Question

4.20. Find the inverse $z$-transform of \begin{equation} X(z) = \frac{z}{z(z-1)(z-2)^2}, \quad |z| > 2 \end{equation}

          4.20. Find the inverse $z$-transform of
\begin{equation}
X(z) = \frac{z}{z(z-1)(z-2)^2}, \quad |z| > 2
\end{equation}

4.20. Find the inverse z-transform of

X(z) = (z)/(z(z-1)(z-2)^2), |z| > 2

Added by Rocio C.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Sri K

09/01/2023

Step 1

x(z) = z / (z(z-1)(z-2)^2) x(z) = A/z + B/(z-1) + C/(z-2) + D/(z-2)^2 Multiplying both sides by z(z-1)(z-2)^2, we get: z = A(z-1)(z-2)^2 + Bz(z-2)^2 + Cz(z-1)(z-2) + Dz(z-1) Now, we can solve for A, B, C, and D by substituting z = 0, 1, 2, and infinity. Show more…

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