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# Test: Introduction to Signals

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## 10 Questions MCQ Test GATE Electrical Engineering (EE) 2023 Mock Test Series | Test: Introduction to Signals

Test: Introduction to Signals for GATE 2022 is part of GATE Electrical Engineering (EE) 2023 Mock Test Series preparation. The Test: Introduction to Signals questions and answers have been prepared according to the GATE exam syllabus.The Test: Introduction to Signals MCQs are made for GATE 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Introduction to Signals below.
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Test: Introduction to Signals - Question 1

### The signal x(t) = A cos(ωt + φ) is:

Detailed Solution for Test: Introduction to Signals - Question 1

All bounded periodic signals are power signals, because they do not converge to a finite value so their energy is infinite and their power is finite.

Test: Introduction to Signals - Question 2

### What is the total energy of the rectangular pulse shown in figure below?

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Test: Introduction to Signals - Question 3

### The auto-correlation function Rx(τ) satisfies which one of the following properties?

Detailed Solution for Test: Introduction to Signals - Question 3

The autocorrelation function of a signal is defined as the measure of similarity or coherence between a signal and its time delayed version. Thus, autocorrelation is the correlation of a signal with itself.

Property of autocorrelation function:

• The autocorrelation function of energy signals exhibits complex conjugate symmetry, which means the real part of autocorrelation function R(τ) is an even function of delay parameter ( τ) and the imaginary part of R(τ) is an odd function of the parameter τ. Thus,

R(τ)=R∗(−τ)

Test: Introduction to Signals - Question 4

The auto-correlation function Rx(τ) of the signal x(t) = V sinωt is given by:

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Test: Introduction to Signals - Question 5

The sampling of a function f(t) = sin(2πf0t) starts from zero-crossing. The signal can be detected, if sampling time T is:

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Because fs ≤ 2f0,

Ts ≤ .

Test: Introduction to Signals - Question 6

What is the power and energy of the unit step sequence u(n) respectively?

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Test: Introduction to Signals - Question 7

Let δ(f) is the delta function the value of integral

Test: Introduction to Signals - Question 8

If a signal f(t) has energy ‘E’ the energy of the signal f(2t) is equal to:

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and

⇒

Test: Introduction to Signals - Question 9

Consider the sequence: x[n] = [- 4 - j5, 1 + j2, 4], the conjugate anti-symmetric part of the sequence is:

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Test: Introduction to Signals - Question 10

The function x(t) is shown in the figure. Even and odd parts of a unit step function u(t) are respectively:

Detailed Solution for Test: Introduction to Signals - Question 10

x(t) = u(t) - u(-t)

u(t) =

u(-t) =

-u(-t) =

Hence,

x(t) = u(t) - u(-t)

even part = [u(t) + u(-t)] / 2 = 1/2

odd part = [u(t) - u(-t)] / 2 = 1/2[x(t)]

## GATE Electrical Engineering (EE) 2023 Mock Test Series

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## GATE Electrical Engineering (EE) 2023 Mock Test Series

20 docs|208 tests