{"id":22030,"date":"2016-10-08T22:03:53","date_gmt":"2016-10-09T03:03:53","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/estg1003\/?p=1718"},"modified":"2026-04-05T16:44:41","modified_gmt":"2026-04-05T21:44:41","slug":"s2eva2017tii_t3-syf-de-la-correlacion-rxt","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/algoritmos101\/stp-ejemplos\/s2eva2017tii_t3-syf-de-la-correlacion-rxt\/","title":{"rendered":"s2Eva2017TII_T3 Sy(f) de la correlaci\u00f3n Rx(t)"},"content":{"rendered":"\n<p><strong>Ejercicio<\/strong>: <a href=\"https:\/\/blog.espol.edu.ec\/algoritmos101\/stp-2eva\/2eva2017tii_t3-syf-de-la-correlacion-rxt\/\" data-type=\"post\" data-id=\"22060\">2Eva2017TII_T3 Sy(f) de la correlaci\u00f3n Rx(t)<\/a><\/p>\n\n\n\n<p><strong>Tema 3<\/strong>.<\/p>\n\n\n\n<p>R<sub>Y<\/sub>(\u03c4)&nbsp; = R<sub>X<\/sub>(\u03c4) cos(2 \u03c0 f<sub>0<\/sub> \u03c4)<\/p>\n\n\n\n<p>R<sub>X<\/sub>(\u03c4) es una funci\u00f3n de autocorrelaci\u00f3n<\/p>\n\n\n\n<p>S<sub>Y<\/sub>(f) = F[R<sub>X<\/sub>(\u03c4) cos(2 \u03c0 f<sub>0<\/sub> \u03c4) ]<\/p>\n\n\n\n<p>=&nbsp; F[R<sub>X<\/sub>(\u03c4) (e<sup>j 2\u03c0 f<sub>0<\/sub> \u03c4<\/sup> +e<sup>-j 2\u03c0 f<sub>0<\/sub> \u03c4<\/sup> )\/2]<\/p>\n\n\n\n<p>=&nbsp; F[R<sub>X<\/sub>(\u03c4) (e<sup>j 2\u03c0 f<sub>0<\/sub> \u03c4<\/sup> )]\/2 + F[R<sub>X<\/sub>(\u03c4) e<sup>-j 2\u03c0 f<sub>0<\/sub> \u03c4<\/sup> )]\/2<\/p>\n\n\n\n<p>= &nbsp;S<sub>X<\/sub>(f - f<sub>0<\/sub> )\/2 + S<sub>X<\/sub>(f + f<sub>0<\/sub> )\/2<\/p>\n\n\n\n<p>la densidad espectral de potencia se determina como:<\/p>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> S_X (f) = F[R_X (\\tau)] <\/span>\n\n\n\n<p>Si <span class=\"wp-katex-eq\" data-display=\"false\"> R_X(\\tau) = \\Lambda \\Big( \\frac{\\tau}{T} \\Big) <\/span><\/p>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> S_X(f) = F \\Big[\\Lambda \\Big(\\frac{t}{\\tau} \\Big) \\Big] <\/span>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> S_X(f) = T [Sa(\\pi fT)]^2 <\/span>\n\n\n\n<p>entonces la densidad espectral de potencia del problema se convierte en:<\/p>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> S_Y (f) = T [Sa(\\pi T(f - f_0)]^2 + T [Sa(\\pi T(f + f_0)]^2 <\/span>\n\n\n\n<p>para el caso de calcular la potencia promedio R<sub>Y<\/sub>(0) = Rx(0) cos(2 \u03c0 f<sub>0<\/sub> 0) = A cos(0) = A.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"619\" height=\"206\" src=\"http:\/\/blog.espol.edu.ec\/algoritmos101\/files\/2018\/02\/Rxtcos_desplazado01.png\" alt=\"Se\u00f1al Rx t coseno desplazado\" class=\"wp-image-22534\" \/><\/figure>\n\n\n\n<p>&nbsp;<\/p>\n\n\n\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Ejercicio: 2Eva2017TII_T3 Sy(f) de la correlaci\u00f3n Rx(t) Tema 3. RY(\u03c4)&nbsp; = RX(\u03c4) cos(2 \u03c0 f0 \u03c4) RX(\u03c4) es una funci\u00f3n de autocorrelaci\u00f3n SY(f) = F[RX(\u03c4) cos(2 \u03c0 f0 \u03c4) ] =&nbsp; F[RX(\u03c4) (ej 2\u03c0 f0 \u03c4 +e-j 2\u03c0 f0 \u03c4 )\/2] =&nbsp; F[RX(\u03c4) (ej 2\u03c0 f0 \u03c4 )]\/2 + F[RX(\u03c4) e-j 2\u03c0 f0 \u03c4 )]\/2 [&hellip;]<\/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-22030","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\/22030","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=22030"}],"version-history":[{"count":4,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/22030\/revisions"}],"predecessor-version":[{"id":23551,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/22030\/revisions\/23551"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/media?parent=22030"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/categories?post=22030"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/tags?post=22030"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}