Fair and square computation of inverse {cal Z} -transforms of rational functions / Marcos Vicente Moreira in IEEE transactions on education, Vol. 55 N° 2 (Mai 2012)  

Public ISBD [article]  inIEEE transactions on education > Vol. 55 N° 2 (Mai 2012) . - pp. 285 - 290 Titre : Fair and square computation of inverse {cal Z} -transforms of rational functions Type de document : texte imprimé Auteurs : Marcos Vicente Moreira, Auteur ; Joao Carlos Basilio, Auteur Année de publication : 2013 Article en page(s) : pp. 285 - 290 Note générale : Education Langues : Anglais (eng) Mots-clés : 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%3Das [...] [article] Fair and square computation of inverse {cal Z} -transforms of rational functions [texte imprimé] / Marcos Vicente Moreira, Auteur ; Joao Carlos Basilio, Auteur . - 2013 . - pp. 285 - 290. Education Langues : Anglais (eng) in IEEE transactions on education > Vol. 55 N° 2 (Mai 2012) . - pp. 285 - 290 Mots-clés : 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%3Das [...]

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