(New page: = Homework 4, ECE301, Spring 2011, Prof. Boutin = WRITING IN PROGRESS. = Due in class, Monday February 14, 2011 = == Important Notes == *Justify all your answers...) |
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== Question 1 == | == Question 1 == | ||
| − | + | The unit impulse response of some LTI systems are given below. Which of these systems are memoryless? Causal? Stable? (Justify your answers mathematically.) | |
| − | a) <math class="inline">h | + | a) <math class="inline">h[n]= e^{j 2 \pi n} \ </math> |
| − | b) <math class="inline">h[n]= \ </math> | + | b) <math class="inline">h(t) = e^{j 2 \pi t} \ </math> |
| + | |||
| + | c) <math class="inline">h(t) = e^{j 2 \pi t} u(-t) \ </math> | ||
| + | |||
| + | d) <math class="inline">h[n]= e^{j 2 \pi n} \delta[n] \ </math> | ||
| + | |||
| + | d) <math class="inline">h[n]= e^{j 2 \pi n} \left( u[n+7] - u[n] \right) \ </math> | ||
== Question 2 == | == Question 2 == | ||
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A system has h(t)=. | A system has h(t)=. | ||
| − | a) Compute the | + | a) Compute the transfer function of this system. |
b) Use your answer in a) to compute the system's response to each of the CT signals in Question 3. | b) Use your answer in a) to compute the system's response to each of the CT signals in Question 3. | ||
| + | |||
== Question 5== | == Question 5== | ||
A system has h[n]=. | A system has h[n]=. | ||
| − | a) Compute the | + | a) Compute the transfer function of this system. |
b) Use your answer in a) to compute the system's response to each of the DT signals in Question 3. | b) Use your answer in a) to compute the system's response to each of the DT signals in Question 3. | ||
==Question 4 == | ==Question 4 == | ||
| − | The signal <math>x(t)=sin (2 pi 440 t)</math> is the input of a system. For each of the outputs listed below, indicate whether the system could be LTI. Justify your answers. | + | The signal <math>x(t)=sin (2 \pi 440 t)</math> is the input of a system. For each of the outputs listed below, indicate whether the system could be LTI. Justify your answers. |
a) | a) | ||
Revision as of 08:46, 7 February 2011
Contents
Homework 4, ECE301, Spring 2011, Prof. Boutin
WRITING IN PROGRESS.
Due in class, Monday February 14, 2011
Important Notes
- Justify all your answers.
- Write your answers clearly and cleaning.
- Write on one side of the paper only.
- Do not permute the order of the problems.
- Make a cover sheet containing your name, course number, semester, instructor, and assignment number.
- Staple your homework.
If you have questions
If you have questions or wish to discuss the homework with your peers, you may use the hw4 discussion page. All students are encouraged to help each other on this page. Your TA and instructor will read this page regularly and attempt to answer your questions as soon as possible.
Question 1
The unit impulse response of some LTI systems are given below. Which of these systems are memoryless? Causal? Stable? (Justify your answers mathematically.)
a) $ h[n]= e^{j 2 \pi n} \ $
b) $ h(t) = e^{j 2 \pi t} \ $
c) $ h(t) = e^{j 2 \pi t} u(-t) \ $
d) $ h[n]= e^{j 2 \pi n} \delta[n] \ $
d) $ h[n]= e^{j 2 \pi n} \left( u[n+7] - u[n] \right) \ $
Question 2
Obtain the Fourier series coefficients of the following signals.
Question 3
What is the Fourier series of the following signals?
Question 4
A system has h(t)=.
a) Compute the transfer function of this system.
b) Use your answer in a) to compute the system's response to each of the CT signals in Question 3.
Question 5
A system has h[n]=.
a) Compute the transfer function of this system.
b) Use your answer in a) to compute the system's response to each of the DT signals in Question 3.
Question 4
The signal $ x(t)=sin (2 \pi 440 t) $ is the input of a system. For each of the outputs listed below, indicate whether the system could be LTI. Justify your answers. a)
Question
The signal $ x[n]=j^n $ is the input of a system. For each of the outputs listed below, indicate whether the system could be LTI. Justify your answers. a)
