Relation Between Spectral Width and Coherence Time. Show that the coherence time T.defined in (12.1-10) is related to the spectral width Ave defined in (12.1-18) by the simple inverserelation Te = 1/Ave. Hint: Use the definitions of Av, and Te, the Fourier-transform relation betweenS(v) and G(r), and Parseval's theorem provided in (A.1-7) [Appendix A].19(7)l* dr(12.1-10)Coherence TimeTe( s(u) duAve(12.1-18)s*(u) dvParseval's Theorem. The signal energy, which is the integral of the signal powerIf(t)P, equals the integral of the energy spectral density F(v)l², so thatsO)P dt = IF(»)P du.(A.1-7)Parseval's Theorem-00S(v) = G(7) exp(-j2mvT) dr.(12.1-17)Power Spectral Density|

Parseval's theorem states that the integral of the signal power equals the integral of the energy…

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