Wigner-Ville analysis of non-stationary random signals. (with application to turbulent microstructure signals)

The Wigner-Ville Distribution (WVD) has recently been shown to be a valuable tool for time-Frequency Signal Analysis. Its first order moments yield directly the instantaneous frequency of the Signal. The problem of applying a window to the WVD is shown to be the same as that occurring when one uses the Fourier Transform. The choice of any classical window does not affect the estimation of the instantaneous frequency fi(t) in both deterministic and random cases. It is shown that the WVD estimator of the "evolutive spectrum" is unbiased in both time and frequency. Accuracy and statistical stability of the method are discussed. Its application to the analysis of microstructure temperature gradient signals shows that the WVD exhibits more information about the turbulence effect than the Short Time Fourier Transform.