1
GATE ECE 2002
+2
-0.6
If the impulse response of a discrete-time system is $$h\left[ n \right]\, = \, - {5^n}\,\,u\left[ { - n\, - 1} \right],$$ then the system function $$H\left( z \right)\,\,\,$$ is equal to
A
$${{ - z} \over {z - 5}}$$ and the system is stable.
B
$${z \over {z - 5}}$$ and the system is stable.
C
$${{ - z} \over {z - 5}}$$ and the system is unstable.
D
$${z \over {z - 5}}$$ and the system is unstable.
2
GATE ECE 2002
+1
-0.3
Consider a sampled signal $$y\left( t \right) = 5 \times {10^{ - 6}}\,x\left( t \right)\,\,\sum\limits_{n = - \infty }^{ + \infty } {\delta \left( {t - n{T_s}} \right)}$$

where $$x\left( t \right) = 10\,\,\cos \,\left( {8\pi \times {{10}^3}} \right)\,\,t$$ and
$${T_s} = 100\,\,\mu \sec .$$ When $$y\left( t \right)$$ is passed through an ideal low-pass filter with a cutoff frequency of 5 KHz, the output of the filter is

A
$$5 \times {10^{ - 6}}\,\,\cos \,\left( {8\pi \times {{10}^3}} \right)\,\,t$$
B
$$5 \times {10^{ - 5}}\,\,\cos \,\left( {8\pi \times {{10}^3}} \right)\,\,t$$
C
$$5 \times {10^{ - 1}}\,\,\cos \,\left( {8\pi \times {{10}^3}} \right)\,\,t$$
D
$$10\cos \,\left( {8\pi \times {{10}^3}} \right)\,\,t$$
3
GATE ECE 2002
+1
-0.3
A linear phase channel with phase delay $${\tau _p}$$ and group delay $${\tau _g}$$ must have
A
$$\,{\tau _p} = {\tau _g} =$$ constant
B
$${\tau _p}\infty \,\,f\,and\,{\tau _g}\infty \,f$$
C
$${\tau _p}$$ = constant and $${\tau _g}\infty \,f$$
D
$${\tau _p}\infty \,f\,and\,\,{\tau _g}$$ =constant ($$f$$denotes frequency)
4
GATE ECE 2002
+2
-0.6
In Fig. m(t) = $$= {{2\sin 2\pi t} \over t}$$, $$s(t) = \cos \,200\pi t\,\,andn(t) = {{\sin 199\pi t} \over t}$$.

The output y(t) will be

A
$${{\sin 2\pi \,t} \over t}$$
B
$${{\sin 2\pi \,t} \over t}\, + {{\sin \pi \,t} \over t}\cos \,3\pi t$$
C
$${{\sin 2\pi \,t} \over t}\, + {{\sin 0.5\,\pi \,t} \over t}\cos \,1.5\pi t$$
D
$${{\sin 2\pi \,t} \over t}\, + {{\sin \pi \,t} \over t}\,\cos \,0.75\pi t\,\,$$
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