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Relation Between Spectral Width and Coherence Time. Show that the coherence time Te defined in (12.1-10) is related to the spectral width Av, defined in (12.1-18) by the simple inverse relation Te = S(v) and G(7), and Parseval's theorem provided in (A.1-7) [Appendix AJ. 1/Ave. Hint: Use the definitions of Ave and Te, the Fourier-transform relation between

Relation Between Spectral Width and Coherence Time. Show that the coherence time Te defined in (12.1-10) is related to the spectral width Av, defined in (12.1-18) by the simple inverse relation Te = S(v) and G(7), and Parseval's theorem provided in (A.1-7) [Appendix AJ. 1/Ave. Hint: Use the definitions of Ave and Te, the Fourier-transform relation between

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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 inverse relation Te = 1/Ave. Hint: Use the definitions of Av, and Te, the Fourier-transform relation between S(v) and G(r), and Parseval's theorem provided in (A.1-7) [Appendix A]. 19(7)l* dr (12.1-10) Coherence Time Te ( s(u) du Ave (12.1-18) s*(u) dv Parseval's Theorem. The signal energy, which is the integral of the signal power If(t)P, equals the integral of the energy spectral density F(v)l², so that sO)P dt = IF(»)P du. (A.1-7) Parseval's Theorem -00 S(v) = G(7) exp(-j2mvT) dr. (12.1-17) Power Spectral Density |
Transcribed Image Text: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 inverse relation Te = 1/Ave. Hint: Use the definitions of Av, and Te, the Fourier-transform relation between S(v) and G(r), and Parseval's theorem provided in (A.1-7) [Appendix A]. 19(7)l* dr (12.1-10) Coherence Time Te ( s(u) du Ave (12.1-18) s*(u) dv Parseval's Theorem. The signal energy, which is the integral of the signal power If(t)P, equals the integral of the energy spectral density F(v)l², so that sO)P dt = IF(»)P du. (A.1-7) Parseval's Theorem -00 S(v) = G(7) exp(-j2mvT) dr. (12.1-17) Power Spectral Density |
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