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I have a sequence which is made of complex exponentials with arbitrary amplitudes and initial phases. No noise. That is it is a sum of the complex exponentials of the form $A_i e^{jnw_i+p_i}$. For example, let us say i ranges from 1 to 10. What is the minimum necessary data (number of samples) to calculate their amplitudes, initial phases and frequencies exactly i.e. $A$, $w$ and $p$ s? And how can we find them? $j$ here is square root of -1 and $n$ is the sample number.

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    $\begingroup$ This looks like an application of Prony's method. $\endgroup$ – Matt L. Jun 8 '15 at 12:12

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