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Test: Continuous Time Signal Analysis


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10 Questions MCQ Test Digital Signal Processing | Test: Continuous Time Signal Analysis

Test: Continuous Time Signal Analysis for Electrical Engineering (EE) 2022 is part of Digital Signal Processing preparation. The Test: Continuous Time Signal Analysis questions and answers have been prepared according to the Electrical Engineering (EE) exam syllabus.The Test: Continuous Time Signal Analysis MCQs are made for Electrical Engineering (EE) 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Continuous Time Signal Analysis below.
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Test: Continuous Time Signal Analysis - Question 1

 The Fourier series representation of any signal x(t) is defined as:

Detailed Solution for Test: Continuous Time Signal Analysis - Question 1

 

Explanation: If the given signal is x(t) and F0 is the reciprocal of the time period of the signal and ck is the Fourier coefficient then the Fourier series representation of x(t) is given as

Test: Continuous Time Signal Analysis - Question 2

 Which of the following is the equation for the Fourier series coefficient?

Detailed Solution for Test: Continuous Time Signal Analysis - Question 2

Explanation: When we apply integration to the definition of Fourier series representation, we get

Test: Continuous Time Signal Analysis - Question 3

Which of the following is a Dirichlet condition with respect to the signal x(t)?

Detailed Solution for Test: Continuous Time Signal Analysis - Question 3

Explanation: For any signal x(t) to be represented as Fourier series, it should satisfy the Dirichlet conditions which are x(t) has a finite number of discontinuities in any period, x(t) has finite number of maxima and minima during any period and x(t) is absolutely integrable in any period.

Test: Continuous Time Signal Analysis - Question 4

The equation  is known as analysis equation. 

Detailed Solution for Test: Continuous Time Signal Analysis - Question 4

Explanation: Since we are synthesizing the Fourier series of the signal x(t), we call it as synthesis equation, where as the equation giving the definition of Fourier series coefficients is known as analysis equation.

Test: Continuous Time Signal Analysis - Question 5

 Which of the following is the Fourier series representation of the signal x(t)?

d) None of the mentioned

Detailed Solution for Test: Continuous Time Signal Analysis - Question 5

Explanation: In general, Fourier coefficients ck are complex valued. Moreover, it is easily shown that if the periodic signal is real, ck and c-k are complex conjugates. As a result
ck=|ck|ejθkand ck=|ck|e-jθk
Consequently, we obtain the Fourier series as

Test: Continuous Time Signal Analysis - Question 6

The equationis the representation of Fourier series. 

Detailed Solution for Test: Continuous Time Signal Analysis - Question 6

Explanation: cos(2πkF0 t+θk)= cos2πkF0 t.cosθk-sin2πkF0 t.sinθk
θk is a constant for a given signal.
So, the other form of Fourier series representation of the signal x(t) is

Test: Continuous Time Signal Analysis - Question 7

 What is the spectrum that is obtained when we plot |ck |2 as a function of frequencies kF0, k=0,±1,±2..?

Detailed Solution for Test: Continuous Time Signal Analysis - Question 7

Explanation: When we plot a graph of |ck |2 as a function of frequencies kF0, k=0,±1,±2… the following spectrum is obtained which is known as Power density spectrum.

Test: Continuous Time Signal Analysis - Question 8

What is the spectrum that is obtained when we plot |ck| as a function of frequency?

Detailed Solution for Test: Continuous Time Signal Analysis - Question 8

Explanation: We know that, Fourier series coefficients are complex valued, so we can represent ck in the following way.
ck=|ck|ejθk
When we plot |ck| as a function of frequency, the spectrum thus obtained is known as Magnitude voltage spectrum.

Test: Continuous Time Signal Analysis - Question 9

What is the equation of the Fourier series coefficient ck of an non-periodic signal?

Detailed Solution for Test: Continuous Time Signal Analysis - Question 9

Explanation: We know that, for an periodic signal, the Fourier series coefficient is

If we consider a signal x(t) as non-periodic, it is true that x(t)=0 for |t|>Tp/2. Consequently, the limits on the integral in the above equation can be replaced by -∞ to ∞. Hence,

Test: Continuous Time Signal Analysis - Question 10

Which of the following relation is correct between Fourier transform X(F) and Fourier series coefficient ck

Detailed Solution for Test: Continuous Time Signal Analysis - Question 10

Explanation: Let us consider a signal x(t) whose Fourier transform X(F) is given as

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