| Titre : | Fair and square computation of inverse {cal Z} -transforms of rational functions (2013) |
| Auteurs : | Marcos Vicente Moreira, Auteur ; Joao Carlos Basilio, Auteur |
| Type de document : | Article : texte imprimé |
| Dans : | IEEE transactions on education (Vol. 55 N° 2, Mai 2012) |
| Article en page(s) : | pp. 285 - 290 |
| Note générale : | Education |
| Langues : | Anglais |
| Tags : | Control education Discrete-time signals systems Inverse {cal Z}-transformation Teaching methodology |
| Résumé : | All methods presented in textbooks for computing inverse 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 Z-transform is X(z) ; 2) computation using the inversion integral method becomes labored when X(z)zk-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 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 Z -transforms of rational functions, presents an easy and straightforward way to overcome the limitation of the inversion integral method when X(z)zk-1 has poles at the origin, and derives five expressions for the pairs of time-domain sequences and corresponding Z-transforms that are actually needed in the computation of inverse Z -transform using partial-fraction expansion. |
| ISSN : | 0018-9359 |
| En ligne : | http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6047582&sortType%3Dasc_p_Sequence%26filter%3DAND%28p_IS_Number%3A6193254%29 |
