The $\text{Z}$-transform of a discrete signal $\text{x[n]}$ is
$\text{X(z)}=\frac{4 z}{\left(z-\frac{1}{5}\right)\left(z-\frac{2}{3}\right)(z-3)}$ with $\text{ROC=R}$
Which one of the following statements is true?
- Discrete-time Fourier transform of $\mathrm{x}[\mathrm{n}]$ converges if $\text{R}$ is $|z|>3$
- Discrete-time Fourier transform of $\mathrm{x}[\mathrm{n}]$ converges if $\text{R}$ is $\frac{2}{3}<|z|<3$
- Discrete-time Fourier transform of $\mathrm{x}[\mathrm{n}]$ converges if $\text{R}$ is such that $ \mathrm{x}[\mathrm{n}]$ is a left-sided sequence
- Discrete-time Fourier transform of $\mathrm{x}[\mathrm{n}]$ converges if $\text{R}$ is such that $ \mathrm{x}[\mathrm{n}]$ is a right-sided sequence