Problem 7-1 This problem consists of 9 questions. Each question is worth 2 points and there is no partial credit for incorrect answers. Answers to parts a and b should both be sketched on the grid provided below. Label each number. (a) Sketch the complex number zi = 3e j (b) Sketch the complex number z₂ = 21. (z₁ is defined in part a.) Imaginary -2 0 2 3 Real (c) Consider the signal x(t) shown below. 6 4 2 0 -2 46 -6 -4 -3-2.5-2-1.5-1 -0.5 0 0.5 1 1.5 2 2.5 3 t (secs) Write an equation for x(t). x(t) = (d) Consider the signal s(t) = 15+ sin(2x(75)). Which of the following sampling rates can be used to sample s(t) without aliasing? Circle all sample rates that will work. 30 Hz. 37.5 Hz 75 Hz 125 Hz 150 Hz 750 Hz Use the spectrogram below to answer questions e and f. Note that the frequency axis is shown in kilohertz (kHz). Frequency (kHz) 1 10 0 0.5 1 1.5 2 2.5 3 3.5 Time (secs) 4 (e) The instantaneous frequency of the signal in Hz is f(!). Write an equation for fi(t). Si(t)= (f) What should the sample rate f, be to avoid aliasing the signal shown in the spectrogram? (g) The figure below shows "semi-quadrants" of the complex plane labeled a through h. IM Re Let 23 = -7 j9. What "semi-quadrant" is 23 in?
Problem 7-1 This problem consists of 9 questions. Each question is worth 2 points and there is no partial credit for incorrect answers. Answers to parts a and b should both be sketched on the grid provided below. Label each number. (a) Sketch the complex number zi = 3e j (b) Sketch the complex number z₂ = 21. (z₁ is defined in part a.) Imaginary -2 0 2 3 Real (c) Consider the signal x(t) shown below. 6 4 2 0 -2 46 -6 -4 -3-2.5-2-1.5-1 -0.5 0 0.5 1 1.5 2 2.5 3 t (secs) Write an equation for x(t). x(t) = (d) Consider the signal s(t) = 15+ sin(2x(75)). Which of the following sampling rates can be used to sample s(t) without aliasing? Circle all sample rates that will work. 30 Hz. 37.5 Hz 75 Hz 125 Hz 150 Hz 750 Hz Use the spectrogram below to answer questions e and f. Note that the frequency axis is shown in kilohertz (kHz). Frequency (kHz) 1 10 0 0.5 1 1.5 2 2.5 3 3.5 Time (secs) 4 (e) The instantaneous frequency of the signal in Hz is f(!). Write an equation for fi(t). Si(t)= (f) What should the sample rate f, be to avoid aliasing the signal shown in the spectrogram? (g) The figure below shows "semi-quadrants" of the complex plane labeled a through h. IM Re Let 23 = -7 j9. What "semi-quadrant" is 23 in?
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
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Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
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Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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I need help with this problem and an explanation of the solution for the image described below. (Introduction to Signals and Systems)
Transcribed Image Text:Problem 7-1
This problem consists of 9 questions. Each question is worth 2 points and there is no partial credit for
incorrect answers.
Answers to parts a and b should both be sketched on the grid provided below. Label each number.
(a) Sketch the complex number zi
=
3e j
(b) Sketch the complex number z₂ = 21. (z₁ is defined in part a.)
Imaginary
-2
0
2
3
Real
(c) Consider the signal x(t) shown below.
6
4
2
0
-2
46
-6
-4
-3-2.5-2-1.5-1 -0.5 0 0.5 1 1.5 2 2.5 3
t (secs)
Write an equation for x(t).
x(t) =
Transcribed Image Text:(d) Consider the signal s(t) = 15+ sin(2x(75)). Which of the following sampling rates can be used
to sample s(t) without aliasing? Circle all sample rates that will work.
30 Hz.
37.5 Hz
75 Hz
125 Hz
150 Hz
750 Hz
Use the spectrogram below to answer questions e and f. Note that the frequency axis is shown in
kilohertz (kHz).
Frequency (kHz)
1
10
0 0.5
1
1.5 2 2.5 3 3.5
Time (secs)
4
(e) The instantaneous frequency of the signal in Hz is f(!). Write an equation for fi(t).
Si(t)=
(f) What should the sample rate f, be to avoid aliasing the signal shown in the spectrogram?
(g) The figure below shows "semi-quadrants" of the complex plane labeled a through h.
IM
Re
Let 23 = -7 j9. What "semi-quadrant" is 23 in?
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