Show that the coherent time (tau_{c}) defined in Eq. (6.43) is related to the spectral width (Delta

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Show that the coherent time \(\tau_{c}\) defined in Eq. (6.43) is related to the spectral width \(\Delta v\) given by Eq. (6.50) by the simple inversion formula \(\tau_{c}=\frac{1}{2 \Delta \omega}\). HINT: Use the Fourier transform relationships between \(S(\omega)\) and \(G(\tau)\) and Parseval's theorem.

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