EE235 Final Exam 2011 Just the task, not including the solution

1. EE-235 Summer 2011 Signals & Systems Leo Lam
Final Exam
Name
Student Number
Notes:
This exam is closed book, closed notes, closed homework and homework solutions. You are
permitted two 8.5” x 11” double-sided sheet of summary notes. No calculator is permitted.
Try to fit your work into the same sheet as the problem itself. If you need to include additional
sheets, place these immediately behind the sheet that the problem is on.
Partial credit will be based upon how well you describe what you are doing. If it isn’t on the
page; it isn’t in the grade. Write CLEARLY! University policies require that grading is by merit.
Answers with no units, when applicable, will receive zero credit. 3 significant figures are
generally good enough for any numerical final answers.
The problems are weighted as shown in the table below.
Good luck!
Points possible Your Score
Problem 1 16
Problem 2 20
Problem 3 20
Problem 4 20
Problem 5 24
Total score: 100

2. 1. Let H() be the transfer function of an LTI system. Sketch the frequency response. What
does each of the following system do? (16 points, 4 for each question)
a.
b.
c.
d.

3. 2. Determine the fundamental frequency 0 and the non-zero Fourier series coefficients for
the follow functions (you can leave the index n in your solution if the series is infinite):
a. (6 points)
b. (a rectified sinewave) (6 points)
c. (8 points)

4. 3. A causal LTI system is described by the following differential equation:
a) Find the transfer function (6 points)
b) What does this system do? (2 points)
c) The bandwidth of a system is the frequency at which the system power drops to half of
its peak value. What is the bandwidth of this system? (hint: find the magnitude of the
transfer function.) (6 points)
d) Find the impulse response h(t) of this system (6 points)

5. 4. Given a signal:
a. What are the Fourier Transforms of and
respectively? (4 points)
b. What is the Fourier Transform of f(t)? You can solve it any way you want (graphically or
mathematically). (8 points)
c. Sketch the frequency response F(). Label the axes. What is the bandwidth B? (4
points)
d. If f(t) is to be sampled properly without aliasing, what is the lowest possible sample
frequency? (4 points)

6. 5. Given the circuit in Figure 1.
a. Derive the differential equation
relating y(t) and x(t). (6 points)
b. What is the general solution to the homogeneous equation? (6 points)
c. Given that the applied voltage is and that the initial condition y(0-
)=0,
what is the complete solution to y(t)? (12 points)
Figure 1, Circuit for Question 5