1
GATE ECE 2009
+1
-0.3
The ROC of Z-transform of the discrete time sequence
x(n)= $${\left( {{1 \over 3}} \right)^{n}}u(n) - {\left( {{1 \over 2}} \right)^{ n}}\,u( - n - 1)$$ is
A
$${1 \over 3} < \left| {z\,} \right| < {1 \over 2}$$
B
$$\left| {z\,} \right| > {1 \over 2}$$
C
$$\left| {z\,} \right| < {1 \over 2}$$
D
$$2 < \left| {z\,} \right| < 3$$
2
GATE ECE 2009
+2
-0.6
Consider a system whose input x and output y are related by the equation $$y(t) = \int\limits_{ - \infty }^\infty {x(t - \tau )\,h(2\tau )\,d\tau }$$\$

Where h(t) is shown in the graph.

Which of the following four properties are possessed by the system?

BIBO: Bounded input gives a bounded output.
Causal: The system is casual.
LP: The system is low pass.
LTI: The system is linear and time- invariant.
A
Causal, LP
B
BIBO, LTI
C
BIBO, Causal, LTI
D
LP, LTI
3
GATE ECE 2009
+2
-0.6
A system with transfer function H(z) has impulse response h(.) defined as h(2) = 1, h(3) = - 1 and h (k) = 0 otherwise. Consider the following statements.
S1: H(z) is a low-pass filter.
S2: H(z) is an FIR filter.

Which of the following is correct?

A
Only S2 is true
B
Both S1 and S2 are false.
C
Both S1 and S2 are true, and S2 is a reason for S1.
D
Both S1 and S2 are true, but S2 is not a reason for S1.
4
GATE ECE 2009
+2
-0.6
An LTI system having transfer function $${{{s^2} + 1} \over {{s^2} + 2s + 1}}$$ and input x(t) = sin (t + 1) is in steady state. The output is sampled at a rate $${\omega _s}\,\,rad/s$$ to obtain the final output {y(k)}. Which of the following is true?
A
y(.) is zero for all sampling frequencies $${\omega _s}$$
B
y(.) is nonzero for all sampling frequencies $${\omega _s}$$
C
y(.) is nonzero for $${\omega _s}$$ > 2, but zero for $${\omega _s}$$ < 2
D
y(.) is zero for $${\omega _s}$$ > 2, but nonzero for $${\omega _s}$$ < 2
GATE ECE Papers
2024
2023
2022
2021
2019
2018
2013
2012
2011
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
EXAM MAP
Medical
NEET