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Ambiguity Function


The ambiguity function of a square-integrable function f is the two-variable correlation

 A_f(tau,nu)=int_(-infty)^inftyf(t+tau/2)f(t-tau/2)^_e^(-2piinut)dt.

It measures the similarity of f to a copy shifted by tau and modulated by frequency nu. The ambiguity function is closely related by a two-dimensional Fourier transform to the Wigner distribution and is used to study simultaneous time and frequency localization.


See also

Correlation, Fourier Transform, Fractional Fourier Transform

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References

Cohen, L. Time-Frequency Analysis. Englewood Cliffs, NJ: Prentice-Hall, 1995.

Cite this as:

Weisstein, Eric W. "Ambiguity Function." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/AmbiguityFunction.html

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