1
GATE ECE 2002
MCQ (Single Correct Answer)
+1
-0.3
The Fourier transform F $$\left\{ {{e^{ - t}}u(t)} \right\}$$ is equal to $${1 \over {1 + j2\pi f}}$$. Therefore, $$F\left\{ {{1 \over {1 + j2\pi t}}} \right\}$$ is
A
$${e^f}u(f)$$
B
$${e^{ - f}}$$ u(f)
C
$${e^f}u(f)$$
D
$${e^{ - f}}$$u(-f)
2
GATE ECE 2002
MCQ (Single Correct Answer)
+2
-0.6
The Laplace transform of a continuous - time signal x(t) is $$X\left( s \right) = {{5 - s} \over {{s^2} - s - 2}}$$. If the Fourier transform of tyhis signal exists, then x(t) is
A
$${e^{2t}}u\left( t \right) - 2\,{e^{ - t}}u\left( t \right)$$
B
$$- {e^{2t}}u\left( { - t} \right) + 2\,{e^{ - t}}u\left( t \right)$$
C
$$- {e^{2t}}u\left( { - t} \right) - 2\,{e^{ - t}}u\left( t \right)$$
D
$${e^{2t}}u\left( { - t} \right) - 2\,{e^{ - t}}u\left( t \right)$$
3
GATE ECE 2002
MCQ (Single Correct Answer)
+1
-0.3
Convolution of x(t + 5) with impulse function $$\delta \left( {t\, - \,7} \right)$$ is equal to
A
$$X\left( {t - 12} \right)$$
B
$$X\left( {t + 12} \right)$$
C
$$X\left( {t - 2} \right)$$
D
$$X\left( {t + 2} \right)$$
4
GATE ECE 2002
Subjective
+5
-0
A deterministic signal x(t) = $$\cos (2\pi t)$$ is passed through a differentiator as shown in Figure.
(a) Determine the autocorrelation Rxx ($$\tau$$) and the power spectral density Sxx(f).
(b) Find the output power spectral density Syy( f ).
(c) Evaluate Rxy(0) and Rxy(1/4).
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