Recent questions tagged z-transform

The $Z$-transform of $\{x(n)\}$ is defined as $X(z)=\sum_{n} x(n) z^{-n}$ (for those $z$ for which the series converges). Let $u(n)=1$ for $n \geq 0$ and $u(n)=0$ for $n<...

The signal $x_{n}=0$ for $n<0$ and $x_{n}=a^{n} / n$ ! for $n \geq 0$. Its $z$-transform $X(z)=\sum_{n=-\infty}^{\infty} x_{n} z^{-n}$ is$1 /\left(z^{-1}-a\right)$, regio...

Let $\mathrm{H}(\mathrm{z})$ be the $z$-transform of the transfer function corresponding to an input output relation $y(n)-\frac{1}{2} y(n-1)=x(n)+\frac{1}{3} x(n-1)$. Th...

The $z$-transform of a sequence $\left\{x_{n}\right\}_{n=-\infty}^{\infty}$ is defined to be $X(z)=\sum_{n=-\infty}^{\infty} x_{n} z^{-n}$. The $z$-transform of the seque...

The $z$-transform $\mathrm{F}(z)$ of the function $f(n \mathrm{T})=a^{\prime \prime T}$ is$\frac{z}{z-a^{\mathrm{T}}}$$\frac{z}{z+a^{\mathrm{T}}}$$\frac{\mathrm{z}}{\math...

The $z$-transform of a signal is given by\[C(z)=\frac{1 z^{-1}\left(1-z^{-4}\right)}{4\left(1-z^{-1}\right)^{2}}\]Its final value is$1 / 4$zero$1.0$infinity

The region of convergence of the $z$-transform of a unit step function is$|z|>1$$|z|<1$(Real part of $z)>0$( Real part of $z)<0$

The $Z$-transform of the time function $\sum_{k=0}^{\infty} \delta(n-k)$ is$\frac{Z-1}{Z}$$\frac{Z}{Z-1}$$\frac{Z}{(Z-1)^2}$$\frac{(Z-1)^2}{Z}$

The $z$-transform of a system is $H(z)=\frac{z}{z-0.2}.$ If the ROC is $|z|<0.2$, then the impulse response of the system is$(0.2)^{n} u[n]$$(0.2)^{n} u[-n-1]$$-(0.2)^{n}...

The region of convergence of $Z$-transform of the sequence$\left(\frac{5}{6}\right)^{n} u(n)-\left(\frac{6}{5}\right)^{n} u(-n-1)$ must be$|z|<\frac{5}{6}$$|z|>\frac{6}{5...

The $z$-transform $X[z]$ of a sequence $x[n]$ is given by $X[z]=\dfrac{0.5}{1-2 z^{-1}}$. It is given that the region of convergence of $X[z]$ includes the unit circle. T...

In the following network, the switch is closed at $t=0$ - and the sampling starts from $t=0$. The sampling frequency is $10 \mathrm{~Hz}$.The expression and the region of...

The $\text{ROC}$ of $\text{Z}$-transform of the discrete time sequence $\quad x(n)=\left(\dfrac{1}{3}\right)^{n} u(n)-\left(\dfrac{1}{2}\right)^{n} u(-n-1) \quad$ is$\fra...

Consider the $z$-transform $X(z)=5 z^2+4 z^{-1}+3 ; 0<|z|<\infty$. The inverse $z$-transform $x[n]$ is$5\; \delta[n+2]+3\; \delta[n]+4\; \delta[n-1]$$5\; \delta[n-2]+3\; ...

The $z$-transform of the sequence $x[n]$ is given by $X(z)=\frac{1}{(1-2z^{-1})^{2}},$ with the region of convergence $\mid z \mid >2$. Then, $x $ is _________.

Let $x[n] = x[-n]$. Let $X(z)$ be the $z$-transform of $x[n]$. If $0.5 + j 0.25$ is a zero of $X(z)$, which one of the following must also be a zero of $x(z)$$0.5 – j 0.2...