Name
Abstract | ||
|---|---|---|
ll methods presented in textbooks for computing inverse $ {\cal Z}$-transforms of rational functions have some limitation: 1) the direct division method does not, in general, provide enough information to derive an analytical expression for the time-domain sequence $x(k)$ whose $ {\cal Z}$-transform is $X(z)$ ; 2) computation using the inversion integral method becomes labored when $X(z)z^{k-1}$ has poles at the origin of the complex plane; 3) the partial-fraction expansion method, in spite of being acknowledged as the simplest and easiest one to compute the inverse $ {\cal Z}$-transform and being widely used in textbooks, lacks a standard procedure like its inverse Laplace transform counterpart. This paper addresses all the difficulties of the existing methods for computing inverse $ {\cal Z}$ -transforms of rational functions, presents an easy and straightforward way to overcome the limitation of the inversion integral method when $X(z)z^{k-1}$ has poles at the origin, and derives five expressions for the pairs of time-domain sequences and corresponding $ {\cal Z}$-transforms that are actually needed in the computation of inverse $ {\cal Z}$ -transform using partial-fraction expansion. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1109/TE.2011.2171185 | IEEE Transactions on Education |
Keywords | DocType | Volume |
Time domain analysis,Polynomials,Education,Laplace equations,Poles and zeros,Convergence | Journal | 55 |
Issue | ISSN | Citations |
2 | 0018-9359 | 0 |
PageRank | References | Authors |
0.34 | 0 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Marcos V. Moreira | 1 | 125 | 13.03 |
| JoãO C. Basilio | 2 | 151 | 15.63 |