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  "body": "\n## Summary\n\nThe ambiguity function of a signal $f$ measures how much $f$ correlates with copies of itself shifted in time and in frequency.\nIn radar it describes how well a transmitted pulse lets one tell targets apart by range (time delay) and by speed (Doppler frequency shift).\nIt is the [[short-time Fourier transform|3DHNP5NEWH]] of $f$ with window $f$, up to a phase factor.\nIt is related to the [[Wigner distribution|FCHW5QGG5V]] by a two-dimensional Fourier transform.\n\n## Explanations\n\n### L1 human\n\nA radar sends a pulse and listens for its echo.\nThe echo comes back delayed, because the target is far, and shifted in frequency, because the target moves.\nThe ambiguity function tells, for each delay and frequency shift, how much the shifted echo still looks like the original pulse.\nA good pulse has an ambiguity function with one sharp peak at zero, so that different targets cannot be confused.\n",
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