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It seems there are several papers from the seventies but backtracking from the references gets quickly difficult. Who calculated for the first time a time-frequency representation of a signal?

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    $\begingroup$ The Wigner Distribution was already used in the 1930s in the context of quantum mechanics. $\endgroup$
    – Matt L.
    Aug 22, 2014 at 12:34
  • $\begingroup$ In modern form, perhaps circa 1800 by Gauss, Fourier and Lagrange (et.al.). But, according to wikipedia, the ancient Babylonians used it for astronomical calculations: en.wikipedia.org/wiki/Fourier_analysis#History $\endgroup$
    – hotpaw2
    Aug 22, 2014 at 17:39
  • $\begingroup$ @hotpaw2: Right, but isn't this about 'pure' Fourier analysis instead of a combined time-frequency analysis approach such as Wigner distribution and Gabor transform etc.? $\endgroup$
    – Matt L.
    Aug 22, 2014 at 19:47

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According to the preface of Foundations of Time-Frequency Analysis, a rough timeline is as follows:

  • 1930 - Early development of quantum mechanics by H. Weyl, E.Wigner, and J. von Neumann.
  • 1946 - Theoretical foundation of information theory and signal analysis by D. Gabor (cf. "Theory of communication").
  • 1980 - Time-frequency analysis established as an independent mathematical field (apart from engineering) by Guido Janssen.
  • 1990 - Development of wavelet theory. Overview of the mutual influence given in "The wavelet transform, time-frequency localization and signal analysis" by Ingrid Daubechies.
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