ELEC 351 Signals and Systems
Lab Exercise # 1
Date 26/3/2026
Group # 6
Name
Student ID
Abdulla Al-Dosari
Khalid Tayeh
202209738
Participation
Percentage
[50 %]
[50 %]
202406243
Grading Rubric
Completeness of the report
Organization of the report
Grading
scheme
10%
Clear PDF, with cover sheet, answers are in the same order
as questions in the assignment, copies of the questions
Quality of figures
10%
Correctly labeled with title, x-axis, y-axis, and name(s)
Understanding of the questions and provide a complete
answers (16 mark for each question)
80%
Note: solve the following questions using either MATLAB or python.
1- Use MATLAB or python to generate plots of the following continues-time signals for −10 ≤ t ≤ 10:
• 𝑥(𝑡) = 𝛿(𝑡)
• 𝑥(𝑡) = 𝑢(𝑡 − 5) − 𝑢(𝑡 + 1) + 8𝛿(𝑡 − 3)
• 𝑥(𝑡) = 3[𝑟(−𝑡) + 𝑟(𝑡)]
, 𝑟(𝑡): 𝑖𝑠 𝑟𝑎𝑚𝑝 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛
2- For the signal 𝑥(𝑡) of Figure(1), Use MATLAB or python to plot:
a. 4𝑥(−𝑡/3)
b. 𝑥(3 + 𝑡)
c. 2𝑥(2𝑡 − 1)
d. −4𝑥(𝑡 − 2)
3- The input 𝑥(𝑡) and the corresponding output 𝑦(𝑡) of a linear time-invariant (LTI) system are
𝑥(𝑡) = 𝑢(𝑡) − 𝑢(𝑡 − 1) ,
𝑦(𝑡) = 𝑟(𝑡) − 2𝑟(𝑡 − 1) + 𝑟(𝑡 − 2)
Determine the outputs 𝑦𝑖 (𝑡), 𝑖 = 1; 2; 3 corresponding to the following inputs
(i)
𝑥1 (𝑡) = 𝑢(𝑡 − 2) − 𝑢(𝑡 − 3);
(ii)
𝑥2 (𝑡) = 𝑢(𝑡 + 3) − 𝑢(𝑡 + 2)
Plot the inputs 𝑥𝑖 (𝑡) and the corresponding output 𝑦𝑖 (𝑡).
What you can notice if we introduce delay into LTI system?
Because the system is Time-Invariant, any delay or advance applied to the input signal x(t) results
in the exact same delay or advance in the output signal y(t). Specifically, for x_1(t), the input was
delayed by 2 seconds, and the resulting output y_1(t) was simply the original y(t) shifted 2 seconds to
the right. This confirms the system follows the Time-Invariance property of LTI systems.
Hint: use Heaviside and below ramp function to plot the signals or just like
what we did in the lab.You can generate the output manually then plot it.
function r = ramp(x)
r = max(0,x)
4- For the input signal 𝑥(𝑡), and the impulse response ℎ(𝑡), find the output signal 𝑦(𝑡) for the following
(Hint: Show your answer all graphs and code):
Figure 4: Question 4 Code Part A
Figure 3: Question 4 Part A
Figure 5: Question 4 Code Part B
Figure 5: Question 4 Part B
5- For the following signals 𝑥1(𝑡) and 𝑥2(𝑡) plot each signal and find the convolution