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  "body": "\n## Summary\n\nA wavelet is a function $\\psi$ on $\\R$ whose dilations by powers of $2$ and integer translations form an [[orthonormal basis|0S9GGTR0EX]] of $L^2(\\R)$.\nEach basis function is localized near a position and at a scale, so a wavelet expansion describes a function at all levels of detail.\nIn a wider sense, any oscillating function with integral zero that is used in a [[continuous wavelet transform|57FR21NDGV]] is called a wavelet.\nWavelets are used in signal and image compression, numerical analysis and harmonic analysis.\n\n## Explanations\n\n### L1 human\n\nA wavelet is a small wave: it wiggles up and down and then dies out.\nStretching it gives slow wiggles for coarse features, and squeezing it gives fast wiggles for fine detail.\nSliding these copies along the line, one can match the features of a signal wherever they occur.\nThe simplest wavelet is the Haar wavelet, which is $+1$ on $[0, \\tfrac12)$, $-1$ on $[\\tfrac12, 1)$ and $0$ elsewhere.\n",
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