Relation Between Spectral Width and Coherence Time. Show that the coherence time 7.defined in (12.1-10) is related to the spectral width Ave defined in (12.1-18) by the simple inverserelation T. = 1/Ave. Hint: Use the definitions of Av, and Te, the Fourier-transform relation betweenS(v) and G(7), and Parseval's theorem provided in (A.1-7) [Appendix A].Te =dr(12.1-10)Coherence Time2S(v).Ave(12.1-18)| s°(v) dv• Parseval's Theorem. The signal energy, which is the integral of the signal power|f(t)l², equals the integral of the energy spectral density [F(v)l², so thatIS)P dt =\F(w)F dv.(A.1-7)Parseval's Theorem

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

Relation Between Spectral Width and Coherence Time. Show that the coherence time T. defined in (12.1-10) is related to the spectral width Av, defined in (12.1-18) by the simple inverse relation T. = 1/Avc. Hint: Use the definitions of Ave and Te, the Fourier-transform relation between S(v) and G(t), and Parseval’s theorem provided in (A.1-7) [Appendix A].

Relation Between Spectral Width and Coherence Time. Show that the coherence time T. defined in (12.1-10) is related to the spectral width Av, defined in (12.1-18) by the simple inverse relation T. = 1/Avc. Hint: Use the definitions of Ave and Te, the Fourier-transform relation between S(v) and G(t), and Parseval’s theorem provided in (A.1-7) [Appendix A].

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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