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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![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 inverse
relation T. = 1/Ave. Hint: Use the definitions of Av, and Te, the Fourier-transform relation between
S(v) and G(7), and Parseval's theorem provided in (A.1-7) [Appendix A].
Te =
dr
(12.1-10)
Coherence Time
2
S(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 that
IS)P dt =
\F(w)F dv.
(A.1-7)
Parseval's Theorem](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe116b05f-4c27-45b1-8d08-00941e4ec3cb%2F0e867231-1652-45cd-a6b1-fac2e4d15126%2F6nna4bc_processed.png&w=3840&q=75)
Transcribed Image Text: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 inverse
relation T. = 1/Ave. Hint: Use the definitions of Av, and Te, the Fourier-transform relation between
S(v) and G(7), and Parseval's theorem provided in (A.1-7) [Appendix A].
Te =
dr
(12.1-10)
Coherence Time
2
S(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 that
IS)P dt =
\F(w)F dv.
(A.1-7)
Parseval's Theorem
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