1 F(w)Fi [f(t)]¸ = Fi [3sgn(3t) − 1 + ]. - jt Ft Applying the linearity of F.T we get : F(w) = 3Fi [sgn(3t)] -Fi [1 + 5t] 1+ jt apply time scaling How did he get the value inside the circle ⇒ F(w) = 2 jw/3 * 278 (4) d
1 F(w)Fi [f(t)]¸ = Fi [3sgn(3t) − 1 + ]. - jt Ft Applying the linearity of F.T we get : F(w) = 3Fi [sgn(3t)] -Fi [1 + 5t] 1+ jt apply time scaling How did he get the value inside the circle ⇒ F(w) = 2 jw/3 * 278 (4) d
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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![We have the following time domain signal :-
1
f(t) = 3sgn(3t).
1 + jt
Taking the Fourier transform of both sides we get :-
F(w)F: [f(t)] = Fr [3sgn(3t) — 1+5tl.
1
Applying the linearity of F.T we get : F(w) = 3Ft [sgn(3t) w-Ft [1 + 5t]
+jt
apply time scaling
How did he get the
value inside the circle
⇒ F(w) =
-
⇒ F(w)
2
jw/3
=
⇒ F(w) =
6
jw
F(w):
6
jw
* 278 (4) d
8
• 5 (4) dø
2πew
Hence the Fourier transform of f(t) = 3sgn(3t)
2πеⓇU(-w)
لها
2πеU(-w)
1
1+ jt
where the (anti-causal) step-function : U(-w) = {1
"
becomes :-
for w> 0
for w≤ 0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe385a283-5604-440f-9f24-4cebee22c35f%2F04ead8c0-f5a1-4c79-bd69-c69cf0ba573f%2Fs4sx38_processed.jpeg&w=3840&q=75)
Transcribed Image Text:We have the following time domain signal :-
1
f(t) = 3sgn(3t).
1 + jt
Taking the Fourier transform of both sides we get :-
F(w)F: [f(t)] = Fr [3sgn(3t) — 1+5tl.
1
Applying the linearity of F.T we get : F(w) = 3Ft [sgn(3t) w-Ft [1 + 5t]
+jt
apply time scaling
How did he get the
value inside the circle
⇒ F(w) =
-
⇒ F(w)
2
jw/3
=
⇒ F(w) =
6
jw
F(w):
6
jw
* 278 (4) d
8
• 5 (4) dø
2πew
Hence the Fourier transform of f(t) = 3sgn(3t)
2πеⓇU(-w)
لها
2πеU(-w)
1
1+ jt
where the (anti-causal) step-function : U(-w) = {1
"
becomes :-
for w> 0
for w≤ 0
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