1
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
A
provide zero phase shift for all frequencies
B
provide constant phase shift for all frequencies
C
provide linear phase shift that is proportional to frequency
D
provide a phase shift that is inversely proportional to frequency
2
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
$$g\left( 0 \right) = 0,\,\,g\left( 1 \right) = g\left( 2 \right) = 1,\,g\left( 3 \right) = g\left( 4 \right) = .... = 0$$ GATE EE 2007 Signals and Systems - Linear Time Invariant Systems Question 5 English

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
$$\left[ { - 1/2,2} \right]$$
3
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
$$\alpha = {\beta ^{ - \left( {1/3} \right)}}$$
4
GATE EE 2007
MCQ (Single Correct Answer)
+2
-0.6
A signal $$x(t)$$ is given by
$$x\left( t \right) = \left\{ {\matrix{ {1, - {\raise0.5ex\hbox{$\scriptstyle T$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 4$}} < t \le {\raise0.5ex\hbox{$\scriptstyle {3T}$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 4$}}} \cr { - 1,{\raise0.5ex\hbox{$\scriptstyle {3T}$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 4$}} < t \le {\raise0.5ex\hbox{$\scriptstyle {7T}$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 4$}},\,\,\,} \cr { - x\left( {t + T} \right)} \cr } } \right.$$ Which among the following gives the fundamental Fourier term of $$x(t)$$?
A
$${4 \over \pi }\cos \left( {{{\pi T} \over T} - {\pi \over 4}} \right)$$
B
$${\pi \over 4}\cos \left( {{{\pi t} \over {2T}} + {\pi \over 4}} \right)$$
C
$${4 \over \pi }sin\left( {{{\pi t} \over T} - {\pi \over 4}} \right)$$
D
$${\pi \over 4}sin\left( {{{\pi t} \over {2T}} + {\pi \over 4}} \right)$$
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