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Fourier transform: $\hat{f}(\xi) = \int_{-\infty}^{\infty} f(t)\ e^{- 2\pi i t \xi}\,dx$ where $t$ can be time and $\xi$ can be frequency. So, the question is how do we prove that $t$ and $\xi$ can in fact be time-frequency combination?

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What is your question? Can you describe a bit further, e.g. what is "time-frequency combination"? – AD. Oct 10 '12 at 12:03
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Multiply them and check that $t\xi\in \Bbb R$.

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