(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Calculate the Z-transform of the function x[n] = u[n]-u[-n-1].

2. Relevant equations

[itex]X(z) = ZT\{x[n]\} = \sum_{n=-\infty}^{\infty}x[n]z^{-n}[/itex]

[itex]ZT\{u[n]\} = \displaystyle\frac{1}{1-z^{-1}}[/itex], ROC: |z| > 1.

[itex]ZT\{-u[-n-1]\} = \displaystyle\frac{1}{1-z^{-1}}[/itex], ROC: |z| < 1.

[itex]ZT\{x[n]\} = X(z)[/itex], ROC: R1

[itex]ZT\{y[n]\} = Y(z)[/itex], ROC: R2

[itex]ZT\{ax[n]+by[n]\} = aX(z)+bY(z)[/itex], ROC: at least [itex]R1\cap R2[/itex]

3. The attempt at a solution

Using formulas in section 2. it is obvious that [itex]X(z) = ZT\{x[n]\} = \displaystyle\frac{2}{1-z^{-1}}[/itex], but which is the ROC? The intersection between |z| > 1 and |z|< 1 is null.

Thank you.

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# ROC in Sign function Z-transform

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