THE WIGNER DISTRIBUTION AS A TOOL FOR SPECTRAL ANALYSIS OF INSTATIONARY SIGNALS

Abstract

The description of non-stationary signals causes problems which are hard to solve with conventional methods for spectral analysis. Examples for rather instationary signals are starting cycles of machines, transients or measuring of flow speed. If the spectral content of a signal changes in time, the periodogram (spectrogram) does not give any possibility to connect the presence of certain frequencies properly to a certain point of time. Methods such as the Wigner-distribution (WD) that display the signal on a time-frequency plane are far better for this purpose. The WD may be interpreted as the power-density spectrum (PDS) of the signal, even though it is not strictly positive for all signals. An interesting property of the WD besides its high time and frequency resolution is, that the first moment of the WD with respect to the frequency is equal to the derivative of the phase, which is to say the instantaneous frequency of the signal. An algorithm to compute the WD in real-time was developed and implemented on a system of four digital signal processors. This system is used for the measurement of blood velocity by ultrasound.