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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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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