The Quadratic TFR Based on Wavelet and the Wavelet Spectral Correlation Function

The wide sense time-frequency representation based on wavelet was recently proposed, which included the wavelet spectral correlation function (WSCF), wavelet ambiguity function (WAF) and scalograms. The WSC theory was expected to perform effectively in the signal processing involving 1/f noise. Yet despite their apparent importance, the lack of theoretic analysis has, at least until recently, strongly limited their popularity. In this paper, we review TF representation based on wavelet, and compare their substantial characteristic with Cohen´s class, such as real value, time-shift and frequency-shift invariability, time-frequency fringe quality, time retractility and bilinear-added principle. Specifically, via several wavelet mother functions, we develop the WSCF of mono-frequency, dual-frequency signal and analyzed their characteristics. Researches show that compared with Cohen´s class the scalograms is rough for energy distribution in the TF domain, but in spectral correlation domain, WSCF is an effective technique in the signal processing