A comparison of the existence of 'cross terms' in the Wigner distribution and the squared magnitude of the wavelet transform and the short-time Fourier transform

Time-frequency analysis using time-order representation and Wigner distribution

“…The various desirable properties of the WVD such as preservation of time and frequency support, infinite time and frequency resolutions, and more, make the WVD a useful tool for signal analysis [8][9]. The main drawback of this distribution is that it is quadratic and the method based on the WVD introduces the cross terms in the time-frequency domain making the transform space difficult to interpret [11]. The WVD of the sum of M signals…”

“…The cross terms can have significant amplitudes and they can corrupt the transform space. The analysis on cross-terms has revealed that the cross terms might have a peak value as high as twice that of the autocomponents, they lie at mid-time and mid-frequency of the auto-components, they are highly oscillatory and the frequency of oscillations increases with the increasing distance in time and frequency [10][11].…”

A new technique to reduce cross terms in the Wigner distribution

“…The various interesting properties of the WVD [2] such as preservation of time and frequency support, instantaneous frequency, group delay, etc., make the WVD useful tool for signal analysis. The main drawback of this method is that it is bilinear in nature, introducing the cross terms in the WVD domain, which make the transform difficult to interpret [7]. the WVD of the sum of n signals…”

Adaptive diffusion as a versatile tool for time-frequency and time-scale representations processing: a review

“…The Cohen class contains all the distributions verifying the following commutativity diagram [5]: (2) i.e., distributions that are covariant with respect to the application of the time-frequency shifts operator to the signal. These distributions can be written in the following parametric form [2], [5]: (3) where denotes the Wigner distribution (4) and stands for a simplified 2-D structure of the more general kernel in (1). Similarly, the affine class contains all the distributions that are covariant with respect to the affine operator of time shifts and scale changes [14], [15] (5)…”

“…In the area of signal analysis, one aims to preserve most of the attractive properties of the WD and also improve its readability. For example, the spectrogram and the scalogram are classical quasi-interference-free representations [3] of the Cohen and the affine classes, respectively, but both offer poor resolution. All this has prompted the development of specific task-oriented TFRs [4]- [7], as well as signal-dependent TFRs Manuscript received July 15, 2004; revised November 24, 2004.…”