- #1
Bromio
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Homework Statement
Calculate the Z-transform of the function x[n] = u[n]-u[-n-1].
Homework 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]
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.