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Determine the z-transform and the ROC of the signal $$ x(n)=\left[3\left(2^n\right)-4\left(3^n\right)\right] u(n) $$
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written 18 months ago by
prajapatijaimin
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Solution:
If we define the signals,
$ x_1(n)=2^n u(n)\\ $
$ x_2(n)=3^n u(n)\\ $
then x(n) can be written as
$ x(n)=3 x_1(n)-4 x_2(n)\\ $
According to (3.2.1), its z-transform is
$ X(z)=3 X_1(z)-4 X_2(z)\\ $
From (3.1.7) we recall that,
$ \alpha^n u(n) \stackrel{\vdots}{\longleftrightarrow} \frac{1}{1-\alpha z^{-1}} \quad \text { …
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