1
GATE ECE 2022
Numerical
+1
-0.33

Let x1(t) = e$$-$$t u(t) and x2(t) = u(t) $$-$$ u(t $$-$$ 2), where u( . ) denotes the unit step function. If y(t) denotes the convolution of x1(t) and x2(t), then $$\mathop {\lim }\limits_{t \to \infty } y(t)$$ = __________ (rounded off to one decimal place).

2
GATE ECE 2022
MCQ (More than One Correct Answer)
+1
-0.33

The outputs of four systems (S1, S2, S3 and S4) corresponding to the input signal sin(t), for all time t, are shown in the figure.

Based on the given information, which of the four systems is/are definitely NOT LTI (linear and time-invariant)? A
S1
B
S2
C
S3
D
S4
3
GATE ECE 2016 Set 1
Numerical
+1
-0
A continuous-time sinusoid of frequency 33 Hz is multiplied with a periodic Dirac impulse train of frequency 46 Hz. The resulting signal is passed through an ideal analog low-pass filter with a cutoff frequency of 23Hz. The fundamental frequency (in Hz) of the output is _____________________.
4
GATE ECE 2014 Set 4
+1
-0.3
A real - values signal x(t) limited to the frequency band $$\left| f \right| \le {W \over 2}$$ is passed through a linear time invariant system whose frequency response is
$$H(f) = \left\{ {\matrix{ {{e^{ - j4\pi f}},} & {\left| f \right| \le \,{W \over 2}} \cr {0,} & {\left| f \right| > \,{W \over 2}} \cr } } \right.$$

The output of the system is

A
x(t + 4)
B
x(t - 4)
C
x(t + 2)
D
x(t - 2)
GATE ECE Subjects
Network Theory
Control Systems
Electronic Devices and VLSI
Analog Circuits
Digital Circuits
Microprocessors
Signals and Systems
Communications
Electromagnetics
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