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  "body": "\n## Summary\n\nTime–frequency analysis studies functions and signals through representations that depend on time and frequency together.\nThe [[Fourier transform|DPVM34ADZV]] shows which frequencies occur in a signal but not when; time–frequency representations try to show both.\nIts main tools are the [[short-time Fourier transform|3DHNP5NEWH]], [[Gabor frames|M9WHY8E2PM]], the [[Wigner distribution|FCHW5QGG5V]] and the [[ambiguity function|CDVA7EJSSD]], and it is close to [[wavelet|4PZ35C0GV3]] analysis.\nThe [[uncertainty principle|S1FB2K14NV]] limits how sharply a function can be located in time and in frequency at once.\n\n## Explanations\n\n### L1 human\n\nA musical score is a time–frequency picture: time runs from left to right, and the height of each note gives its pitch.\nA recording is just a pressure wave in time, and its Fourier transform is a list of pitches with no times.\nTime–frequency analysis builds pictures like the score from the recording.\nA common method looks at the signal through a short window, takes the Fourier transform of what it sees, and slides the window along.\nThe price is a trade-off: a shorter window gives better timing but blurrier pitch.\n",
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