1. Consider a continuous-time periodic signal x(t) = x(t +T) with Fourier series representation where 1 0.8 29 0.6 0.4 0.2 Xk = -12 It is straightforward to show that these Fourier series coefficients correspond to a continuous- time periodic trapezoidal signal, plotted below for T = 4 seconds. -10 00 x(t) = Σ Xke/2mkt/T k=-∞0 -8 Xo = 0.5 0, k even 6 π² k² www -2 sin -6 (1) S 2 (TLK), 6 -4 sin k odd 04 t 2 4 6 8 10 12
1. Consider a continuous-time periodic signal x(t) = x(t +T) with Fourier series representation where 1 0.8 29 0.6 0.4 0.2 Xk = -12 It is straightforward to show that these Fourier series coefficients correspond to a continuous- time periodic trapezoidal signal, plotted below for T = 4 seconds. -10 00 x(t) = Σ Xke/2mkt/T k=-∞0 -8 Xo = 0.5 0, k even 6 π² k² www -2 sin -6 (1) S 2 (TLK), 6 -4 sin k odd 04 t 2 4 6 8 10 12
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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Question
![(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 T=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)
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%2F8b207c38-3ae5-4958-b6f8-8e524b4be30c%2F4de8c192-2afd-4a7f-9cef-de7285ee475b%2Fiuaifw8_processed.jpeg&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 T=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)
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
1
0.8
0.6
0.4
0.2
Xk
-12
-10
=
x(t) =
-8
=
00
k=-00
It is straightforward to show that these Fourier series coefficients correspond to a continuous-
time periodic trapezoidal signal, plotted below for T = 4 seconds.
-6
Xo
0, k even
6
π²k²
www
-2
sin
Xkej²πkt/T
= 0.5
sin
(TTK), i
k odd
0
t
2
4
6
8
10
12](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8b207c38-3ae5-4958-b6f8-8e524b4be30c%2F4de8c192-2afd-4a7f-9cef-de7285ee475b%2Fa28leem_processed.png&w=3840&q=75)
Transcribed Image Text:1. Consider a continuous-time periodic signal x(t) = x(t + T) with Fourier series representation
where
1
0.8
0.6
0.4
0.2
Xk
-12
-10
=
x(t) =
-8
=
00
k=-00
It is straightforward to show that these Fourier series coefficients correspond to a continuous-
time periodic trapezoidal signal, plotted below for T = 4 seconds.
-6
Xo
0, k even
6
π²k²
www
-2
sin
Xkej²πkt/T
= 0.5
sin
(TTK), i
k odd
0
t
2
4
6
8
10
12
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