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Signals that can be calculated from their ambiguity function

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1 Author(s)

A new lemma relates the analytic extensions of two time functions u(t) and v(t) to the Laplace transform of their ambiguity function \psi_{uv} . This lemma is used to derive necessary conditions for u and v from two bounds on the behavior of \psi_{uv} , at infinity. In particular, if the first bound is fulfilled, then u(z) and v(z) must be integral analytic functions. If both bounds are fulfilled, then u and v are each equal to \exp {- \pi t^2 } times a polynomial in t , and the two polynomials can be found from \psi_{uv} by comparing coefficients.

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Information Theory, IEEE Transactions on  (Volume:16 ,  Issue: 2 )