The Wigner Distribution in the Doppler Sonography

TLDR: In this article, the authors present a method for finding a time window for which the signal is more or less stationary in a Doppler sonography image, where the time window h(t) is chosen to obtain short segments of the signal without substantial changes of parameters.

Abstract: In the field of Doppler sonography one has to carry out some spectrum analysis generally. Today the Fourier analysis is the most used method. The spectrogram S(ω,t) is currently the standard method for the investigation of time-varying signals s(t): $$ S(\omega ,t) = \int {s(\tau )} h(\tau - t){e^{ - j\omega \tau }}d{\tau ^2} $$ (1) with the time window h(t). This window is chosen to obtain short segments of the signal without substantial changes of parameters. If we can obtain such segments the spectrogram gives a good time-frequency representation of the signal energy. However, there exist a large variety of signals whose spectra are changing so rapidly that finding a time window for which the signal is more or less stationary is very difficult. Additional to this problem the instantaneous spectra of the signal at distinct times are required in some cases. In the spectrogram the time window can not be shorted infinitly to solve the mentioned problems.