1
GATE ECE 2013
+1
-0.3
Two system with impulse responses h1(t) and h2(t) are connected in cascade. Then the overall impulse response of the cascaded system is given by
A
Product of h1(t) and h2(t).
B
Sum of h1(t) and h2(t).
C
Convolution of h1(t) and h2(t).
D
Subtraction of h1(t) and h2(t)
2
GATE ECE 2013
+1
-0.3
The impulse response of a system is h(t) = t u(t). For an input u(t - 1), the output is
A
$${{{t^2}} \over 2}u\left( t \right)$$
B
$${{t\left( {t - 1} \right)} \over 2}u\left( {t - 1} \right)$$
C
$${{{{\left( {t - 1} \right)}^2}} \over 2}u\left( {t - 1} \right)\,$$
D
$${{{t^2} - 1} \over 2}u\left( {t - 1} \right)$$
3
GATE ECE 2011
+1
-0.3
The differential equation $$100{{{d^2}y} \over {dt}} - 20{{dy} \over {dt}} + y = x\left( t \right)$$ describes a system with an input x(t) and output y(t). The system, which is initially relaxed, is excited by a unit step input. The output y(t) can be represented by the waveform
A
B
C
D
4
GATE ECE 2008
+1
-0.3
The input and output of a continuous system are respectively denoted by x(t) and y(t). Which of the following descriptions corresponds to a causal system?
A
$$y\left( t \right) = x\left( {t - 2} \right) + x\left( {t + 4} \right)$$
B
$$y\left( t \right) = \left( {t - 4} \right)x\left( {t + 1} \right)$$
C
$$y\left( t \right) = \left( {t + 4} \right)x\left( {t - 1} \right)$$
D
$$y\left( t \right) = \left( {t + 5} \right)x\left( {t + 5} \right)$$
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