1
GATE ECE 2010
MCQ (Single Correct Answer)
+2
-0.6
The transfer function of a discrete time LTI system is given by
$$H\left( z \right) = {{2 - {3 \over 4}{z^{ - 1}}} \over {1 - {3 \over 4}{z^{ - 1}} + {1 \over 8}{z^{ - 2}}}}$$

Consider the following statements:
S1: The system is stable and causal for $$ROC:\,\,\,\left| z \right| > \,1/2$$
S2: The system is stable but not causal for $$ROC:\,\,\,\left| z \right| < \,1/4$$
S3: The system is neither stable nor causal for $$ROC:\,\,1/4\, < \,\left| z \right| < \,{\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}$$

Which one of the following statements is valid?

A
Both S1 and S2 are true
B
Both S2 and S3 are true
C
Both S1 and S3 are true
D
S1, S2 and S3 are all true
2
GATE ECE 2010
MCQ (Single Correct Answer)
+1
-0.3
Consider the pulse shape s(t) as shown. The impulse response h(t) of the filter matched to this pulse is GATE ECE 2010 Signals and Systems - Transmission of Signal Through Continuous Time LTI Systems Question 29 English
A
GATE ECE 2010 Signals and Systems - Transmission of Signal Through Continuous Time LTI Systems Question 29 English Option 1
B
GATE ECE 2010 Signals and Systems - Transmission of Signal Through Continuous Time LTI Systems Question 29 English Option 2
C
GATE ECE 2010 Signals and Systems - Transmission of Signal Through Continuous Time LTI Systems Question 29 English Option 3
D
GATE ECE 2010 Signals and Systems - Transmission of Signal Through Continuous Time LTI Systems Question 29 English Option 4
3
GATE ECE 2010
MCQ (Single Correct Answer)
+1
-0.3
A system with the transfer function $${{Y(s)} \over {X(s)}} = {s \over {s + p}}\,\,$$ has an output
$$y(t) = \cos \left( {2t - {\pi \over 3}} \right)\,$$ for the input signal
$$x(t) = p\cos \left( {2t - {\pi \over 2}} \right)$$. Then, the system parameter 'p' is
A
$$\sqrt 3 $$
B
$$\,{2 \over {\sqrt 3 \,}}$$
C
1
D
$${{\sqrt 3 \,} \over 2}$$
4
GATE ECE 2010
MCQ (Single Correct Answer)
+2
-0.6
The Nyquist sampling rate for the signal $$s(t) = {{\sin \,(500\pi t)} \over {\pi \,t}} \times {{\sin \,(700\pi t)} \over {\pi \,t}}$$ is given by
A
400 Hz
B
600 Hz
C
1200 Hz
D
1400 Hz
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