1
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 $$0\pm j1$$ 2 GATE EE 2008 MCQ (Single Correct Answer) +2 -0.6 Given X(z)=$$\frac z{\left(z-a\right)^2}$$ with $$\left|z\right|$$ > a, the residue of X(z)zn-1 at z = a for n $$\geq$$ 0 will be A an-1 B an C nan D nan-1 3 GATE EE 2006 MCQ (Single Correct Answer) +2 -0.6 The discrete-time signal $$x\left[n\right]\leftrightarrow X\left(z\right)={\textstyle\sum_{n=0}^\infty}\frac{3^n}{2+n}z^{2n}$$$ where $$\leftrightarrow$$ denote a transform-pair relationship, is orthogonal to the signal
A
$$y_1\left[n\right]\leftrightarrow Y_1\left(z\right)={\textstyle\sum_{n=0}^\infty}\left(\frac23\right)^nz^{-n}$$
B
$$y_2\left[n\right]\leftrightarrow Y_2\left(z\right)={\textstyle\sum_{n=0}^\infty}\left(5^n-n\right)z^{-\left(2n+1\right)}$$
C
$$y_3\left[n\right]\leftrightarrow Y_3\left(z\right)={\textstyle\sum_{n=-\infty}^\infty}2^{-\left|n\right|}z^{-n}$$
D
$$y_4\left[n\right]\leftrightarrow Y_4\left(z\right)=2z^{-4}\;+\;3z^{-2}+1$$
4
GATE EE 2005
+2
-0.6
If u(k) is the unit step and $$\delta\left(k\right)$$ is the unit impulse function, the inverse z-transform of $$F\left(z\right)=\frac1{z+1}$$ for k>0 is:
A
$$\left(-1\right)^k\delta\left(k\right)$$
B
$$\delta\left(k\right)-\left(-1\right)^k$$
C
$$\left(-1\right)^ku\left(k\right)$$
D
$$u\left(k\right)-\left(-1\right)^k$$
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