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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 2021
MCQ (Single Correct Answer)
+1
-0.33

Consider a real-valued base-band signal $x(t)$. band limited to 10 kHz . The Nyquist rate for the signal $y(t)=x(t) \times \left(1+\frac{t}{2}\right)$ is

A

20 kHz

B

30 kHz

C

60 kHz

D

15 kHz

3
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
$$\sin ({\omega _0}t)$$
4
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 ____
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Network Elements State Equations For Networks Network Graphs Miscellaneous Sinusoidal Steady State Response Network Theorems Two Port Networks Transient Response
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Pin Details of 8085 and Interfacing with 8085 Instruction Set and Programming with 8085
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Discrete Fourier Transform and Fast Fourier Transform Discrete Time Signal Fourier Series Fourier Transform Continuous Time Signal Laplace Transform Fourier Transform Representation of Continuous Time Signal Fourier Series Transmission of Signal Through Continuous Time LTI Systems Miscellaneous Sampling Continuous Time Linear Invariant System Discrete Time Linear Time Invariant Systems Discrete Time Signal Z Transform Transmission of Signal Through Discrete Time Lti Systems
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Probability and Statistics Transform Theory Numerical Methods Calculus Differential Equations Linear Algebra Vector Calculus Complex Variable
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Frequency Response Operational Amplifier Power Amplifier Diodes Oscillators Feedback Amplifier 555 Timer Bipolar Junction Transistor FET and MOSFET
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