Editing Time–frequency analysis (section)

==History==
{{see also|History of wavelets}}

Early work in time–frequency analysis can be seen in the [[Haar wavelet]]s (1909) of [[Alfréd Haar]], though these were not significantly applied to signal processing. More substantial work was undertaken by [[Dennis Gabor]], such as [[Gabor atom]]s (1947), an early form of [[wavelet]]s, and the [[Gabor transform]], a modified [[short-time Fourier transform]]. The [[Wigner–Ville distribution]] (Ville 1948, in a signal processing context) was another foundational step.

Particularly in the 1930s and 1940s, early time–frequency analysis developed in concert with [[quantum mechanics]] (Wigner developed the Wigner–Ville distribution in 1932 in quantum mechanics, and Gabor was influenced by quantum mechanics – see [[Gabor atom]]); this is reflected in the shared mathematics of the position-momentum plane and the time–frequency plane – as in the [[Heisenberg uncertainty principle]] (quantum mechanics) and the [[Gabor limit]] (time–frequency analysis), ultimately both reflecting a [[Symplectic geometry|symplectic]] structure.

An early practical motivation for time–frequency analysis was the development of radar – see [[ambiguity function]].