GATE ECE 2002 | GATE ECE Year Wise Previous Years Questions

GATE ECE 2002

MCQ (Single Correct Answer)

-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

$${e^{2t}}u\left( t \right) - 2\,{e^{ - t}}u\left( t \right)$$

$$ - {e^{2t}}u\left( { - t} \right) + 2\,{e^{ - t}}u\left( t \right)$$

$$ - {e^{2t}}u\left( { - t} \right) - 2\,{e^{ - t}}u\left( t \right)$$

$${e^{2t}}u\left( { - t} \right) - 2\,{e^{ - t}}u\left( t \right)$$

GATE ECE 2002

MCQ (Single Correct Answer)

-0.3

Convolution of x(t + 5) with impulse function $$\delta \left( {t\, - \,7} \right)$$ is equal to

$$X\left( {t - 12} \right)$$

$$X\left( {t + 12} \right)$$

$$X\left( {t - 2} \right)$$

$$X\left( {t + 2} \right)$$

GATE ECE 2002

Subjective

-0

A deterministic signal x(t) = $$\cos (2\pi t)$$ is passed through a differentiator as shown in Figure. GATE ECE 2002 Signals and Systems - Continuous Time Linear Invariant System Question 1 English

(a) Determine the autocorrelation R_xx($$\tau $$) and the power spectral density S_xx(f).
(b) Find the output power spectral density S_yy( f ).
(c) Evaluate R_xy(0) and R_xy(1/4).

GATE ECE 2002

MCQ (Single Correct Answer)

-0.6

If the impulse response of a discrete-time system is $$h\left[ n \right]\, = \, - {5^n}\,\,u\left[ { - n\, - 1} \right],$$ then the system function $$H\left( z \right)\,\,\,$$ is equal to

$${{ - z} \over {z - 5}}$$ and the system is stable.

$${z \over {z - 5}}$$ and the system is stable.

$${{ - z} \over {z - 5}}$$ and the system is unstable.

$${z \over {z - 5}}$$ and the system is unstable.

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