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Test: Continuous Time Signals - Electrical Engineering (EE) MCQ


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10 Questions MCQ Test Signals and Systems - Test: Continuous Time Signals

Test: Continuous Time Signals for Electrical Engineering (EE) 2024 is part of Signals and Systems preparation. The Test: Continuous Time Signals questions and answers have been prepared according to the Electrical Engineering (EE) exam syllabus.The Test: Continuous Time Signals MCQs are made for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Continuous Time Signals below.
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Test: Continuous Time Signals - Question 1

The condition for periodicity of continuous time signal is:

Detailed Solution for Test: Continuous Time Signals - Question 1

Concept:

  • A continuous-time signal x(t) is said to be periodic if it repeats itself after its time period 'T0'.
  • A continuous-time signal x(t) satisfies:
     

x(t) = x(t + T0) for all t; where T0

The smallest value of T0 that satisfies the periodicity condition is called the fundamental time period of x(t).

Test: Continuous Time Signals - Question 2

The signal denoted by x(t) is known as 

Detailed Solution for Test: Continuous Time Signals - Question 2

The signal denoted by x(t) is known as a continuous-time signal.

Continuous-Time Signal:

  • A continuous-time (CT) signal is a function that is continuous, meaning there are no breaks in the signal.
  • For all real values of 't' we will get a value f(t), t ⊂ R.
  • CT signals are usually represented by using x(t), having parentheses and the variable 't'.

Discrete-time signal:

  • A discrete-time signal is a signal whose value is taken at discrete measurements.
  • With a discrete-time signal, there will be time periods of 'n' where we do not have a value.
  • DT signals are represented using the form x[n].
  • Discrete signals are approximations of CT signals

A system is continuous-time when its Input/Output signals are continuous-time. A system is discrete-time when its Input/Output signals are discrete-time.

Important Points:

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Test: Continuous Time Signals - Question 3

The function which has its Fourier transform, Laplace transform and Z-transform unity is

Detailed Solution for Test: Continuous Time Signals - Question 3

Concept:

The Fourier transform of a signal in the time domain is given as:

The Laplace transform F(s) of a function f(t) is defined by:

The definition of z-transform is given by,

Calculations:

Unit impulse signal:

It is defined as, 

For f(t) = δ(t)

The spectrum is represented as:

The Laplace transform of unit impulse is 1 i.e. unity.

Discrete-time Laplace transform is Z- transform.

Test: Continuous Time Signals - Question 4

Let f(t) be a continuous-time signal and let F(ω) be its Fourier Transform defined by

Define g(t) by

What is the relationship between f(t) and g(t)?

Detailed Solution for Test: Continuous Time Signals - Question 4

Given the Fourier transform pair,

The Inverse Fourier transform of F (ω) is given as

Replacing t by ‘ –t ‘ and ω by u in the above expression, we have,

If f (t) is even, then f (-t) = f (t)

∴ g (t) = 2π f (t)

⇒ g (t) will be proportional to f (t), if f (t) is an even function.

Test: Continuous Time Signals - Question 5

Consider a signal x(t) = 4 cos (2t/3) + 8 sin (0.5t) + 7 sin (t/3 – π/6)

Calculate the fundamental period.

Detailed Solution for Test: Continuous Time Signals - Question 5

Concept:

Continious time signal x(t) is given as,

x(t) = x1(t) + x2(t) 

Then, Time period of x(t) is (N) = LCM (T1, T2,)

Time period of x1(t) is Given as:

T1 = 2π / ω01    

Time period of x2(t) is Given as:

T= 2π / ω02   

Calculation:

Given:

T1 = 2π / 2/3 = 3π

T2 = 2π / .5 = 4π

T3 = 2π / 13 = 6π

Time period = L.C.M. (T1, T2, T3)

= L.C.M. (3π, 4π, 6π)

= 12π

Test: Continuous Time Signals - Question 6

The impulse response h(t) of a continuous time, linear time invariant system is described by h(t) = eat u(t) + ebt u(-t) where, u(t) denots the unit step function and a and b are real constants. This system is stable if 

Detailed Solution for Test: Continuous Time Signals - Question 6

Concept:

An LTI system is stable if and only if its impulse response is absolutely integrable.

Calculation:

Given,

h(t) = eat u(t) + ebt u(-t)

h(t) = h1(t) + h2(t)

∵ τ > 0 therefore, for absolute integrability a < 0

∵ τ < 0 therefore, for absolute integrability b > 0

∴ h(t) should be in the form shown in the figure below:

Test: Continuous Time Signals - Question 7

A sinusoidal signal x(t) = 2sin(100t + π/3) is passed through a square law device defined by input-output relation y(t) = x2(t), then the DC component in the signal is:

Detailed Solution for Test: Continuous Time Signals - Question 7

2: 4

The square law device produces an output signal that is equal to the square of the input signal. When a sinusoidal signal is passed through a square law device, the output signal will contain both the fundamental frequency and harmonics at higher frequencies. The DC component of the output signal is the average value of the output signal over time, and it is equal to the sum of the DC component of the input signal and the DC component of the harmonics.

In this case, the input signal is x(t) = 2sin(100t + π/3). The DC component of this signal is 0, since the average value of a sinusoidal signal over one period is 0. The output signal is y(t) = x^2(t) = (2sin(100t + π/3))^2 = 4cos^2(100t + π/3) = 4(1 - sin^2(100t + π/3)) = 4(1 - (2sin^2(100t + π/3)/2)) = 4(1 - sin^2(100t + π/3)/2). The DC component of this signal is 4/2 = 2.

Therefore, the correct answer is 2: 4.

Test: Continuous Time Signals - Question 8

Consider the following system ‘S’ where x(n) is the input and y(n) is the output

Detailed Solution for Test: Continuous Time Signals - Question 8

Here the input is bounded and the output is also bounded.

Hence the system is stable.

The system is non-linear as it follows y(n) = x3(n).

The system is time-invariant as no operations are made on n.

Test: Continuous Time Signals - Question 9

For a periodic signal v(t) = 30 sin100t + 10 cos300t + 6 sin(500t + π/4), the fundamental frequency in rad/s is _____.

Detailed Solution for Test: Continuous Time Signals - Question 9

Given, the signal

V (t) = 30 sin 100t + 10 cos 300 t + 6 sin (500t+π/4)

So, we have

ω= 100 rads

ω= 300 rads

ω= 500 rads

∴ The respective time periods are

So, the fundamental time period of the signal is

as, 

∴ The fundamental frequency,

*Answer can only contain numeric values
Test: Continuous Time Signals - Question 10

A moving average function is given by . If the input u is a sinusoidal signal of frequency , then in steady state, the output will lag u (in degree) by


Detailed Solution for Test: Continuous Time Signals - Question 10

Concept:

Definite Integral:

If

Calculation:

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