{"id":1354,"date":"2017-05-13T11:35:08","date_gmt":"2017-05-13T16:35:08","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/telg1001\/?p=1354"},"modified":"2026-04-05T23:30:25","modified_gmt":"2026-04-06T04:30:25","slug":"transformada-laplace-tabla-de-propiedades","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/algoritmos101\/ss-u04\/transformada-laplace-tabla-de-propiedades\/","title":{"rendered":"4.6.2 Transformada de Laplace - Tabla de Propiedades"},"content":{"rendered":"\n

Referencia<\/strong><\/em>: Oppenheim tabla 9.3 p717 pdf 748. Lathi tabla 4.2 p361. Hsu tabla 3-2 p119<\/p>\n\n\n\n

Propiedad<\/th>Se\u00f1al<\/th>Transformada de Laplace<\/th><\/tr>
 <\/td>x(t)
x1<\/sub>(t)
x2<\/sub>(t)<\/td>		X(s)
X1<\/sub>(s)
X2<\/sub>(s)<\/td><\/tr>
Linealidad<\/td>ax1<\/sub>(t) + bx2<\/sub>(t)<\/td>a X1<\/sub>(s) + b X2<\/sub>(s)<\/td><\/tr>
Desplazamiento en t<\/td>x(t-t0<\/sub>)<\/td>e-st0<\/sub><\/sup>X(s)<\/td><\/tr>
Desplazamiento
en domino de s<\/td>		es0<\/sub>t<\/sup>x(t)<\/td>X(s-s0<\/sub>)<\/td><\/tr>
Escalamiento
en tiempo<\/td>		x(at), a>0<\/td>\\frac{1}{a} X\\Big(\\frac{s}{a}\\Big)<\/span><\/td><\/tr>
inversi\u00f3n
en tiempo<\/td>		x(-t)<\/td>X(-s)<\/td><\/tr>
Conjugaci\u00f3n<\/td>x*<\/sup>(t)<\/td>X*<\/sup>(s)<\/td><\/tr>
Convoluci\u00f3n
(suponiendo que
x1<\/sub>(t) y x2<\/sub>(t) son cero
para t<0)<\/td>		x_1 (t) \\circledast x_2 (t)<\/span><\/td>X1<\/sub>(s)X2<\/sub>(s)<\/td><\/tr>
Diferenciaci\u00f3n en
el dominio t<\/td>		 \\frac{\\delta}{\\delta t} x(t)<\/span><\/td>sX(s)-x(0-<\/sup>)<\/td><\/tr>
 <\/td> \\frac{\\delta^2}{\\delta t^2} x(t)<\/span><\/td>s2<\/sup>X(s)-sx(0-<\/sup>)-x(0-<\/sup>)<\/td><\/tr>
 <\/td> \\frac{\\delta^3}{\\delta t^3} x(t)<\/span><\/td>s3<\/sup>X(s) -s2<\/sup>x(0-<\/sup>)-sx(0-<\/sup>)-x'(0-<\/sup>)<\/td><\/tr>
 <\/td> \\frac{\\delta^n}{\\delta t^n} x(t)<\/span><\/td> s^n X(s) -\\sum_{k=1}^{n}s^{(n-k)}x^{(k-1)} (0^{-})<\/span><\/td><\/tr>
Diferenciaci\u00f3n en
el dominio s<\/td>		-tx(t)<\/td> \\frac{\\delta}{\\delta s} X(s)<\/span><\/td><\/tr>
Integraci\u00f3n en
en el dominio t<\/td>		\\int_{0^-}^t x(\\tau) \\delta \\tau <\/span><\/td> \\frac{1}{s} X(s)<\/span><\/td><\/tr>
 <\/td>\\int_{-\\infty}^t x(\\tau) \\delta \\tau <\/span><\/td> \\frac{1}{s} X(s)+\\frac{1}{s} \\int_{-\\infty}^{0^{-}} x(t) \\delta t <\/span><\/td><\/tr>
Convoluci\u00f3n en frecuencia<\/td>x1<\/sub>(t) x2<\/sub>(t)<\/td> \\frac{1}{2 \\pi j} X_1(s) \\circledast X_2(s) <\/span><\/td><\/tr>
valor inicial<\/td>x(0+<\/sup>)<\/td> \\lim _{s \\rightarrow \\infty} s X(s) <\/span>
n>m<\/td><\/tr>
valor final<\/td>x(\u221e)<\/td> \\lim _{s \\rightarrow 0} s X(s) <\/span>
polos de sX(s) en LHP (izquierda)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

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

Referencia: Oppenheim tabla 9.3 p717 pdf 748. Lathi tabla 4.2 p361. Hsu tabla 3-2 p119 Propiedad Se\u00f1al Transformada de Laplace   x(t)x1(t)x2(t) X(s)X1(s)X2(s) Linealidad ax1(t) + bx2(t) a X1(s) + b X2(s) Desplazamiento en t x(t-t0) e-st0X(s) Desplazamientoen domino de s es0tx(t) X(s-s0) Escalamientoen tiempo x(at), a>0 inversi\u00f3nen tiempo x(-t) X(-s) Conjugaci\u00f3n x*(t) X*(s) Convoluci\u00f3n(suponiendo […]<\/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-1354","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\/1354","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=1354"}],"version-history":[{"count":4,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/1354\/revisions"}],"predecessor-version":[{"id":24019,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/1354\/revisions\/24019"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/media?parent=1354"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/categories?post=1354"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/tags?post=1354"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}