{"id":1413,"date":"2017-08-26T22:12:50","date_gmt":"2017-08-27T03:12:50","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/telg1001\/?p=1413"},"modified":"2026-04-06T06:33:52","modified_gmt":"2026-04-06T11:33:52","slug":"transformada-z-tabla","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/algoritmos101\/ss-u07\/transformada-z-tabla\/","title":{"rendered":"7.6.3 Transformada z -Tabla"},"content":{"rendered":"\n

Referencia<\/strong><\/em>: Lathi Tabla 5.1 Transformada z p492. Oppenheim tabla 10.2 p776, Schaum Hsu Tabla 4-1 p170.<\/p>\n\n\n\n

No.<\/th>x[n]<\/th>X[z]<\/th> <\/th>ROC<\/th><\/tr>
1a<\/td>\u03b4[n]<\/td>1<\/td> <\/td>Toda z<\/td><\/tr>
1b<\/td>\u03b4[n-m]<\/td>z-m<\/sup><\/td>Toda z excepto
0 (si m>0) \u00f3
\u221e (si m<0)<\/td><\/tr>
2a<\/td>\u03bc[n]<\/td> \\frac{z}{z-1}<\/span><\/td> \\frac{1}{1-z^{-1}}<\/span><\/td>|z|>1<\/td><\/tr>
2b<\/td>-\u03bc[-n-1]<\/td> \\frac{z}{z-1}<\/span><\/td> \\frac{1}{1-z^{-1}}<\/span><\/td>|z|<1<\/td><\/tr>
3<\/td>n \u03bc[n]<\/td> \\frac{z}{(z-1)^2}<\/span><\/td> \\frac{z^{-1}}{(1- z^{-1})^2}<\/span><\/td>|z|>1<\/td><\/tr>
4<\/td>n2<\/sup> \u03bc[n]<\/td> \\frac{z(z+1)}{(z-1)^3}<\/span><\/td> <\/td> <\/td><\/tr>
5<\/td>n3<\/sup> \u03bc[n]<\/td> \\frac{z(z^2 + 4z + 1)}{(z-1)^4}<\/span><\/td> <\/td> <\/td><\/tr>
6a<\/td>\u03b3n<\/sup> \u03bc[n]<\/td> \\frac{z}{z-\\gamma}<\/span><\/td> \\frac{1}{1-\\gamma z^{-1}}<\/span><\/td>|z|>|\u03b3|<\/td><\/tr>
6b<\/td>-\u03b3n<\/sup> \u03bc[-n-1]<\/td> \\frac{z}{z-\\gamma}<\/span><\/td> \\frac{1}{1-\\gamma z^{-1}}<\/span><\/td>|z|<|\u03b3|<\/td><\/tr>
7<\/td>\u03b3n-1<\/sup> \u03bc[n-1]<\/td> \\frac{1}{z-\\gamma}<\/span><\/td> <\/td> <\/td><\/tr>
8a<\/td>n \u03b3n<\/sup> \u03bc[n]<\/td> \\frac{\\gamma z}{(z-\\gamma)^2}<\/span><\/td> \\frac{\\gamma z^{-1}}{(1- \\gamma z^{-1})^2}<\/span><\/td>|z|>|\u03b3|<\/td><\/tr>
8b<\/td>-n \u03b3n<\/sup> \u03bc[-n-1]<\/td> \\frac{\\gamma z}{(z-\\gamma)^2}<\/span><\/td> \\frac{\\gamma z^{-1}}{(1- \\gamma z^{-1})^2}<\/span><\/td>|z|<|\u03b3|<\/td><\/tr>
8c<\/td>(n+1) \u03b3n<\/sup> \u03bc[n]<\/td> \\Big[ \\frac{z}{z-\\gamma}\\Big]^2 <\/span><\/td> \\frac{1}{(1- \\gamma z^{-1})^2}<\/span><\/td>|z|>|\u03b3|<\/td><\/tr>
9<\/td>n2<\/sup> \u03b3n<\/sup> \u03bc[n]<\/td> \\frac{\\gamma z (z + \\gamma)}{(z - \\gamma)^3 }<\/span><\/td> <\/td> <\/td><\/tr>
10<\/td>\\frac{n(n-1)(n-2) \\text{...} (n-m+1)}{\\gamma^m m!}\\gamma^n \\mu[n] <\/span><\/td> \\frac{ z}{(z-\\gamma)^{m+1}}<\/span><\/td> <\/td> <\/td><\/tr>
11a<\/td>|\u03b3|n<\/sup> cos(\u03b2n) \u03bc[n]<\/td> \\frac{ z \\big(z-|\\gamma | \\cos (\\beta ) \\big)}{z^2-(2|\\gamma | \\cos (\\beta ))z +|\\gamma |^2}<\/span><\/td> <\/td>|z|>\u03b3<\/td><\/tr>
11b<\/td>|\u03b3|n<\/sup> sin(\u03b2n) \u03bc[n]<\/td> \\frac{ z |\\gamma | \\sin (\\beta )}{z^2-(2|\\gamma | \\cos (\\beta ))z +|\\gamma |^2}<\/span><\/td> <\/td>|z|>\u03b3<\/td><\/tr>
12a<\/td>r|\u03b3|n<\/sup> cos(\u03b2n+\u03b8) \u03bc[n]<\/td> \\frac{ rz[z \\cos (\\theta) - |\\gamma | \\cos (\\beta -\\theta)]}{z^2-(2|\\gamma | \\cos (\\beta ))z +|\\gamma |^2}<\/span><\/td> <\/td> <\/td><\/tr>
12b<\/td>r|\u03b3|n<\/sup> cos(\u03b2n+\u03b8) \u03bc[n]
\u03b3 = |\u03b3| ej\u03b2<\/sup><\/td>		 \\frac{\\big(0.5r e^{j \\theta} \\big)z}{z - \\gamma} + \\frac{\\big(0.5r e^{-j \\theta} \\big)z}{z - \\gamma^{*}}<\/span><\/td> <\/td> <\/td><\/tr>
12c<\/td>r|\u03b3|n<\/sup> cos(\u03b2n+\u03b8) \u03bc[n]<\/td>\\frac{z(Az +B)}{z^2 + 2az + |\\gamma|2} <\/span><\/td><\/tr>
 <\/td>r = \\sqrt{\\frac{A^2|\\gamma |^2 + B^2 - 2AaB}{|\\gamma |^2 - a^2}}<\/span><\/td>\\beta = \\cos ^{-1} \\frac{-a}{|\\gamma |}<\/span>

\\theta = tan^{-1} \\frac{ Aa - B}{A \\sqrt{|\\gamma |^2 - a^2}}<\/span><\/td><\/tr>
13<\/td>{an<\/sup> ; 0\u2264 n \u2264 N-1
{0  ; otro caso<\/td>		\\frac{1-a^N z^{-n}}{1-az^{-1}}<\/span><\/td><\/td>|z|>0<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Transformada z - Tabla de propiedades<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Referencia: Lathi Tabla 5.1 Transformada z p492. Oppenheim tabla 10.2 p776, Schaum Hsu Tabla 4-1 p170. No. x[n] X[z]   ROC 1a \u03b4[n] 1   Toda z 1b \u03b4[n-m] z-m Toda z excepto0 (si m>0) \u00f3\u221e (si m<0) 2a \u03bc[n] |z|>1 2b -\u03bc[-n-1] |z|<1 3 n \u03bc[n] |z|>1 4 n2 \u03bc[n]     5 n3 […]<\/p>\n","protected":false},"author":8043,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"wp-custom-template-entrada-ss-unidades","format":"standard","meta":{"footnotes":""},"categories":[177],"tags":[],"class_list":["post-1413","post","type-post","status-publish","format-standard","hentry","category-ss-u07"],"_links":{"self":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/1413","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/users\/8043"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/comments?post=1413"}],"version-history":[{"count":4,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/1413\/revisions"}],"predecessor-version":[{"id":24048,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/1413\/revisions\/24048"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/media?parent=1413"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/categories?post=1413"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/tags?post=1413"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}