GATE EE 2014 Set 3 | GATE EE Year Wise Previous Years Questions

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 2014 Set 3

MCQ (Single Correct Answer)

-0.6

A differentiable non constant even function x(t) has a derivative y(t), and their respective Fourier Transforms are X($$\omega$$) and Y($$\omega$$). Which of the following statements is TRUE?

X($$\omega$$) and Y($$\omega$$) are both real.

X($$\omega$$) is real and Y($$\omega$$) is imaginary.

X($$\omega$$) and Y($$\omega$$) are both imaginary.

X($$\omega$$) is imaginary and Y($$\omega$$) is real.

GATE EE 2014 Set 3

Numerical

-0

For the signal f(t) = 3 sin8$$\mathrm\pi$$t + 6sin12$$\mathrm\pi$$t + sin14$$\mathrm\pi$$t, the minimum sampling frequency (in Hz) satisfying the Nyquist criterion is _________.

Your input ____

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