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1
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
$$\sqrt \pi {e^{ - {{{\omega ^2}} \over 2}}}$$
2
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
$${\left( {{{\sin (t)} \over {\pi t}}} \right)^2}$$
3
GATE ECE 2016 Set 2
Numerical
+1
-0
The energy of the signal x(t) =$${{\sin (4\pi t)} \over {4\pi t}}$$ is ___________.
Your input ____
4
GATE ECE 2016 Set 1
MCQ (Single Correct Answer)
+1
-0.3
Which one of the following is an eight function of the class of all continuous-time, linear, time- invariant systems u(t) denotes the unit-step function?
A
$${e^{j{\omega _0}t}}u(t)$$
B
$$\cos ({\omega _0}t)$$
C
$${e^{j{\omega _0}t}}$$
D
$$\sin ({\omega _0}t)$$
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GATE ECE Subjects
Signals and Systems
Representation of Continuous Time Signal Fourier Series Discrete Time Signal Fourier Series Fourier Transform Discrete Time Signal Z Transform Continuous Time Linear Invariant System Transmission of Signal Through Continuous Time LTI Systems Discrete Time Linear Time Invariant Systems Sampling Continuous Time Signal Laplace Transform Discrete Fourier Transform and Fast Fourier Transform Transmission of Signal Through Discrete Time Lti Systems Miscellaneous Fourier Transform
Network Theory
State Equations For Networks Network Elements Network Theorems Two Port Networks Transient Response Sinusoidal Steady State Response Network Graphs Miscellaneous
Control Systems
Signal Flow Graph and Block Diagram Time Response Analysis Compensators Basic of Control Systems Frequency Response Analysis Stability Root Locus Diagram State Space Analysis
Digital Circuits
Logic Gates Boolean Algebra Analog to Digital and Digital to Analog Converters Sequential Circuits Combinational Circuits Logic Families Number System and Code Convertions Semiconductor Memories
General Aptitude
Verbal Ability Logical Reasoning Numerical Ability
Electronic Devices and VLSI
PN Junction Semiconductor Physics IC Basics and MOSFET BJT and FET
Analog Circuits
Bipolar Junction Transistor FET and MOSFET Oscillators Operational Amplifier 555 Timer Frequency Response Diodes Feedback Amplifier Power Amplifier
Engineering Mathematics
Linear Algebra Calculus Vector Calculus Complex Variable Probability and Statistics Differential Equations Numerical Methods Transform Theory
Microprocessors
Instruction Set and Programming with 8085 Pin Details of 8085 and Interfacing with 8085
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
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