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  "body": "\n## Summary\n\nThe continuous wavelet transform compares a function $f$ with all rescaled and shifted copies $\\abs{a}^{-1/2} \\psi((t - b)/a)$ of one analyzing function $\\psi$.\nIt gives a function of scale $a$ and position $b$, which shows where $f$ has features of each size.\nWhen $\\psi$ satisfies the [[admissibility condition|2BBB8NY5ZA]], the transform preserves energy up to a constant, and $f$ can be rebuilt from it.\nUnlike the [[short-time Fourier transform|3DHNP5NEWH]], its time resolution adapts to the scale.\n\n## Explanations\n\n### L1 human\n\nPick a small wave shape, like the Mexican hat curve.\nStretch it to many widths and slide it to every position.\nAt each width and position, measure how well the signal matches the shape.\nWide shapes pick out slow trends and narrow shapes pick out sharp details, such as a jump in the signal.\nThe resulting map of matches, scale against position, is the continuous wavelet transform.\n",
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