1
GATE EE 2014 Set 3
MCQ (Single Correct Answer)
+1
-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 10 English The Fourier transform F($$\mathrm\omega$$) of f(t) is
A
real and even function of $$\mathrm\omega$$
B
real and odd function of $$\mathrm\omega$$
C
imaginary and odd function of $$\mathrm\omega$$
D
imaginary and even function of $$\mathrm\omega$$
2
GATE EE 2014 Set 3
MCQ (Single Correct Answer)
+1
-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
A
$$\frac4{\omega^2}\sin\left(\frac\omega2\right)\sin\left(2\omega\right)$$
B
$$\frac4{\omega^2}\sin\left(\frac\omega2\right)$$
C
$$\frac4{\omega^2}\sin\left(2\omega\right)$$
D
$$\frac4{\omega^2}\sin^2\left(\omega\right)$$
3
GATE EE 2014 Set 3
MCQ (Single Correct Answer)
+2
-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?
A
X($$\omega$$) and Y($$\omega$$) are both real.
B
X($$\omega$$) is real and Y($$\omega$$) is imaginary.
C
X($$\omega$$) and Y($$\omega$$) are both imaginary.
D
X($$\omega$$) is imaginary and Y($$\omega$$) is real.
4
GATE EE 2014 Set 3
Numerical
+1
-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 _________.
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