1. Consider a continuous-time periodic signal x(t) = x(t +T) with Fourier series representation where (a) (b) € 1 0.8 0.6 0.4 0.2 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 -12 Xk= -10 -8 x(t) = [Xke/2nkt/T 00 -6 k=-00 0, k even 6 π²k² Xo = 0.5 -3π/4 sin (2) sin(), k odd -4 -2 1 W 0 t H(Q) 2 Suppose another periodic continuous-time signal z(t) is created having Fourier series = coefficients given by ZkXkejk. Using the Time Shift property of the continuous-time Fourier Series, sketch z(t), where T = 4 seconds. 6 Suppose the original periodic signal x(t) is input to a continuous-time LTI system with fre response H() shown below. With the signal period still T=4 seconds, find an expression for the LTI system output signal y(t) and sketch y(t) 8 10 3π/4 12 (rad/s)
1. Consider a continuous-time periodic signal x(t) = x(t +T) with Fourier series representation where (a) (b) € 1 0.8 0.6 0.4 0.2 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 -12 Xk= -10 -8 x(t) = [Xke/2nkt/T 00 -6 k=-00 0, k even 6 π²k² Xo = 0.5 -3π/4 sin (2) sin(), k odd -4 -2 1 W 0 t H(Q) 2 Suppose another periodic continuous-time signal z(t) is created having Fourier series = coefficients given by ZkXkejk. Using the Time Shift property of the continuous-time Fourier Series, sketch z(t), where T = 4 seconds. 6 Suppose the original periodic signal x(t) is input to a continuous-time LTI system with fre response H() shown below. With the signal period still T=4 seconds, find an expression for the LTI system output signal y(t) and sketch y(t) 8 10 3π/4 12 (rad/s)
Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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Please help explain the steps for this question, I am stuck. This is all one question! If you could just help with part A and B i would appreciate it!
Transcribed Image Text:1. Consider a continuous-time periodic signal x(t) = x(t +T) with Fourier series representation
where
(a)
(b)
(c)
€
1
0.8
0.6
0.4
0.2
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
-12
Xk=
-10
-8
x(t) = [Xke/2nkt/T
00
-6
k=-00
0, k even
6
π²k²
Xo = 0.5
-3π/4
sin (2) sin(), k odd
-4
-2
1
W
0
t
H(Q)
2
Suppose another periodic continuous-time signal z(t) is created having Fourier series
=
coefficients given by ZkXkejk. Using the Time Shift property of the continuous-time
Fourier Series, sketch z(t), where T = 4 seconds.
6
Suppose the original periodic signal x(t) is input to a continuous-time LTI system with
fre response H() shown below. With the signal period still T=4 seconds, find an
expression for the LTI system output signal y(t) and sketch y(t)
8 10
3π/4
12
(rad/s)
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).
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