Abstract
Although time–frequency analysis of signals had its origin almost 50 years ago, there has been major development of the time–frequency distributions approach in the last two decades. The basic idea of the method is to develop a joint function of time and frequency, known as a time–frequency distribution, that can describe the energy density of a signal simultaneously in both time and frequency. In principle, the time–frequency distributions characterize phenomena in a two-dimensional time–frequency plane. Basically, there are two kinds of time–frequency representations. One is the quadratic method covering the time–frequency distributions, and the other is the linear approach including the Gabor transform, the Zak transform, and the wavelet transform analysis.
As long as a branch of knowledge offers an abundance of problems, it is full of vitality.
David Hilbert
Besides linear time-frequency representations like the short-time Fourier transform, the Gabor transform, and the wavelet transform, an important contribution to this development has undoubtedly been the Wigner distribution (WD) which holds an exceptional position within the field of bilinear/quadratic time-frequency representations.
W. Mecklenbräuker and F. Hlawatsch
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Debnath, L., Shah, F.A. (2015). The Wigner–Ville Distribution and Time–Frequency Signal Analysis. In: Wavelet Transforms and Their Applications. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8418-1_5
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DOI: https://doi.org/10.1007/978-0-8176-8418-1_5
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