ENDP 350 Digital Signal Processing Assignment 1 2026 - University of Dubai

ENDP 350 Digital Signal Processing Assignment 1

This instrument assesses the following Course Learning Outcomes (CLO):

Linkages to Program Outcomes and Concentration Outcomes are provided in the Syllabus.

Question 1:

Consider the following signal:

x(t)=6sin⁡(33t+7)−sin⁡(12πt−8)x(t) = 6\sin(33t + 7) - \sin(12\pi t - 8)x(t)=6sin(33t+7)−sin(12πt−8)

a) Compute the maximum signal frequency.
b) What is the Nyquist frequency?

Question 2:

Use Matlab in order to compute and plot the sampled signal for sampling rates following (pick proper values for the range of t):

a) Fs of 3 times the maximum frequency
b) Fs = maximum frequency
c) Fs of 6 times the maximum frequency

What can you observe for each case?

Note: Ensure to include your code and add comments. Also, take screenshots of your outputs for each case. (Don’t use ChatGPT)

Question 3:

Given the following discrete signal:

y[n]=0.3y[n−1]+0.25y[n−2]−0.1x[n]+0.75x[n−2]y[n] = 0.3y[n-1] + 0.25y[n-2] - 0.1x[n] + 0.75x[n-2]y[n]=0.3y[n−1]+0.25y[n−2]−0.1x[n]+0.75x[n−2]

a) What is the transfer function H(z)?
b) Determine the poles and zeros location (show your work in details).
c) Confirm the answers you got in Part b and use Matlab to plot z-plane.
d) Comment on the stability of the system.

Question 4:

For the transfer function obtained in Question 3:

a) Calculate the magnitude of the gain of this filter at 2 kHz, given that the sampling frequency is 6 kHz.
b) Use Matlab to plot the magnitude of the gain.