Consider the signal (et+2, t<-2 f(t) = {1, -2≤t <2 e²-t, t22 (a) Is the signal time-limited? Justify. (b) Find the Fourier transform of the signal. Simplify your answer. (c) Is the signal band-limited? Justify. (d) Explain in words the relationship between the signal f given above and the signal g given below e²/2+3 g(t) = 1, t<-4 -4 < t < 4 e2-1/2, t24 (e) Use your answer to parts (b) to obtain ĝ(a), without computing it from definition.
Consider the signal (et+2, t<-2 f(t) = {1, -2≤t <2 e²-t, t22 (a) Is the signal time-limited? Justify. (b) Find the Fourier transform of the signal. Simplify your answer. (c) Is the signal band-limited? Justify. (d) Explain in words the relationship between the signal f given above and the signal g given below e²/2+3 g(t) = 1, t<-4 -4 < t < 4 e2-1/2, t24 (e) Use your answer to parts (b) to obtain ĝ(a), without computing it from definition.
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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Transcribed Image Text:Consider the signal
f(t)
et+2, t < -2
1,
e²-1, t22
-2 ≤t <2
(a) Is the signal time-limited? Justify.
(b) Find the Fourier transform of the signal. Simplify your answer.
(c) Is the signal band-limited? Justify.
(d) Explain in words the relationship between the signal f given above and the signal g given below
Je¹/2+2, 1<-4
-4≤t<4
€2-4/2, 124
(e) Use your answer to parts (b) to obtain ĝ(a), without computing it from definition.
g(t) = 1,
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Step 1: To determine if the signal is time-limited,
VIEWStep 2: (b) The Fourier transform of the signal f(t)
VIEWStep 3: if the signal is band-limited,
VIEWStep 4: Explain in words the relationship between the signal ƒ
VIEWStep 5: parts (b) to obtain hats g(alpha), without computing it from definition.
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