3. Sketch the following functions and determine the Fourier series expansions of the following: (a) || on (-л, π] (b) | cost (c) Jo -T/2
3. Sketch the following functions and determine the Fourier series expansions of the following: (a) || on (-л, π] (b) | cost (c) Jo -T/2
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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Question
Please do #5
![3. Sketch the following functions and determine the Fourier series expansions of the following:
(a) || on (-л, π]
(b) | cost
(c)
f(t) =
-T/2<t<0
+1 0≤t≤T/2
4. In Eq. 1, express the cosine and sine in terms of complex exponentials, and show that the function
f(t) can be written as
k=∞
where
f(t) = Σ
Σ cheint
k=-8
1
T/2
f(t)e-jkt dt
Ck
=
T
5. Determine the complex Fourier expansion for the functions in Problem 3.
(3)
(4)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd936c6c0-8e3b-4a92-9646-2c460fec57ae%2Fc2eca76e-02e4-4a17-89e5-6ab1c7cf17ba%2Fjrczo4m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. Sketch the following functions and determine the Fourier series expansions of the following:
(a) || on (-л, π]
(b) | cost
(c)
f(t) =
-T/2<t<0
+1 0≤t≤T/2
4. In Eq. 1, express the cosine and sine in terms of complex exponentials, and show that the function
f(t) can be written as
k=∞
where
f(t) = Σ
Σ cheint
k=-8
1
T/2
f(t)e-jkt dt
Ck
=
T
5. Determine the complex Fourier expansion for the functions in Problem 3.
(3)
(4)
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