GATE ECE 2023 | Fourier Transform Question 3 | 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 1

MCQ (Single Correct Answer)

-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?

$${e^{j{\omega _0}t}}u(t)$$

$$\cos ({\omega _0}t)$$

$${e^{j{\omega _0}t}}$$

$$\sin ({\omega _0}t)$$

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Questions Asked from Marks 1

GATE ECE 2025 (1) GATE ECE 2023 (2) GATE ECE 2016 Set 2 (1) GATE ECE 2016 Set 1 (1) GATE ECE 2016 Set 3 (1) GATE ECE 2006 (1) GATE ECE 2004 (1) GATE ECE 2002 (1) GATE ECE 2001 (1) GATE ECE 2000 (1) GATE ECE 1999 (2) GATE ECE 1998 (3) GATE ECE 1997 (1) GATE ECE 1996 (1)

GATE ECE Subjects

Signals and Systems

Network Theory

Control Systems

Digital Circuits

General Aptitude

Electronic Devices and VLSI

Analog Circuits

Engineering Mathematics

Microprocessors

Communications

Electromagnetics