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Determine the z transform & the ROC of the discrete time signal. $X[n] = \{ 2, 10, 1, 2, 5, 7, 2\}$
written 9.2 years ago by gravatar for teamques10 teamques10 ★ 70k •   modified 9.2 years ago

Mumbai University > EXTC > Sem 4 > Signals and Systems

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Year : MAY 2014
signals and systems
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written 9.2 years ago by gravatar for teamques10 teamques10 ★ 70k

We have $x(-3) = 2, x(-2) = 10, x(-1) =1, x(0) = 2, x(1) = 5, x(2) = 7, x(3) =2$

By using z-transform,

$X (z) = ∑\limits_{n=-∞}^∞ x [n] z^{-n} \\ ∴X (z)= ∑\limits_{n=-3}^3 \space x[n]z^{-n} \\ = x(-3)z^{-3} + x(-2) z^{-2} +x(-1)z^{-1} +x(0)z^0+x(1)z^1+ x(2)z^2+x(3)z^3 \\ =2z^{-3} + 10z^{-2}+1z^{-1}+2z^0+5z^1+ …

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