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[2] and x[3] 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...