ECE45 Midterm 1 – 100 points total
ECE 45, Fall 2022
Oct 20, 2022
Exam procedures Take a moment to read these instructions before getting started. Please
write out your solutions in the space provided.
• Please writ
...
ECE45 Midterm 1 – 100 points total
ECE 45, Fall 2022
Oct 20, 2022
Exam procedures Take a moment to read these instructions before getting started. Please
write out your solutions in the space provided.
• Please write your full name and SID on each page.
• Show your thinking process. However you reason about the problem, communicate it clearly to us.
• Clearly circle any solutions you find.
The exam will take 80 minutes to complete
You may paper resources only. No electronics. If you have clarifying questions, please ask.
The exam is worth 80 points. Show all works and you will receive partial credit for reasonable attempts at
each problem.
Name:
SID:
1
Name: SID:
1 LTI System Analysis using Input Output Pairs
6 questions, 14 points total You are given the following input/output combinations. You are asked to
determine if the observations are consistent with linearity and/or time invariance. In other words: is it
possible the system is linear or time invariant, or do the examples clearly prove it is not? For each case,
check the box next to yes or no for each property then briefly explain your reasoning.
a) cos(wt) → H1 → sin(wt) and sin(wt) → H1 → sin(wt), ω ̸= 0. (2 pts)
time invariant? □ yes, it could be □ no, it definitely is not
explanation:
b) sin(wt) → H2 → 1 + cos(wt), ω ̸= 0 (2 pts)
linear? □ yes, it could be □ no, it definitely is not
explanation:
c) cos(5t) → H3 → 1 (2 pts)
linear? □ yes, it could be □ no, it definitely is not
explanation:
d) cos(5t) → H4 → 0 (2 pts)
linear? □ yes, it could be □ no, it definitely is not
explanation:
2
Name: SID:
e) f(t) → H5 → g(t) and 3f(2t - 10) → H5 → 3g(2(t - 10)) (4 pts)
linear □ yes, it could be □ no, it definitely is not
explanation:
time invariant? □ yes, it could be □ no, it definitely is not
explanation:
f) ej5t + e-j5t → H7 → 2cos(5t) (2 pts)
linear? □ yes, it could be □ no, it definitely is not
explanation:
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