Ambiguity function

Summary

The ambiguity function of a signal $f$ measures how much $f$ correlates with copies of itself shifted in time and in frequency. In radar it describes how well a transmitted pulse lets one tell targets apart by range (time delay) and by speed (Doppler frequency shift). It is the short-time Fourier transform of $f$ with window $f$, up to a phase factor. It is related to the Wigner distribution by a two-dimensional Fourier transform.