Wigner-Ville Distribution, its corresponding Choi-Williams and end with a proposed array of Duffing oscillators.

1. Introduction

The study on the detection of weak signals, i.e. signal immersed in an environment with high levels of noise has been of great interest in different scientific fields such as Communications, Structure Health, radar signals, Geology (particularly in the recognition of earthquakes), and interesting enough, in the medical field when measuring biological signals. Recently, many current research studies have focused on the analysis of chaotic oscillators as a tool for the detection of signals with a very low signal to noise ratio (SNR). The results obtained have been very good for cases when constant frequency signals are involved and the chaotic oscillator employed is the Duffing oscillator [5], [8], [12], [13] and [16].