GATE ECE 2002 | Fourier Transform Question 18 | Signals and Systems

The Fourier transform F $$\left\{ {{e^{ - t}}u(t)} \right\}$$ is equal to $${1 \over {1 + j2\pi f}}$$. Therefore, $$F\left\{ {{1 \over {1 + j2\pi t}}} \right\}$$ is

$${e^f}u(f)$$

$${e^{ - f}}$$ u(f)

$${e^f}u(f)$$

$${e^{ - f}}$$u(-f)

GATE ECE 2001

MCQ (Single Correct Answer)

-0.3

If a signal f(t) has energy E, the energy of the signal f(2t) is equal to

E/2

GATE ECE 2000

MCQ (Single Correct Answer)

-0.3

The Fourier Transform of the signal $$x(t) = {e^{ - 3{t^2}}}$$ is of the following form, where A and B are constants:

$$A{e^{ - B\left| f \right|}}$$

$$A{e^{ - Bf}}$$

$$A + B{\left| f \right|^2}$$

$$A{e^{ - B{f^2}}}$$

GATE ECE 1999

MCQ (Single Correct Answer)

-0.3

A signal x(t) has a Fourier transform X ($$\omega $$). If x(t) is a real and odd function of t, then X($$\omega $$) is

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

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

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

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

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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