1
GATE EE 2007
+2
-0.6
A signal is processed by a causal filter with transfer function $$G(s).$$ For a distortion free output signal waveform, $$G(s)$$ must.

$$G\left( z \right) = a{z^{ - 1}} + \beta \,\,{z^{ - 3}}$$ is a low-pass digital filter with a phase characteristic same as that of the above question if

A
$$\alpha = \beta$$
B
$$\alpha = - \beta$$
C
$$\alpha = {\beta ^{\left( {1/3} \right)}}$$
D
$$\alpha = {\beta ^{ - \left( {1/3} \right)}}$$
2
GATE EE 2006
+2
-0.6
A discrete real all pass system has a pole at $$z = 2\angle {30^ \circ };\,$$ it, therefore,
A
also has a pole at $$1/2\angle {30^ \circ }$$
B
has a constant phase response over the $$z$$-plane: $$\arg |H\left( z \right)| = const$$
C
is stable only if it is anticausal
D
has a constant phase response over the unit circle: $$\arg |H\left( {{e^{j\Omega }}} \right)| = const$$
3
GATE EE 2006
+2
-0.6
A continuous-time system is described by $$y\left( t \right) = {e^{ - |x\left( t \right)|}},$$ where $$y(t)$$ is the output and $$x(t)$$ is the input. $$y(t)$$ is bounded
A
only when $$x(t)$$ is bounded
B
only when $$x(t)$$ is non-negative
C
only for $$t \ge 0$$ if $$x(t)$$ is bounded for $$t \ge 0$$
D
even when $$x(t)$$ is not bounded
4
GATE EE 2006
+2
-0.6
$$y\left[ n \right]$$ denotes the output and $$x\left[ n \right]$$ denotes the input of a discrete-time system given by the difference equation $$y\left[ n \right] - 0.8y\left[ {n - 1} \right] = x\left[ n \right] + 1.25\,x\left[ {n + 1} \right].$$ Its right-sided impulse response is
A
causal
B
unbounded
C
periodic
D
non-negative
GATE EE Subjects
Electromagnetic Fields
Signals and Systems
Engineering Mathematics
General Aptitude
Power Electronics
Power System Analysis
Analog Electronics
Control Systems
Digital Electronics
Electrical Machines
Electric Circuits
Electrical and Electronics Measurement
EXAM MAP
Joint Entrance Examination