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Find Z-transform of {k2 - 2k + 3}k ≥ 0
1 Answer
written 2.9 years ago by |
We assume
([f(k)]=0 \ for \ k \ < 0)
Here, $f(k)=k^2-2k+3, \ By\ definition,$
$Z[f(k)]=\sum_{k=-\infty}^{\infty} f(k).z^{-k}$
$Z[k^2-2k+3]$
$=\sum_{k=-\infty}^{-1}0+\sum_{k=0}^{\infty}(k^2-2k+3)\dfrac {1}{z^k}$
$=\dfrac {3} {z^0}+\dfrac {2} {z^1}+\dfrac {3} {z^2}+ \dfrac {6} {z^3}+\dfrac {11} {z^4}+...$
$=3+\dfrac {2} {z}+\dfrac {3} {z^2}+ \dfrac {6} {z^3}+\dfrac {11} {z^4}+...$