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Proof of the Wiener-Khinchin Theorem. Use the definitions in (12.1-4), (12.1-14), and (12.1-15) to prove that the spectral density S(v) is the Fourier transform of the autocorre- lation function G(r). Prove that the intensity I is the integral of the power spectral density S(v). G(7) = (U*(t) U (t + r)) (12.1-4) Temporal Coherence Function -T/2 =LU(t) exp(-j2nvt) dt (12.1-14) -T/2 S(1) = Jim (V+(»)P}; (12.1-15) T00 |

Proof of the Wiener-Khinchin Theorem. Use the definitions in (12.1-4), (12.1-14), and (12.1-15) to prove that the spectral density S(v) is the Fourier transform of the autocorre- lation function G(r). Prove that the intensity I is the integral of the power spectral density S(v). G(7) = (U*(t) U (t + r)) (12.1-4) Temporal Coherence Function -T/2 =LU(t) exp(-j2nvt) dt (12.1-14) -T/2 S(1) = Jim (V+(»)P}; (12.1-15) T00 |

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Proof of the Wiener-Khinchin Theorem. Use the definitions in (12.1-4), (12.1-14), and (12.1-15) to prove that the spectral density S(v) is the Fourier transform of the autocorre- lation function G(r). Prove that the intensity I is the integral of the power spectral density S(v). G(r) = (U* (t) U (t + T)) (12.1-4) Temporal Coherence Function -T/2 Vr(v) = | U(t) exp(-j2nvt) dt (12.1-14) -T/2 S(v) = lim =(Vr(v)|P); (12.1-15) | TH00 T
Transcribed Image Text:Proof of the Wiener-Khinchin Theorem. Use the definitions in (12.1-4), (12.1-14), and (12.1-15) to prove that the spectral density S(v) is the Fourier transform of the autocorre- lation function G(r). Prove that the intensity I is the integral of the power spectral density S(v). G(r) = (U* (t) U (t + T)) (12.1-4) Temporal Coherence Function -T/2 Vr(v) = | U(t) exp(-j2nvt) dt (12.1-14) -T/2 S(v) = lim =(Vr(v)|P); (12.1-15) | TH00 T
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