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The pole-zero plots of three discrete-time systems P, Q and R on the z-plane are shown below. Which one of the followin...
GATE EE 2017 Set 2
The z-Transform of a sequence x[n] is given as X(z) = 2z+4−4/z+3/z2. If y[n] is the first difference of x[n], then Y(Z) ...
GATE EE 2015 Set 2

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A cascade system having the impulse responses $$\begin{array}{l}h_1\left(n\right)=\left\{1,\;-1\right\}\;\;\;and\;\;h_2... GATE EE 2017 Set 2 Consider a discrete time signal given by x[n]=(-0.25)nu[n]+(0.5)nu[-n-1] The region of convergence of its Z-transform wo... GATE EE 2015 Set 1 A discrete system is represented by the difference equation$$\$\begin{bmatrix}X_1\left(k+1\right)\\X_2\left(k+2\right)\e...
GATE EE 2014 Set 2
Let $$X\left(z\right)=\frac1{1-z^{-3}}$$ be the Z–transform of a causal signal x[n]. Then, the values of x and x a...
GATE EE 2014 Set 1
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 $$\geq$$ ...
GATE EE 2008
The discrete-time signal $$x\left[n\right]\leftrightarrow X\left(z\right)={\textstyle\sum_{n=0}^\infty}\frac{3^n}{2+n}z... GATE EE 2006 If u(k) is the unit step and$$\delta\left(k\right)$$is the unit impulse function, the inverse z-transform of$$F\left(...
GATE EE 2005

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