1
GATE ECE 2008
MCQ (Single Correct Answer)
+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
$$y\left( t \right) = \left( {t + 5} \right)x\left( {t + 5} \right)$$
2
GATE ECE 2008
MCQ (Single Correct Answer)
+2
-0.6
A linear, time-invariant, causal continuous time system has a rational transfer function with simple poles at s = - 2 and s = - 4, and one simple zero at s = - 1. A unit step u(t) is applied at the input of the system. At steady state, the output has constant value of 1. The impulse response of this system is
A
[exp( -2t) + exp( -4t)]u(t)
B
[ -4exp( -2t) + 12 exp( -4t) - exp( -t)]u(t)
C
[ -4 exp( -2t) +12 exp(-4t)]u(t)
D
[-0.5 exp(-2t) +1.5 exp(-4t)]u(t)
3
GATE ECE 2008
MCQ (Single Correct Answer)
+2
-0.6
Let x(t) be the input and y(t) be the output of a continuous time system. Match the system properties P1, P2 and P3 with system relations R1, R2, R3, R4.

Properties


P1 : Linear but NOT time-invariant
P2: Time-invariant but NOT linear
P3: Linear and time-invariant

Relations


R1: y(t) = $${t^2}$$ x(t)
R2: y(t) = t$$\left| {x(t)} \right|$$
R3: y(t) = $$\left| {x(t)} \right|$$
R4: y(t) = x(t-5)
A
(P1, R1), (P2, R3), (P3, R4)
B
(P1, R2), (P2, R3), (P3, R4)
C
(P1, R3), (P2, R1), (P3, R2)
D
(P1, R1), (P2, R2), (P3, R3)
4
GATE ECE 2008
MCQ (Single Correct Answer)
+2
-0.6
The signal x(t) is described by $$x\left( t \right) = \left\{ {\matrix{ {1\,\,\,for\,\, - 1 \le t \le + 1} \cr {0\,\,\,\,\,\,\,\,\,\,\,\,\,\,otherwise} \cr } } \right.$$

Two of the angular frequencies at which its Fourier transform becomes zero are

A
$$\pi ,\,2\pi $$
B
$$0.5\,\pi ,\,1.5\,\pi $$
C
$$0,\,\pi $$
D
$$2\,\pi ,\,2.5\,\pi $$
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
CBSE
Class 12