1
GATE EE 2017 Set 2
+2
-0.6
A cascade system having the impulse responses $$\begin{array}{l}h_1\left(n\right)=\left\{1,\;-1\right\}\;\;\;and\;\;h_2\left(n\right)=\left\{1,\;1\right\}\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\uparrow\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\uparrow\end{array}$$$is shown in the figure below, where symbol $$\uparrow$$ denotes the time origin. The input sequence x(n) for which the cascade system produces an output sequence $$\begin{array}{l}y\left(n\right)=\left\{1,\;2,\;1,\;-1,\;-2,\;-1\right\}\;\;is\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\uparrow\end{array}$$$
A
$$\begin{array}{l}x\left(n\right)=\left\{1,\;2,\;1,\;1\right\}\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\uparrow\end{array}$$
B
$$\begin{array}{l}x\left(n\right)=\left\{1,\;1,\;2,\;2\right\}\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\uparrow\end{array}$$
C
$$\begin{array}{l}x\left(n\right)=\left\{1,\;1,\;1\right\}\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\uparrow\end{array}$$
D
$$\begin{array}{l}x\left(n\right)=\left\{1,\;2,\;2,\;1\right\}\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\uparrow\end{array}$$
2
GATE EE 2015 Set 1
+2
-0.6
Consider a discrete time signal given by
x[n]=(-0.25)nu[n]+(0.5)nu[-n-1]
The region of convergence of its Z-transform would be
A
the region inside the circle of radius 0.5 and centered at origin.
B
the region outside the circle of radius 0.25 and centered at origin.
C
the annular region between the two circles, both centered at origin and having radii 0.25 and 0.5.
D
the entire Z plane.
3
GATE EE 2014 Set 1
+2
-0.6
Let $$X\left(z\right)=\frac1{1-z^{-3}}$$ be the Zâ€“transform of a causal signal x[n]. Then, the values of x[2] and x[3] are
A
0 and 0
B
0 and 1
C
1 and 0
D
1 and 1
4
GATE EE 2014 Set 2
+2
-0.6
A discrete system is represented by the difference equation $$\begin{bmatrix}X_1\left(k+1\right)\\X_2\left(k+2\right)\end{bmatrix}=\begin{bmatrix}a&a-1\\a+1&a\end{bmatrix}\begin{bmatrix}X_1\left(k\right)\\X_2\left(k\right)\end{bmatrix}$$\$ It has initial condition $$X_1\left(0\right)=1;\;X_2\left(0\right)=0$$. The pole location of the system for a = 1, are
A
$$1\pm j0$$
B
$$-1\pm j0$$
C
$$\pm1+j0$$
D
$$0\pm j1$$
EXAM MAP
Medical
NEET