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Electronics and Communication Engineering (ECE) Exam  >  Electronics and Communication Engineering (ECE) Tests  >  Test: Fourier Series Representation of Continuous Periodic Signals - Electronics and Communication Engineering (ECE) MCQ

Test: Fourier Series Representation of Continuous Periodic Signals - Electronics and Communication Engineering (ECE) MCQ


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5 Questions MCQ Test - Test: Fourier Series Representation of Continuous Periodic Signals

Test: Fourier Series Representation of Continuous Periodic Signals for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Test: Fourier Series Representation of Continuous Periodic Signals questions and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus.The Test: Fourier Series Representation of Continuous Periodic Signals MCQs are made for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Fourier Series Representation of Continuous Periodic Signals below.
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Test: Fourier Series Representation of Continuous Periodic Signals - Question 1
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The average value of the periodic waveform shown.

Detailed Solution for Test: Fourier Series Representation of Continuous Periodic Signals - Question 1

The average value


Test: Fourier Series Representation of Continuous Periodic Signals - Question 2
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Find the value of A and B for signal, g(t) = Ay (Bt), such that y(t) = x (t) * h(t) and g(t) = x(3t) * h (3t) is

Detailed Solution for Test: Fourier Series Representation of Continuous Periodic Signals - Question 2

We know that,

Given form is,

So, we can write it as,

Comparing both equations, we get,

Taking Inverse Fourier Transform,

Comparing with given signal, g(t) = Ay (Bt)
A = 1/3 and B = 3

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Test: Fourier Series Representation of Continuous Periodic Signals - Question 3
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The ratio of powers present in 3rd harmonic to 5th harmonic for a square periodic signal.

Detailed Solution for Test: Fourier Series Representation of Continuous Periodic Signals - Question 3

We know that from Fourier Series coefficient of square periodic signal, power is proportional to (1/n2).



-  P3   =  (1/3)2

- P5  = (1/5)2

Ratio of Powers =  

Test: Fourier Series Representation of Continuous Periodic Signals - Question 4
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For a signal u(sint); Fourier series is having
Detailed Solution for Test: Fourier Series Representation of Continuous Periodic Signals - Question 4

Given x(t) = u(sint)
Drawing waveform

We know for waveform like y(t) shown

DC component is zero and have sine odd harmonics.
Performing upward shift in y(t) by adding dc value of 0.5, then
x(t) = y(t) + 0.5
So, x(t) → DC + sine odd harmonics

Test: Fourier Series Representation of Continuous Periodic Signals - Question 5
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Which of the following statements regarding the Fourier series are correct?
A. For an even symmetry, only sine terms exist.
B. For an even symmetry, only cosine terms exist.
C. For an odd symmetry, only cosine terms exist.
D. For an odd symmetry, only sine terms exist.
Choose the correct answer from the options given below:
Detailed Solution for Test: Fourier Series Representation of Continuous Periodic Signals - Question 5

Consider the following table for Relationship between time domain signal and trigonometric F.S coefficient


Consider the following table for Relationship between time domain signal and trigonometric F.S coefficient
Therefore, Correct option is b) B and D only

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