Question

Determine the inverse transform of (a) $X(z) = \frac{z}{2z^2 - 3z + 1}$, $|z| < \frac{1}{2}$ using Long Division Method (b) $X(z) = \frac{z^{-1}}{3z^{-2} - 4z^{-1} + 1}$, $|z| < \frac{1}{3}$ using Partial Fraction Expansion Method

Name: determine the inverse transform of a xz fracz2z2 3z 1 z frac12 using long division method b xz fracz 13z 2 4z 1 1 z frac13 using partial fraction expansion method 77028
Uploaded: 2023-11-23T09:21:54-08:00
Duration: 2 min 39 s
Channel: Adi S
Description: determine the inverse transform of a xz fracz2z2 3z 1 z frac12 using long division method b xz fracz 13z 2 4z 1 1 z frac13 using partial fraction expansion method 77028

          Determine the inverse transform of
(a) $X(z) = \frac{z}{2z^2 - 3z + 1}$, $|z| < \frac{1}{2}$
using Long Division Method
(b) $X(z) = \frac{z^{-1}}{3z^{-2} - 4z^{-1} + 1}$, $|z| < \frac{1}{3}$
using Partial Fraction Expansion Method

$determine the inverse transform of a xz fracz2z2 3z 1 z frac12 using long division method b xz fracz 13z 2 4z 1 1 z frac13 using partial fraction expansion method 77028$

Added by Marcus L.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Adi S

11/23/2023

Step 1

If $z = \frac{1}{2}$, $1 = -\frac{1}{2}A$, so $A = -2$. $\frac{z}{2z^2 - 3z + 1} = \frac{1}{2} \left( \frac{-2}{2z - 1} + \frac{2}{z - 1} \right) = \frac{1}{2} \left( \frac{-1}{z - \frac{1}{2}} + \frac{2}{z - 1} \right) = \frac{1}{2} \left( \frac{1}{\frac{1}{2} - Show more…

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Determine the inverse transform of (a) $X(z) = \frac{z}{2z^2 - 3z + 1}$, $|z| < \frac{1}{2}$ using Long Division Method (b) $X(z) = \frac{z^{-1}}{3z^{-2} - 4z^{-1} + 1}$, $|z| < \frac{1}{3}$ using Partial Fraction Expansion Method