1
GATE ECE 2015 Set 3
Numerical
+2
-0
Two sequence $${x_1}\left[ n \right]$$ and $${x_2}\left[ n \right]$$ have the same energy.
Suppose $${x_1}\left[ n \right]$$ $$= \alpha \,{0.5^n}\,u\left[ n \right],$$ where $$\alpha$$ is a positive real number and $$u\left[ n \right]\,$$ is the unit step sequence. Assume $${x_2}\left[ n \right] = \,\left\{ {\matrix{ {\sqrt {1.5} } & {for\,\,\,n = 0,1} \cr 0 & {otherwise} \cr } } \right.$$\$

Then the value of $$\,\alpha$$ is________.

2
GATE ECE 2014 Set 2
Numerical
+2
-0
Consider a discrete-time signal
$$x\left[ n \right] = \left\{ {\matrix{ {n\,\,for\,\,0 \le n \le 10} \cr {0\,\,otherwise} \cr } } \right.$$

If $$y\left[ n \right]$$ is the convolution of $$x\left[ n \right]$$ with itself, the value of $$y\left[ 4 \right]$$ is

3
GATE ECE 2012
+2
-0.6
Let $$y\left[ n \right]$$ denote the convolution of $$h\left[ n \right]$$ and $$g\left[ n \right]$$, where $$h\left[ n \right]$$ $$= \,{\left( {1/2} \right)^2}\,\,u\left[ n \right]$$ and $$g\left[ n \right]\,$$ is a causal sequence. If $$y\left[ 0 \right]\,$$ $$= \,1$$ and $$y\left[ 1 \right]\,$$ $$= \,1/2,$$ then $$g\left[ 1 \right]$$ equals
A
0
B
1/2
C
1
D
3/2
4
GATE ECE 2011
+2
-0.6
Two system $${H_1}\left( z \right)$$ and $${H_2}\left( z \right)$$ are connected in cascade as shown below. The overall output $$y\left( n \right)$$ is the same as the input $$x\left( n \right)$$ with a one unit delay. The transfer function of the second system $${H_2}\left( z \right)$$ is
A
$${{\left( {1 - 0.6\,{z^{ - 1}}} \right)} \over {{z^{ - 1}}\left( {1 - 0.4\,{z^{ - 1}}} \right)}}\,$$
B
$${{{z^{ - 1}}\left( {1 - 0.6\,{z^{ - 1}}} \right)} \over {\left( {1 - 0.4\,{z^{ - 1}}} \right)}}$$
C
$${{{z^{ - 1}}\left( {1 - 0.4\,{z^{ - 1}}} \right)} \over {\left( {1 - 0.6\,{z^{ - 1}}} \right)}}$$
D
$${{\left( {1 - 0.4\,{z^{ - 1}}} \right)} \over {{z^{ - 1}}\left( {1 - 0.6\,{z^{ - 1}}} \right)}}$$
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