GATE EE 2024 | Continuous Time Signal Fourier Transform Question 2 | Signals and Systems

GATE EE 2024

Numerical

-0

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)

-0.3

A function f(t) is shown in the figure. GATE EE 2014 Set 3 Signals and Systems - Continuous Time Signal Fourier Transform Question 14 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)

-0.3

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

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

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

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

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

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