{"id":22031,"date":"2016-10-22T07:53:35","date_gmt":"2016-10-22T12:53:35","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/estg1003\/?p=1806"},"modified":"2026-04-05T16:42:58","modified_gmt":"2026-04-05T21:42:58","slug":"s3eva2017tii_t5-sistema-lineal","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/algoritmos101\/stp-ejemplos\/s3eva2017tii_t5-sistema-lineal\/","title":{"rendered":"s3Eva2017TII_T5 Sistema lineal"},"content":{"rendered":"\n<p><strong>Ejercicio<\/strong>: <a href=\"https:\/\/blog.espol.edu.ec\/algoritmos101\/stp-3eva\/3eva2017tii_t5-sistema-lineal\/\" data-type=\"post\" data-id=\"22063\">3Eva2017TII_T5 Sistema lineal<\/a><\/p>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> Z(t) = X(t) -Y(t) <\/span>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> Y(t) = h(t)*X(t) <\/span>\n\n\n\n<p>a) autocorrelaci\u00f3n de Z(t)<\/p>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> E[Z(t_1)Z(t_2)] = E[(X(t_1) - Y(t_1))(X(t_2) -Y(t_2))] <\/span>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> = E[X(t_1)(X(t_2) - X(t_1)Y(t_2) - Y(t_1)X(t_2) + Y(t_1)Y(t_2)] <\/span>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> = E[X(t_1)(X(t_2)] - E[X(t_1)Y(t_2)] - E[Y(t_1)X(t_2)] + E[Y(t_1)Y(t_2)] <\/span>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> = R_X(\\tau) - R_{XY}(\\tau) - R_{YX}(\\tau) + R_Y(\\tau)<\/span>\n\n\n\n<p>b) Densidad espectral de potencia de Z(t)<\/p>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> Sz(f) = F[R_X(\\tau)] - F[R_{XY}(\\tau)] - F[R_{YX}(\\tau)] + F[R_Y(\\tau)]<\/span>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> = S_X(f) - S_{XY}(f) - S_{YX}(f) + S_Y(f)<\/span>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> = S_X(f) - S_{XY}(f) - S_{XY}^* (f) + S_Y(f)<\/span>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> = S_X(f) - H(f) S_{X}(f) - H^* (f) S_{X}(f) + S_Y(f)<\/span>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> = [1 - H(f) - H^* (f) + |H(f)|^2] S_X(f)<\/span>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> = [1 - 2Re[H(f)] + |H(f)|^2 ] S_X(f)<\/span>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> Sz(f) = |1 - H(f)|^2 S_X(f)<\/span>\n","protected":false},"excerpt":{"rendered":"<p>Ejercicio: 3Eva2017TII_T5 Sistema lineal a) autocorrelaci\u00f3n de Z(t) b) Densidad espectral de potencia de Z(t)<\/p>\n","protected":false},"author":8043,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"wp-custom-template-entrada-stp-ejercicios","format":"standard","meta":{"footnotes":""},"categories":[203],"tags":[58,237],"class_list":["post-22031","post","type-post","status-publish","format-standard","hentry","category-stp-ejemplos","tag-ejemplos-python","tag-pestocasticos"],"_links":{"self":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/22031","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=22031"}],"version-history":[{"count":4,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/22031\/revisions"}],"predecessor-version":[{"id":23546,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/22031\/revisions\/23546"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/media?parent=22031"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/categories?post=22031"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/tags?post=22031"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}