Test: Fourier Series Representation of Continuous Periodic Signals - Electrical Engineering (EE) MCQ

# Test: Fourier Series Representation of Continuous Periodic Signals - Electrical Engineering (EE) MCQ

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

Test: Fourier Series Representation of Continuous Periodic Signals for Electrical Engineering (EE) 2024 is part of Signals and Systems preparation. The Test: Fourier Series Representation of Continuous Periodic Signals questions and answers have been prepared according to the Electrical Engineering (EE) exam syllabus.The Test: Fourier Series Representation of Continuous Periodic Signals MCQs are made for Electrical Engineering (EE) 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

### 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

### The Fourier series coefficient of a periodic signal, x(t) is defined as Which of the following statement is correct.

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

CASE 1: Let us assume that x(t) is real, then x(t) = x*(t). This implies that for x(t) to be real, ak = a*-k. Since this is not true. So, x(t) is not real.
CASE 2: Let us assume that x(t) is even, then x(t) = x(-t) and ak = a–k. Since this is true for this case, hence x(t) is even.
CASE 3: Let us assume

Therefore,

Since bk is not even, So, g(t) is not even.

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

### 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 3

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

Test: Fourier Series Representation of Continuous Periodic Signals - Question 4

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 4

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 5

For a signal u(sint); Fourier series is having

Detailed Solution for Test: Fourier Series Representation of Continuous Periodic Signals - Question 5

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

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