GATE EE 2024 | Continuous Time Signal Fourier Transform Question 1 | 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 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)

-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

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

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

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

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

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

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

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