Q: How to use IFT to prove A(T) to the following formula A" (w) = |A(w – wo) = [ "s(w³, - -00 H have already known A'(w) = S(w, T) = 00 = - || -00 | ² {27__*_sw',7) dt] exp(-iw't)dw')} exp (iwt)dt t)dt 00 { A" (w) 1 2π F.T. A(W) ET > A(Z) > {}(w, z) = {{|estiv) L {'cw, z) 1. F. T. A(Z) = 10: A(t)e-iwot x A(t + T)e-iwo(t+t) x etwt dt Xxelier de 2 A(t) A(t + T) exp(-iwot) exp[i(w - 2wo) (w, T) = s(w, T) = |(w2wo, T)|².. A(T) = f (w, 7)dw] [ f $(w, 0)dw]] 2πT Note: A(t) and A(w) are a Fourier transform pair.< A(t)A(t + T) exp(iwt) dtt....... de ******** k ********* (3 5
Q: How to use IFT to prove A(T) to the following formula A" (w) = |A(w – wo) = [ "s(w³, - -00 H have already known A'(w) = S(w, T) = 00 = - || -00 | ² {27__*_sw',7) dt] exp(-iw't)dw')} exp (iwt)dt t)dt 00 { A" (w) 1 2π F.T. A(W) ET > A(Z) > {}(w, z) = {{|estiv) L {'cw, z) 1. F. T. A(Z) = 10: A(t)e-iwot x A(t + T)e-iwo(t+t) x etwt dt Xxelier de 2 A(t) A(t + T) exp(-iwot) exp[i(w - 2wo) (w, T) = s(w, T) = |(w2wo, T)|².. A(T) = f (w, 7)dw] [ f $(w, 0)dw]] 2πT Note: A(t) and A(w) are a Fourier transform pair.< A(t)A(t + T) exp(iwt) dtt....... de ******** k ********* (3 5
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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![Q: How to use IFT to prove A(T) to the following formula
2
A" (w) = |A(w - wo) |² =
have already known
A'(W) = S(w, T) =
-110
00
1
= L = L L der"}}
{ f
-00
-0
1. F. T.
F.T.
A/(w) ET > A[t) { (w₁ 2) = || (844)
_ _ >
T
LⓇ
A" (w)
A(t)e-iwot
s(w', t)dt exp(-iw':
‚1) dre
A(Z)
-
(w, t) = f(t)A(t + t) exp(iwt) d...….........
s(w, T) = |(w2w0, T)| ².
-00
A(T) = [1 § (w, t)dw] [21/1 f (w, 0)dw]]
2π 00
-00
Note: A(t) and A(w) are a Fourier transform pair.
(cwiz گی دی
X A(t + T)e-iwo(t+1) X el
giwt dt
x elute del
[t] dt [²
A(t)A(t + T) exp(-iwot) exp[i(w - 2wo)t]
dw' exp (iwt)dt
R
k
(3)
(4)
..5<](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4f7f7e91-311f-40b2-8ef2-058480eb16a0%2F0adc3add-ade7-4a36-b4d5-cdc5c9021698%2F8hv64w_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Q: How to use IFT to prove A(T) to the following formula
2
A" (w) = |A(w - wo) |² =
have already known
A'(W) = S(w, T) =
-110
00
1
= L = L L der"}}
{ f
-00
-0
1. F. T.
F.T.
A/(w) ET > A[t) { (w₁ 2) = || (844)
_ _ >
T
LⓇ
A" (w)
A(t)e-iwot
s(w', t)dt exp(-iw':
‚1) dre
A(Z)
-
(w, t) = f(t)A(t + t) exp(iwt) d...….........
s(w, T) = |(w2w0, T)| ².
-00
A(T) = [1 § (w, t)dw] [21/1 f (w, 0)dw]]
2π 00
-00
Note: A(t) and A(w) are a Fourier transform pair.
(cwiz گی دی
X A(t + T)e-iwo(t+1) X el
giwt dt
x elute del
[t] dt [²
A(t)A(t + T) exp(-iwot) exp[i(w - 2wo)t]
dw' exp (iwt)dt
R
k
(3)
(4)
..5<
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