DEVELOPMENT OF ENHANCED WIGNER–VILLE DISTRIBUTION FUNCTION

Development of an enhanced version of the Wigner–Ville distribution function (WDF) is reported in this paper. As a preliminary study, the original WDF is compared to two other time–frequency representation techniques: the short-time Fourier transform (STFT) and the wavelet transform. Comparison of the time–frequency representations of a highly transient signal obtained by the three techniques shows that the primary advantage of WDF over the other techniques is its superior time and frequency resolutions. This advantage is diminished in the smoothed WDF, which is used to reduce the oscillating and zero-crossing phenomena of the original WDF representation. The new version of WDF developed in this work actually improves the resolutions while minimising the oscillating and zero-crossing phenomena. This enhanced WDF is defined by the convolution integral of the original WDFs of the input to the system and the system impulse response function. Theoretical and practical aspects of the proposed enhanced WDF are discussed in comparison to those of the original and the smoothed WDFs. Advantages of the enhanced WDF are demonstrated by three distinct numerical examples.