{"id":1580,"date":"2016-12-21T08:12:49","date_gmt":"2016-12-21T13:12:49","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/estg1003\/?p=1580"},"modified":"2026-04-04T10:55:43","modified_gmt":"2026-04-04T15:55:43","slug":"autocorrelacion-am","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/algoritmos101\/stp-u02eva\/autocorrelacion-am\/","title":{"rendered":"autocorrelacion AM"},"content":{"rendered":"\n<p><em><strong>Referencia<\/strong><\/em>: Problema Le\u00f3n Garc\u00eda 10.3 p.635<\/p>\n\n\n\n<p>a) Encuentre la densidad espectral de potencia S<sub>Y<\/sub>(f) de un proceso aleatorio con funci\u00f3n de autocorrelaci\u00f3n R<sub>X<\/sub>(\u03c4) cos(2\u03c0 f<sub>0<\/sub> \u03c4), donde R<sub>X<\/sub>(\u03c4) es tambi\u00e9n una funci\u00f3n de autocorrelaci\u00f3n.<\/p>\n\n\n\n<p>b) Grafique S<sub>Y<\/sub>(f) si R<sub>X<\/sub>(\u03c4) como en el problema 10.1a.<\/p>\n\n\n\n<p><em><strong>Soluci\u00f3n propuesta<\/strong><\/em>:<\/p>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> R_Y(\\tau) = R_X(\\tau) \\cos(2\\pi f_0 \\tau) <\/span>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> S_Y(f) = F\\Big[ R_X(\\tau) \\cos(2\\pi f_0 \\tau) \\Big] <\/span>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> = F\\Big[ R_X(\\tau) \\frac {e^{j2\\pi f_0 \\tau} + e^{-j2\\pi f_0 \\tau}}{2} \\Big] <\/span>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> = \\frac{1}{2} F\\Big[ R_X(\\tau) e^{j2\\pi f_0 \\tau} \\Big] + \\frac{1}{2} F\\Big[ R_X(\\tau) e^{-j2\\pi f_0 \\tau} \\Big] <\/span>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> = \\frac{1}{2} S_X(f-f_0) + \\frac{1}{2} S_X(f+f_0) <\/span>\n\n\n\n<p>donde S<sub>X<\/sub> (f) = F[R<sub>X<\/sub>(\u03c4)]<\/p>\n\n\n\n<figure class=\"wp-block-image\"><a href=\"https:\/\/blog.espol.edu.ec\/algoritmos101\/estg1003\/files\/2018\/01\/triangular02.png\"><img decoding=\"async\" src=\"https:\/\/blog.espol.edu.ec\/algoritmos101\/estg1003\/files\/2018\/01\/triangular02.png\" alt=\"\" class=\"wp-image-1585\" \/><\/a><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Referencia: Problema Le\u00f3n Garc\u00eda 10.3 p.635 a) Encuentre la densidad espectral de potencia SY(f) de un proceso aleatorio con funci\u00f3n de autocorrelaci\u00f3n RX(\u03c4) cos(2\u03c0 f0 \u03c4), donde RX(\u03c4) es tambi\u00e9n una funci\u00f3n de autocorrelaci\u00f3n. b) Grafique SY(f) si RX(\u03c4) como en el problema 10.1a. Soluci\u00f3n propuesta: donde SX (f) = F[RX(\u03c4)]<\/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-1580","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\/1580","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=1580"}],"version-history":[{"count":2,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/1580\/revisions"}],"predecessor-version":[{"id":23054,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/1580\/revisions\/23054"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/media?parent=1580"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/categories?post=1580"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/tags?post=1580"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}