1
GATE ECE 2018
+1
-0.33
A discrete time all-pass system has two of its poles at 0.25$$\angle 0^\circ$$ and $$\angle 30^\circ$$. Which one of the following statements about the system is TRUE?
A
It has two more poles at 0.5$$\angle 30^\circ$$ and 4$$\angle 0^\circ$$.
B
It is stable only when the impulse response is two-sided.
C
It has constant phase response over all frequencies.
D
It has constant phase response over the entire z-plane.
2
GATE ECE 2016 Set 3
+1
-0.3
A discrete-time signal$$x\left[ n \right]\, = \delta \left[ {n - 3} \right]\, + 2\delta \left[ {n - 5} \right]$$ has z-transform x(z). If Y (z)=X (-z) is the z-transform of another signal y$$\left[ n \right]$$, then
A
$$y\left[ n \right] = x\left[ n \right]$$
B
$$y\left[ n \right] = x\left[ { - n} \right]$$
C
$$y\left[ n \right] = - x\left[ n \right]$$
D
$$y\left[ n \right] = - x\left[ { - n} \right]$$
3
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
$$\left| a \right| < \left| z \right| < \left| b \right|$$
4
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 _____________________