(a) (b) (c) Suppose another periodic continuous-time signal z(t) is created having Fourier series coefficients given by Zk=Xkejk. Using the Time Shift property of the continuous-time Fourier Series, sketch z(t), where T=4 seconds. Suppose the original periodic signal x(t) is input to a continuous-time LTI system with frequency response H() shown below. With the signal period still 7 = 4 seconds, find an expression for the LTI system output signal y(t) and sketch y(t) -3π/4 1 H(Q) 3π/4 (rad/s) [Extra Credit] Write a routine (you are encouraged to use sq_wave.m as a guide) to numerically compute and plot several periods of the partial sums of the continuous-time Fourier series. Use enough terms so that you obtain a close approximation to x(t). 1. Consider a continuous-time periodic signal x(t) = x(t+T) with Fourier series representation where x(t) 1 0.8 0.6 0.4 It is straightforward to show that these Fourier series coefficients correspond to a continuous- time periodic trapezoidal signal, plotted below for T = 4 seconds. 0.2 0 -12 Xk= -10 -8 00 x(t) = Σ Xxelzmkt/T k=-00 -6 Xo = 0.5 0, k even 6 π²k² sin n (7) sin(7), ko T -2 , k odd 0 t 2 4 6 8 10 12
(a) (b) (c) Suppose another periodic continuous-time signal z(t) is created having Fourier series coefficients given by Zk=Xkejk. Using the Time Shift property of the continuous-time Fourier Series, sketch z(t), where T=4 seconds. Suppose the original periodic signal x(t) is input to a continuous-time LTI system with frequency response H() shown below. With the signal period still 7 = 4 seconds, find an expression for the LTI system output signal y(t) and sketch y(t) -3π/4 1 H(Q) 3π/4 (rad/s) [Extra Credit] Write a routine (you are encouraged to use sq_wave.m as a guide) to numerically compute and plot several periods of the partial sums of the continuous-time Fourier series. Use enough terms so that you obtain a close approximation to x(t). 1. Consider a continuous-time periodic signal x(t) = x(t+T) with Fourier series representation where x(t) 1 0.8 0.6 0.4 It is straightforward to show that these Fourier series coefficients correspond to a continuous- time periodic trapezoidal signal, plotted below for T = 4 seconds. 0.2 0 -12 Xk= -10 -8 00 x(t) = Σ Xxelzmkt/T k=-00 -6 Xo = 0.5 0, k even 6 π²k² sin n (7) sin(7), ko T -2 , k odd 0 t 2 4 6 8 10 12
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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Can yo help me with question 1, parts A, B and C? Thank you.
![(a)
(b)
(c)
Suppose another periodic continuous-time signal z(t) is created having Fourier series
coefficients given by Zk=Xkejk. Using the Time Shift property of the continuous-time
Fourier Series, sketch z(t), where T=4 seconds.
Suppose the original periodic signal x(t) is input to a continuous-time LTI system with
frequency response H() shown below. With the signal period still 7 = 4 seconds, find an
expression for the LTI system output signal y(t) and sketch y(t)
-3π/4
1
H(Q)
3π/4
(rad/s)
[Extra Credit] Write a routine (you are encouraged to use sq_wave.m as a guide) to
numerically compute and plot several periods of the partial sums of the continuous-time
Fourier series. Use enough terms so that you obtain a close approximation to x(t).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc23eb98a-2dff-445f-a3f1-279aad19fd90%2F6c735bdf-a158-4a64-8412-cbc48464f744%2F0xwmczd_processed.png&w=3840&q=75)
Transcribed Image Text:(a)
(b)
(c)
Suppose another periodic continuous-time signal z(t) is created having Fourier series
coefficients given by Zk=Xkejk. Using the Time Shift property of the continuous-time
Fourier Series, sketch z(t), where T=4 seconds.
Suppose the original periodic signal x(t) is input to a continuous-time LTI system with
frequency response H() shown below. With the signal period still 7 = 4 seconds, find an
expression for the LTI system output signal y(t) and sketch y(t)
-3π/4
1
H(Q)
3π/4
(rad/s)
[Extra Credit] Write a routine (you are encouraged to use sq_wave.m as a guide) to
numerically compute and plot several periods of the partial sums of the continuous-time
Fourier series. Use enough terms so that you obtain a close approximation to x(t).
Transcribed Image Text:1. Consider a continuous-time periodic signal x(t) = x(t+T) with Fourier series representation
where
x(t)
1
0.8
0.6
0.4
It is straightforward to show that these Fourier series coefficients correspond to a continuous-
time periodic trapezoidal signal, plotted below for T = 4 seconds.
0.2
0
-12
Xk=
-10
-8
00
x(t) = Σ Xxelzmkt/T
k=-00
-6
Xo = 0.5
0, k even
6
π²k²
sin
n (7) sin(7), ko
T
-2
, k odd
0
t
2
4
6
8
10
12
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