1
GATE ECE 2016 Set 1
+1
-0.3
Consider the sequence
$$x\left[ n \right]$$= $${a^n}u\left[ n \right] + {b^{\partial n}}u\left[ n \right]$$ , where u[n] denotes the unit step sequence and 0<$$\left| a \right| < \left| b \right| < 1.$$
The region of convergence (ROC) of the z-transform of $$\left[ n \right]$$ is
A
$$\left| z \right| > \left| a \right|$$
B
$$\left| z \right| > \left| b \right|$$
C
$$\left| z \right| < \left| a \right|$$
D
$$\left| a \right| < \left| z \right| < \left| b \right|$$
2
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 _____________________
3
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 ____________.
4
GATE ECE 2014 Set 3
+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
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