{"id":1344,"date":"2017-05-12T11:00:32","date_gmt":"2017-05-12T16:00:32","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/telg1001\/?p=1344"},"modified":"2026-04-05T23:29:53","modified_gmt":"2026-04-06T04:29:53","slug":"transformada-laplace-tabla","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/algoritmos101\/ss-u04\/transformada-laplace-tabla\/","title":{"rendered":"4.6.1 Transformada de Laplace - Tabla"},"content":{"rendered":"\n

Referencia<\/strong><\/em>: Lathi Tabla 4.1 p334. Oppenheim Tabla 9.2 p692. Hsu Tabla 3-1 p115<\/p>\n\n\n\n

No.<\/th>x(t)<\/th>X(s)<\/th>ROC<\/th><\/tr>
1a<\/td>\u03b4(t)<\/td>1<\/td>Toda s<\/td><\/tr>
1b<\/td>\u03b4(t-T)<\/td>e-sT<\/sup><\/td>Toda s<\/td><\/tr>
2a<\/td>\u03bc(t)<\/td>\\frac{1}{s}<\/span><\/td>Re{s}>0<\/td><\/tr>
2b<\/td>-\u03bc(-t)<\/td>\\frac{1}{s}<\/span><\/td>Re{s}<0<\/td><\/tr>
3<\/td>t\u03bc(t)<\/td>\\frac{1}{s^2}<\/span><\/td>Re{s}>0<\/td><\/tr>
4a<\/td>tn<\/sup>\u03bc(t)<\/td>\\frac{n!}{s^{n+1}}<\/span><\/td>Re{s}>0<\/td><\/tr>
4b<\/td> \\frac{t^{n-1}}{(n-1)!} \\mu (t)<\/span><\/td>\\frac{1}{s^n}<\/span><\/td>Re{s}>0<\/td><\/tr>
4c<\/td> -\\frac{t^{n-1}}{(n-1)!} \\mu (-t)<\/span><\/td>\\frac{1}{s^n}<\/span><\/td>Re{s}<0<\/td><\/tr>
5<\/td>e\u03bbt<\/sup>\u03bc(t)<\/td>\\frac{1}{s-\\lambda}<\/span><\/td>Re{s}>0<\/td><\/tr>
6<\/td>te\u03bbt<\/sup>\u03bc(t)<\/td>\\frac{1}{(s-\\lambda)^2}<\/span><\/td>Re{s}>0<\/td><\/tr>
7<\/td>tn<\/sup>e\u03bbt<\/sup>\u03bc(t)<\/td>\\frac{n!}{(s-\\lambda)^{n+1}}<\/span><\/td> <\/td><\/tr>
8a<\/td>cos (bt) \u03bc(t)<\/td>\\frac{s}{s^2+b^2}<\/span><\/td>Re{s}>0<\/td><\/tr>
8b<\/td>sin (bt) \u03bc(t)<\/td>\\frac{b}{s^2+b^2}<\/span><\/td>Re{s}>0<\/td><\/tr>
9a<\/td>e-at<\/sup>cos (bt) \u03bc(t)<\/td>\\frac{s+a}{(s+a)^2+b^2}<\/span><\/td>Re{s}>-a<\/td><\/tr>
9b<\/td>e-at<\/sup>sin (bt) \u03bc(t)<\/td>\\frac{b}{(s+a)^2+b^2}<\/span><\/td>Re{s}>-a<\/td><\/tr>
10<\/td>\\mu_n (t) = \\frac{\\delta ^n}{\\delta t^n} \\delta (t)<\/span><\/td>sn<\/sup><\/td>Toda s<\/td><\/tr>
11<\/td> \\mu_{-n} (t) = \\mu (t) \\circledast \\text{...} \\circledast \\mu (t) <\/span>

n veces<\/p><\/td>

\\frac{1}{s^n}<\/span><\/td>Re{s}>0<\/td><\/tr>
12a<\/td>re-at<\/sup>cos (bt+\u03b8) \u03bc(t)<\/td>\\frac{\\Big( r\\cos (\\theta)s + (ar \\cos (\\theta) - br \\sin (\\theta)\\Big)}{s^2+2as+(a^2+b^2)}<\/span><\/td><\/tr>
12b<\/td>re-at<\/sup>cos (bt+\u03b8) \u03bc(t)<\/td>\\frac{0.5 re^{j \\theta}}{s+a-jb} + \\frac{0.5 re^{-j \\theta}}{s+a+jb}<\/span><\/td><\/tr>
12c<\/td>re-at<\/sup>cos (bt+\u03b8) \u03bc(t)<\/td> \\frac{As+B}{s^2+2as+c}<\/span><\/td><\/tr>
<\/td>r = \\sqrt{\\frac{A^2 c +B^2 -2ABa}{c-a^2}}<\/span><\/td> \\theta = \\tan ^{-1} \\Big( \\frac{Aa-B}{A\\sqrt{c-a^2}}\\Big)<\/span>

b = \\sqrt{c-a^2}<\/span><\/td><\/tr>
12d<\/td> e^{-at}\\Big[A \\cos (bt) + \\frac{B-Aa}{b} \\sin (bt) \\Big] \\mu (t) <\/span> <\/td>\\frac{As+B}{s^2 + 2as+c}<\/span>

b = \\sqrt{c-a^2}<\/span> <\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Transformada Laplace - Tabla de Propiedades<\/a><\/p>\n\n\n\n

Transformada de Laplace \u2013 Concepto con Python<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Referencia: Lathi Tabla 4.1 p334. Oppenheim Tabla 9.2 p692. Hsu Tabla 3-1 p115 No. x(t) X(s) ROC 1a \u03b4(t) 1 Toda s 1b \u03b4(t-T) e-sT Toda s 2a \u03bc(t) Re{s}>0 2b -\u03bc(-t) Re{s}<0 3 t\u03bc(t) Re{s}>0 4a tn\u03bc(t) Re{s}>0 4b Re{s}>0 4c Re{s}<0 5 e\u03bbt\u03bc(t) Re{s}>0 6 te\u03bbt\u03bc(t) Re{s}>0 7 tne\u03bbt\u03bc(t)   8a cos (bt) […]<\/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":[174],"tags":[],"class_list":["post-1344","post","type-post","status-publish","format-standard","hentry","category-ss-u04"],"_links":{"self":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/1344","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=1344"}],"version-history":[{"count":5,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/1344\/revisions"}],"predecessor-version":[{"id":24018,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/1344\/revisions\/24018"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/media?parent=1344"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/categories?post=1344"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/tags?post=1344"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}