1
GATE EE 2007
MCQ (Single Correct Answer)
+2
-0.6
Consider the discrete-time system shown in the figure where the impulse response of $$G\left( z \right)$$ is
$$g\left( 0 \right) = 0,\,\,g\left( 1 \right) = g\left( 2 \right) = 1,\,g\left( 3 \right) = g\left( 4 \right) = .... = 0$$

This system is stable for range of values of $$K$$

A
$$\left[ { - 1,1/2} \right]$$
B
$$\left[ { - 1,1} \right]$$
C
$$\left[ { - 1/2,1} \right]$$
D
$$\left[ { - 1/2,2} \right]$$
2
GATE EE 2007
MCQ (Single Correct Answer)
+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
$$\alpha = {\beta ^{ - \left( {1/3} \right)}}$$
3
GATE EE 2006
MCQ (Single Correct Answer)
+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: $$\arg |H\left( {{e^{j\Omega }}} \right)| = const$$
4
GATE EE 2006
MCQ (Single Correct Answer)
+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
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