ELEC1010
Homework 1 [20]
Deadline: 10 pm on 27 Sep (Fri)
Please submit ONE soft copy (pdf only) of your assignment to Canvas (Assignments)
before the deadline. NO LATE Submission! (Zero mark!)
1. Consider two signals: [6]
𝑥1 = 2 sin(784𝜋𝑡) + 3 sin(2352𝜋𝑡) + sin⁡(3920𝜋𝑡)
𝑥2 = sin(1568πt) + 2 sin(3136πt) + 3⁡ sin⁡(5488𝜋𝑡)
a) Find the period of 𝑥1 and 𝑥2 .
b) Do they have the same pitch? Explain your answer with justifications.
c) Do they have the same quality? Explain your answer with justifications.
2. Consider the following system. [10]
a) Write the mathematical expression of 𝑠(𝑡).
b) What is the fundamental frequency of 𝑠(𝑡).
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c) What are the harmonics of 𝑌(𝑓).
d) If we use a filter H(f) to obtain 𝑌(𝑓), what kind of filter will H(f) be?
e) Draw the filter H(f) and briefly describe the filter with appropriate values.
3. Microsoft Excel Question: [4]
A signal is a sum of its first 4 harmonics (first to fourth harmonic). The graph below is
showing its 3rd harmonic of this signal. The amplitudes of the first harmonic, 2nd harmonic
and the fourth harmonic are 2, 1 and 3 respectively (Note: The amplitude of the 3rd
harmonic is given in the plot below).
a) Plot the fundamental frequency of this signal ONLY in the time domain and show
TWO completed cycles (periods) only of that signal using Microsoft Excel.
b) Plot the entire signal in the time domain and show TWO completed cycles (periods)
only using Microsoft Excel.
[*Note: guidelines on using EXCEL for plotting the sine function are provided on Canvas]
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