GATE ECE 2023 | Fourier Transform Question 2 | Signals and Systems

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

$${E \over 4}$$

$${E \over 2}$$

GATE ECE 2023

MCQ (Single Correct Answer)

-0.33

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

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

$$\sqrt \pi {e^{{{{\omega ^2}} \over 2}}}$$

$${{{e^{ - {{{\omega ^2}} \over 4}}}} \over {2\sqrt \pi }}$$

$$\sqrt \pi {e^{ - {{{\omega ^2}} \over 4}}}$$

$$\sqrt \pi {e^{ - {{{\omega ^2}} \over 2}}}$$

GATE ECE 2016 Set 2

Numerical

-0

The energy of the signal x(t) =$${{\sin (4\pi t)} \over {4\pi t}}$$ is ___________.

Your input ____

GATE ECE 2016 Set 3

MCQ (Single Correct Answer)

-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

$${{\sin (t)} \over {\pi t}}$$

$${{\sin (2t)} \over {\pi t}}$$

$${{2\sin (t)} \over {\pi t}}$$

$${\left( {{{\sin (t)} \over {\pi t}}} \right)^2}$$

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

Basic of Control Systems Signal Flow Graph and Block Diagram Time Response Analysis Stability Root Locus Diagram Frequency Response Analysis Compensators 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

Numerical Ability Logical Reasoning Verbal Ability

Electronic Devices and VLSI

Semiconductor Physics PN Junction BJT and FET IC Basics and MOSFET

Analog Circuits

Diodes Bipolar Junction Transistor Frequency Response FET and MOSFET Oscillators Operational Amplifier Feedback Amplifier Power Amplifier 555 Timer

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

Maxwell Equations Transmission Lines Uniform Plane Waves Waveguides Antennas Miscellaneous