GATE EE 2024 | Continuous Time Signal Fourier Transform Question 1 | Signals and Systems

GATE EE 2024

Numerical

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Let $X(\omega)$ be the Fourier transform of the signal

$x(t) = e^{-t^4} \cos t, \quad -\infty < t < \infty$.

The value of the derivative of $X(\omega)$ at $\, \omega = 0$ is ______ (rounded off to 1 decimal place).

Your input ____

GATE EE 2014 Set 3

MCQ (Single Correct Answer)

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A function f(t) is shown in the figure. GATE EE 2014 Set 3 Signals and Systems - Continuous Time Signal Fourier Transform Question 11 English

The Fourier transform F($$\mathrm\omega$$) of f(t) is

real and even function of $$\mathrm\omega$$

real and odd function of $$\mathrm\omega$$

imaginary and odd function of $$\mathrm\omega$$

imaginary and even function of $$\mathrm\omega$$

GATE EE 2014 Set 3

MCQ (Single Correct Answer)

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A signal is represented by $$$x\left(t\right)=\left\{\begin{array}{l}1\;\;\;\left|t\right|\;<\;1\\0\;\;\;\left|t\right|\;>\;1\end{array}\right.$$$ The Fourier transform of the convolved signal y(t)=x(2t) * x(t/2) is

$$\frac4{\omega^2}\sin\left(\frac\omega2\right)\sin\left(2\omega\right)$$

$$\frac4{\omega^2}\sin\left(\frac\omega2\right)$$

$$\frac4{\omega^2}\sin\left(2\omega\right)$$

$$\frac4{\omega^2}\sin^2\left(\omega\right)$$

GATE EE Subjects

Electromagnetic Fields

Time Varying Fields Electrostatics Magnetostatics

Signals and Systems

Linear Time Invariant Systems Continuous and Discrete Time Signals Continuous Time Signal Fourier Transform Continuous Time Periodic Signal Fourier Series Discrete Time Signal Z Transformation Miscellaneous Continuous Time Signal Laplace Transform Sampling Theorem

Engineering Mathematics

Linear Algebra Differential Equations Calculus Probability and Statistics Numerical Methods Vector Calculus Transform Theory Complex Variable

General Aptitude

Verbal Ability Logical Reasoning Numerical Ability

Power Electronics

Choppers and Commutation Techniques Ac Voltage Controllers Single and Three Phase Rectifier Power Semiconductor Devices Inverters

Power System Analysis

Parameters and Performance of Transmission Lines Power Generation Cost Power System Stability Symmetrical Components and Symmetrical and Unsymmetrical Faults Circuit Breaker Switch Gear and Protection Per Unit System Load Flow Studies High Voltage Dc Transmission Generating Power Station

Analog Electronics

Diode Circuits and Applications Bjt and Mosfet Biasing Small Signal Modeling Feedback Amplifiers and Oscillator Circuits Operational Amplifier Frequency Response 555 Timer

Control Systems

Time Response Analysis Block Diagram and Signal Flow Graph Polar Nyquist and Bode Plot State Variable Analysis Root Locus Techniques Basics of Control System Routh Hurwitz Stability Controller and Compensator

Digital Electronics

Sequential Circuits Microprocessor Boolean Algebra Analog to Digital and Digital to Analog Converter Combinational Circuits Minimization Logic Families and Memories Logic Gates

Electrical Machines

Induction Machines D.C Machines Synchronous Machines Transformers

Electric Circuits

Three Phase Circuits Transient Response Graph Theory Two Port Networks Sinusoidal Steady State Analysis Network Elements Network Theorems

Electrical and Electronics Measurement

Error Analysis and Measurement Basic of Indicating Instruments Potentiometer and Instrument Transformers Measurement of Resistance and A.C Bridges Measurement of Energy and Power Digital Voltmeters Questions Cathode Ray Oscilloscope