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1
GATE ECE 2025
MCQ (Single Correct Answer)
+1
-0.33

Consider a continuous-time, real-valued signal $f(t)$ whose Fourier transform $F(\omega)=$$\mathop f\limits_{ - \infty }^\infty $$ f(t) \exp (-j \omega t) d t$ exists.

Which one of the following statements is always TRUE?

A
$|F(\omega)| \leq \mathop f\limits_{ - \infty }^\infty|f(t)| d t$
B
$|F(\omega)|>\mathop f\limits_{ - \infty }^\infty|f(t)| d t$
C
$|F(\omega)| \leq \mathop f\limits_{ - \infty }^\infty f(t) d t$
D
$|F(\omega)| \geq \mathop f\limits_{ - \infty }^\infty f(t) d t$
2
GATE ECE 2023
MCQ (Single Correct Answer)
+1
-0.33

Let $$m(t)$$ be a strictly band-limited signal with bandwidth B and energy E. Assuming $${\omega _0} = 10B$$, the energy in the signal $$m(t)\cos {\omega _0}t$$ is

A
$${E \over 4}$$
B
$${E \over 2}$$
C
E
D
2E
3
GATE ECE 2023
MCQ (Single Correct Answer)
+1
-0.33

The Fourier transform $$x(\omega )$$ of $$x(t) = {e^{ - {t^2}}}$$ is

Note : $$\int\limits_{ - \infty }^\infty {{e^{ - {y^2}}}dy = \sqrt \pi } $$

A
$$\sqrt \pi {e^{{{{\omega ^2}} \over 2}}}$$
B
$${{{e^{ - {{{\omega ^2}} \over 4}}}} \over {2\sqrt \pi }}$$
C
$$\sqrt \pi {e^{ - {{{\omega ^2}} \over 4}}}$$
D
$$\sqrt \pi {e^{ - {{{\omega ^2}} \over 2}}}$$
4
GATE ECE 2016 Set 3
MCQ (Single Correct Answer)
+1
-0.3
If the signal x(t) = $${{\sin (t)} \over {\pi t}}*{{\sin (t)} \over {\pi t}}$$ with * denoting the convolution operation, then x(t) is equal to
A
$${{\sin (t)} \over {\pi t}}$$
B
$${{\sin (2t)} \over {\pi t}}$$
C
$${{2\sin (t)} \over {\pi t}}$$
D
$${\left( {{{\sin (t)} \over {\pi t}}} \right)^2}$$
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GATE ECE Subjects
Network Theory
State Equations For Networks Network Elements Network Theorems Two Port Networks Transient Response Sinusoidal Steady State Response Network Graphs Miscellaneous
Control Systems
Basic of Control Systems Signal Flow Graph and Block Diagram Time Response Analysis Stability Root Locus Diagram Frequency Response Analysis Compensators State Space Analysis
Electronic Devices and VLSI
PN Junction Semiconductor Physics IC Basics and MOSFET BJT and FET
Analog Circuits
Diodes Bipolar Junction Transistor Frequency Response FET and MOSFET Oscillators Operational Amplifier Feedback Amplifier Power Amplifier 555 Timer
Digital Circuits
Number System and Code Convertions Boolean Algebra Logic Gates Combinational Circuits Sequential Circuits Semiconductor Memories Logic Families Analog to Digital and Digital to Analog Converters
Microprocessors
Instruction Set and Programming with 8085 Pin Details of 8085 and Interfacing with 8085
Signals and Systems
Representation of Continuous Time Signal Fourier Series Fourier Transform Continuous Time Signal Laplace Transform Discrete Time Signal Fourier Series Fourier Transform Discrete Fourier Transform and Fast Fourier Transform Discrete Time Signal Z Transform Continuous Time Linear Invariant System Discrete Time Linear Time Invariant Systems Transmission of Signal Through Continuous Time LTI Systems Sampling Transmission of Signal Through Discrete Time Lti Systems Miscellaneous
Communications
Fundamentals of Information Theory Noise In Digital Communication Analog Communication Systems Digital Communication Systems Random Signals and Noise
Electromagnetics
Waveguides Antennas Miscellaneous Transmission Lines Maxwell Equations Uniform Plane Waves
General Aptitude
Verbal Ability Logical Reasoning Numerical Ability
Engineering Mathematics
Linear Algebra Calculus Vector Calculus Complex Variable Probability and Statistics Differential Equations Numerical Methods Transform Theory
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