1
GATE ECE 2016 Set 3
+2
-0.6
The ROC (region of convergence) of the z-transform of a discrete-time signal is represented by the shaded region in the z-plane. If the signal $$x\left[ n \right] = \,{\left( {2.0} \right)^{\left| n \right|}}$$ , $$- \infty < n < + \infty$$ then the ROC of its z-transform is represented by
A B C D 2
GATE ECE 2016 Set 1
Numerical
+2
-0
A sequence x$$\left[ n \right]$$ is specified as $$\left[ {\matrix{ {x\left[ n \right]} \cr {x\left[ {n - 1} \right]} \cr } } \right] = {\left[ {\matrix{ 1 \cr 1 \cr } \,\matrix{ 1 \cr 0 \cr } } \right]^n}\left[ {\matrix{ 1 \cr 0 \cr } } \right]$$, for n $$\ge$$2.
The initial conditions are x$$\left[ 0 \right]$$ = 1, x$$\left[ 1 \right]$$=1 and x$$\left[ n \right]$$=0 for n< 0. The value of x$$\left[ 12 \right]$$ is _____________________.
3
GATE ECE 2015 Set 3
+2
-0.6
A realization of a stable discrete time system is shown in the figure. If the system is excited by a unit step sequence input x[n ] , the response y[ n] is A
$$4{\left( { - {1 \over 3}} \right)^n}u\left[ n \right] - 5{\left( { - {2 \over 3}} \right)^n}u\left[ n \right]$$
B
$$5{\left( { - {2 \over 3}} \right)^n}u\left[ n \right] - 3{\left( { - {1 \over 3}} \right)^n}u\left[ n \right]$$
C
$$5{\left( {{1 \over 3}} \right)^n}u\left[ n \right] - 5{\left( {{2 \over 3}} \right)^n}u\left[ n \right]$$
D
$$5{\left( {{2 \over 3}} \right)^n}u\left[ n \right] - 5{\left( {{1 \over 3}} \right)^n}u\left[ n \right]$$
4
GATE ECE 2015 Set 3
+2
-0.6
Suppose x $$\left[ n \right]$$ is an absolutely summable discrete-time signal. Its z-transform is a rational function with two poles and two zeroes. The poles are at z = ± 2j. Which one of the following statements is TRUE for the signal x=$$\left[ n \right]$$ ?
A
It is a finite duration signal.
B
It is a causal signal.
C
It is a non-causal signal.
D
It is a periodic signal.
GATE ECE Subjects
Network Theory
Control Systems
Electronic Devices and VLSI
Analog Circuits
Digital Circuits
Microprocessors
Signals and Systems
Communications
Electromagnetics
General Aptitude
Engineering Mathematics
EXAM MAP
Joint Entrance Examination