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1. Sketch the graph for the following square wave function using 3 periods.

19 / 01 / 2019 Maths

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Question 1 

1. Sketch the graph for the following square wave function using 3 periods.

𝑓(𝑡) = {

0, −𝜋 ≤ 𝑡 < 0

𝜋, 0 ≤ 𝑡 < 𝜋

2.Determine the coefficients for the first six non zero terms using Fourier Series.

3.Using the coefficients write the function in its expanded form.

4 What is the name given to this wave in electrical Engineering?

5.Why is a sine wave used for transmission and not a square or triangular wave inelectrical Engineering?

Question 2 

1. For 0 ≤ 𝑡 ≤ 6 create tables for the first six nonzero terms. The increments of t

must be 0.1. 

2. For 0 ≤ 𝑡 ≤ 6 create tables to show the following data. Use the same increment

of 0.1. 

3. Plot the following graphs using Excel

a. t vs A

b. t vs B

c. t vs C

d. t vs D

e. t vs E

f. t vs F 

4. Make a suitable comparison between the graphs and then draw conclusions ofyour observations. 

5. Research Gibbs Phenomenon

6. Which of the graphs best shows Gibbs phenomenon and at which points of thegraphs does this occurs?

7. Mention a few areas of Engineering where Fourier series play an important role.Minimum 3 areas.

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