In contrast, the magnitude of the Fourier transform (FT) of the signal may be considered as a representation with perfect spectral resolution but with no time information because the magnitude of the FT conveys frequency content but it fails to convey when, in time, different events occur in the signal.
One form of TFR (or TFD) can be formulated by the multiplicative comparison of a signal with itself, expanded in different directions about each point in time.
This formulation was first described by Eugene Wigner in 1932 in the context of quantum mechanics and, later, reformulated as a general TFR by Ville in 1948 to form what is now known as the Wigner–Ville distribution, as it was shown in [2] that Wigner's formula needed to use the analytic signal defined in Ville's paper to be useful as a representation and for a practical analysis.
Continuous wavelet transform analysis is very useful for identifying non-stationary signals in time series,[3] such as those related to climate[4] or landslides.
[5] The notions of time, frequency, and amplitude used to generate a TFR from a wavelet transform were originally developed intuitively.