1
GATE ECE 2015 Set 2
Numerical
+1
-0
Two casual discrete-time signals $$x\left[ n \right]$$ and $$y\left[ n \right]$$ =$$\sum\limits_{m = 0}^n x \left[ m \right]$$. If the z-transform of y$$\left[ n \right]$$=$${2 \over {z{{(z - 1)}^2}}}$$ , the value of $$x\left[ 2 \right]$$ is _____________________
Your input ____
2
GATE ECE 2014 Set 4
Numerical
+1
-0
The sequence x $$\left[ n \right]$$ = $${0.5^n}$$ u[n], where u$$\left[ n \right]$$ is the unit step sequence, is convolved with itself to obtain y $$\left[ n \right]$$ . Then $$\sum\limits_{n = \infty }^{ + \infty } y \left[ n \right]$$ is ____________.
Your input ____
3
GATE ECE 2014 Set 3
MCQ (Single Correct Answer)
+1
-0.3
For an all-pass system H(z)= $${{({z^{ - 1}} - b)} \over {(1 - a{z^{ - 1}})}}$$ where $$\left| {H({e^{ - j\omega }})} \right| = \,1$$ , for all $$\omega $$. If Re (a) $$ \ne $$ 0,$${\mathop{\rm Im}\nolimits} (a) \ne 0$$ then b equals
A
a
B
a*
C
1/a*
D
1/a
4
GATE ECE 2014 Set 2
MCQ (Single Correct Answer)
+1
-0.3
Let x$$\left[ n \right]$$ = x$$\left[- n \right]$$ . Let X(z) be the z-transform of x$$\left[ n \right]$$. if 0.5 +j 0.25 is a zero of X(z), which one of the folowing must also be a zero of X (z)
A
0.5 - j0.25
B
1/ (0.5 + j0.25)
C
1/ (0.5 - j 0.25)
D
2 + j4
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