1
GATE EE 2022
+1
-0.33

Let an input x(t) = 2 sin(10$$\pi$$t) + 5 cos(15$$\pi$$t) + 7 sin(42$$\pi$$t) + 4 cos(45$$\pi$$t) is passed through an LTI system having an impulse response,

$$h(t) = 2\left( {{{\sin (10\pi t)} \over {\pi t}}} \right)\cos (40\pi t)$$

The output of the system is

A
$$2\sin (10\pi t) + 5cos(15\pi t)$$
B
$$5\cos (15\pi t) + 7sin(42\pi t)$$
C
$$7\sin (42\pi t) + 4cos(45\pi t)$$
D
$$2\sin (10\pi t) + 4cos(45\pi t)$$
2
GATE EE 2014 Set 3
+1
-0.3
A function f(t) is shown in the figure. 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 $$\mathrm\omega$$
3
GATE EE 2014 Set 3
+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
$$\frac4{\omega^2}\sin^2\left(\omega\right)$$
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