GATE EE
Signals and Systems
Discrete Time Signal Z Transformation
Previous Years Questions

## Marks 1

The pole-zero plots of three discrete-time systems P, Q and R on the z-plane are shown below. Which one of the following is TRUE about the frequency ...
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) is given by

## Marks 2

A cascade system having the impulse responses $$\begin{array}{l}h_1\left(n\right)=\left\{1,\;-1\right\}\;\;\;and\;\;h_2\left(n\right)=\left\{1,\;1\ri... Consider a discrete time signal given by x[n]=(-0.25)nu[n]+(0.5)nu[-n-1] The region of convergence of its Z-transform would be... A discrete system is represented by the difference equation$$$\begin{bmatrix}X_1\left(k+1\right)\\X_2\left(k+2\right)\end{bmatrix}=\begin{bmatrix}a&a... 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 are 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 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 $$\leftrightarr... If u(k) is the unit step and$$\delta\left(k\right)$$is the unit impulse function, the inverse z-transform of$$F\left(z\right)=\frac1{z+1} for k&g...
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