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)
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3ba4444f-52d8-4cb6-baca-4b647a1d76d0%2F25eb0fc6-559c-450f-89ca-5283fc94897d%2Fcn17bca_processed.jpeg&w=3840&q=75)
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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