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17.17 Given f(t) = fi(t)f2(t), show that 00 F(w) (1/2π) F₁(u)F2(u) du. 8 Hint: First, use the defining integral to express F(w) as F(w) = √ fi(t)f2(t)e -jwt dt. Second, use the inversion integral to write 8 1 fi(t) F₁(u)ejot du. 2πT Third, substitute the expression for fi(t) into the defining integral and then interchange the order of integration.

17.17 Given f(t) = fi(t)f2(t), show that 00 F(w) (1/2π) F₁(u)F2(u) du. 8 Hint: First, use the defining integral to express F(w) as F(w) = √ fi(t)f2(t)e -jwt dt. Second, use the inversion integral to write 8 1 fi(t) F₁(u)ejot du. 2πT Third, substitute the expression for fi(t) into the defining integral and then interchange the order of integration.

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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17.17 Given f(t) = fi(t)f2(t), show that 00 F(w) (1/2π) F₁(u)F2(u) du. 8 Hint: First, use the defining integral to express F(w) as F(w) = √ fi(t)f2(t)e -jwt dt. Second, use the inversion integral to write 8 1 fi(t) F₁(u)ejot du. 2πT Third, substitute the expression for fi(t) into the defining integral and then interchange the order of integration.
Transcribed Image Text:17.17 Given f(t) = fi(t)f2(t), show that 00 F(w) (1/2π) F₁(u)F2(u) du. 8 Hint: First, use the defining integral to express F(w) as F(w) = √ fi(t)f2(t)e -jwt dt. Second, use the inversion integral to write 8 1 fi(t) F₁(u)ejot du. 2πT Third, substitute the expression for fi(t) into the defining integral and then interchange the order of integration.
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