Z-Transform (EE)

If the Z-transform of a finite-duration discrete-time signal $x[n]$ is $X(z)$, then the Z-transform of the signal $y[n] = x[2n]$ is

The period of the discrete-time signal $$x[n]$$ described by the equation below is $$N=$$ __________ (Round off to the nearest integer). $$x[n] = 1 + 3\sin \left( {{{15\pi } \over 8}n + {{3\pi } \over 4}} \right) - 5\sin...

The Z-transform of a discrete signal $$x[n]$$ is $$X(z) = {{4z} \over {(z - {1 \over 5})(z - {2 \over 3})(z - 3)}}$$ with $$ROC = R$$. Which one of the following statements is true?

The causal signal with $z$-transform $z^2(z-a)^{-2}$ is ( $u[n]$ is the unit step signal)

Consider a discrete time signal given by x[n]=(-0.25) n u[n]+(0.5) n u[-n-1] The region of convergence of its Z-transform would be

The z-Transform of a sequence x[n] is given as X(z) = 2z+4−4/z+3/z 2 . If y[n] is the first difference of x[n], then Y(Z) is given by

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\rig...

An input signal x(t) = 2 + 5sin(100$$\mathrm\pi$$t) is sampled with a sampling frequency of 400 Hz and applied to the system whose transfer function is represented by $$$\frac{Y\left(z\right)}{X\left(z\right)}=\frac1N\le...

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

If $$x\left[ N \right] = {\left( {1/3} \right)^{\left| n \right|}} - {\left( {1/2} \right)^n}\,u\left[ n \right],$$ then the region of convergence $$(ROC)$$ of its $$Z$$-transform in the $$Z$$-plane will be

The $$z$$$$-$$ transform of a signal $$x\left[ n \right]$$ is given by $$4{z^{ - 3}} + 3{z^{ - 1}} + 2 - 6{z^2} + 2{z^3}.$$ It is applied to a system, with a transfer function $$H\left( z \right) = 3{z^{ - 1}} - 2.$$ Let...

Given X(z)=$$\frac z{\left(z-a\right)^2}$$ with $$\left|z\right|$$ > a, the residue of X(z)z n-1 at z = a for n $$\geq$$ 0 will be

A signal is processed by a causal filter with transfer function $$G(s).$$ For a distortion free output signal waveform, $$G(s)$$ must. $$G\left( z \right) = a{z^{ - 1}} + \beta \,\,{z^{ - 3}}$$ is a low-pass digital filt...

$$X\left( z \right) = 1 - 3\,\,{z^{ - 1}},\,\,Y\left( z \right) = 1 + 2\,\,{z^{ - 2}}$$ are $$Z$$-transforms of two signals $$x\left[ n \right],\,\,y\left[ n \right]$$ respectively. A linear time invariant system has the...

$$y\left[ n \right]$$ denotes the output and $$x\left[ n \right]$$ denotes the input of a discrete-time system given by the difference equation $$y\left[ n \right] - 0.8y\left[ {n - 1} \right] = x\left[ n \right] + 1.25\...

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 discrete real all pass system has a pole at $$z = 2\angle {30^ \circ };\,$$ it, therefore,

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: