1
GATE EE 2014 Set 2
MCQ (Single Correct Answer)
+1
-0.3
Consider an LTI system with impulse response $$h\left(t\right)=e^{-5t}u\left(t\right)$$ . If the output of the system is $$y\left(t\right)=e^{-3t}u\left(t\right)-e^{-5t}u\left(t\right)$$ then the input, x(t), is given by
A
$$e^{-3t}u\left(t\right)$$
B
$$2e^{-3t}u\left(t\right)$$
C
$$e^{-5t}u\left(t\right)$$
D
$$2e^{-5t}u\left(t\right)$$
2
GATE EE 2014 Set 1
MCQ (Single Correct Answer)
+1
-0.3
x(t) is nonzero only for $$T_x\;<\;t\;<\;T_x^1$$ , and similarly, y(t) is nonzero only for $$T_y\;<\;t\;<\;T_y^1$$ . Let z(t) be convolution of x(t) and y(t). Which one of the following statements is TRUE?
A
z(t) can be nonzero over an unbounded interval
B
z(t) is nonzero for $$t\;<\;T_x+T_y$$
C
z(t) is zero outside of $$T_x+T_y\;<\;t\;<\;T_x^1+T_y^1$$
D
z(t) is nonzero for $$t\;>\;T_x^1+T_y^1$$
3
GATE EE 2013
MCQ (Single Correct Answer)
+1
-0.3
The impulse response of a system is h(t) = tu(t). For an input u(t − 1), the output is
A
$$\frac{t^2}2u\left(t\right)$$
B
$$\frac{t\left(t-1\right)}2u\left(t-1\right)$$
C
$$\frac{\left(t-1\right)^2}2u\left(t-1\right)$$
D
$$\frac{t^2-1}2u\left(t-1\right)$$
4
GATE EE 2013
MCQ (Single Correct Answer)
+1
-0.3
Two systems 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 h2(t) and h1(t)
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