{"id":1612,"date":"2016-12-23T10:31:20","date_gmt":"2016-12-23T15:31:20","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/estg1003\/?p=1612"},"modified":"2026-04-04T10:56:06","modified_gmt":"2026-04-04T15:56:06","slug":"correlacion-suma-de-procesos","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/algoritmos101\/stp-u02eva\/correlacion-suma-de-procesos\/","title":{"rendered":"correlacion suma de procesos"},"content":{"rendered":"<p><em><strong>Referencia<\/strong><\/em>: Problema Le\u00f3n Garc\u00eda 10.6 p.636<\/p>\n<p>Sea Z(t) = X(t) + Y(t)<\/p>\n<p>\u00bfBajo qu\u00e9 condiciones S<sub>Z<\/sub>(f) = S<sub>X<\/sub>(f) + S<sub>Y<\/sub>(f)?<\/p>\n<p><em><strong>Soluci\u00f3n Propuesta<\/strong><\/em>:<\/p>\n<p>E[ Z(t)Z(t+\u03c4) ] = E[ [X(t) + Y(t)][X(t+\u03c4) + Y(t+\u03c4)] ]<\/p>\n<p>= E[ X(t)X(t+\u03c4) + Y(t) X(t+\u03c4) + X(t)Y(t+\u03c4) + Y(t)Y(t+\u03c4) ]<\/p>\n<p>= E[ \u00a0X(t)X(t+\u03c4) ] +E[ Y(t) X(t+\u03c4) ] + E[ X(t)Y(t+\u03c4) ] + E[ Y(t)Y(t+\u03c4) ]<\/p>\n<p>R<sub>Z<\/sub>(\u03c4) = R<sub>X<\/sub>(\u03c4) + R<sub>YX<\/sub>(\u03c4)\u00a0 + R<sub>XY<\/sub>(\u03c4)\u00a0 + R<sub>Y<\/sub>(\u03c4)<\/p>\n<p>S<sub>Z<\/sub>(f) = S<sub>X<\/sub>(f) + S<sub>YX<\/sub>(f)\u00a0 + S<sub>XY<\/sub>(f)\u00a0 + S<sub>Y<\/sub>(f)<\/p>\n<p>Si X(t) y Y(t) <em><strong>son ortogonales<\/strong><\/em>, entonces:<\/p>\n<p>R<sub>XY<\/sub>(\u03c4)\u00a0 = R<sub>YX<\/sub>(\u03c4) = 0<\/p>\n<p>S<sub>Z<\/sub>(f) = S<sub>X<\/sub>(f) + 0\u00a0 + 0\u00a0 + S<sub>Y<\/sub>(f)<\/p>\n<p>S<sub>Z<\/sub>(f) = S<sub>X<\/sub>(f) +\u00a0 S<sub>Y<\/sub>(f)<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Referencia: Problema Le\u00f3n Garc\u00eda 10.6 p.636 Sea Z(t) = X(t) + Y(t) \u00bfBajo qu\u00e9 condiciones SZ(f) = SX(f) + SY(f)? Soluci\u00f3n Propuesta: E[ Z(t)Z(t+\u03c4) ] = E[ [X(t) + Y(t)][X(t+\u03c4) + Y(t+\u03c4)] ] = E[ X(t)X(t+\u03c4) + Y(t) X(t+\u03c4) + X(t)Y(t+\u03c4) + Y(t)Y(t+\u03c4) ] = E[ \u00a0X(t)X(t+\u03c4) ] +E[ Y(t) X(t+\u03c4) ] + E[ X(t)Y(t+\u03c4) [&hellip;]<\/p>\n","protected":false},"author":8043,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"wp-custom-template-entrada-stp-unidades","format":"standard","meta":{"footnotes":""},"categories":[214],"tags":[],"class_list":["post-1612","post","type-post","status-publish","format-standard","hentry","category-stp-u02eva"],"_links":{"self":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/1612","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=1612"}],"version-history":[{"count":1,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/1612\/revisions"}],"predecessor-version":[{"id":22136,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/1612\/revisions\/22136"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/media?parent=1612"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/categories?post=1612"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/tags?post=1612"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}