f(t) Answer the following (5 only): k c/2 0 T c/2 -C y(t) k 0 с с g(t) k/2 The function f(t) graphed as shown in the figure above can represent in Fourier series as 2k f(t) = + (cost-cos 3t+cos 5t- + ...). 1-k/2 1. y(t) is an odd function. (true or false). 2. y(t) ao 3. If y(t) shifted down by k/2 will equal to g(t), then bn of g(t) = bn of y(t). (true or false) 4. Fourier series of y(t) is only (sine/ cosine) -----------terms. 5. Fourier series of g(t) is only (even/ odd) -----------harmonics.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.1: Tables And Trends
Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...
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f(t)
c/2
T
k
0
c/2
y(t) multiplied by (-1). (true or false).
B. If the F.T. of the signal f(t) is given by
y(t)
F(w) =
k
1
1+w²
0
The function f(t) graphed as shown in the figure above can represent in Fourier series as
2k
f(t) = + (cost - cos 3t+cos 5t- + ...).
T
C
Answer the following (5 only):
1. y(t) is an odd function. (true or false).
2. y(t) ao=.
3. If y(t) shifted down by k/2 will equal to g(t), then bn of g(t) = bn of y(t). (true or false)
4. Fourier series of y(t) is only (sine/ cosine) -----------terms.
5. Fourier series of g(t) is only (even/ odd) -----------harmonics.
6. If g(t) is reflected about the y-axis, then its Fourier series is the same as the Fourier series of
g(t)
k/2
-2w2
e1+w²
-k/2
Transcribed Image Text:f(t) c/2 T k 0 c/2 y(t) multiplied by (-1). (true or false). B. If the F.T. of the signal f(t) is given by y(t) F(w) = k 1 1+w² 0 The function f(t) graphed as shown in the figure above can represent in Fourier series as 2k f(t) = + (cost - cos 3t+cos 5t- + ...). T C Answer the following (5 only): 1. y(t) is an odd function. (true or false). 2. y(t) ao=. 3. If y(t) shifted down by k/2 will equal to g(t), then bn of g(t) = bn of y(t). (true or false) 4. Fourier series of y(t) is only (sine/ cosine) -----------terms. 5. Fourier series of g(t) is only (even/ odd) -----------harmonics. 6. If g(t) is reflected about the y-axis, then its Fourier series is the same as the Fourier series of g(t) k/2 -2w2 e1+w² -k/2
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