{"id":22025,"date":"2016-12-20T07:22:46","date_gmt":"2016-12-20T12:22:46","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/estg1003\/?p=1565"},"modified":"2026-04-04T10:55:33","modified_gmt":"2026-04-04T15:55:33","slug":"psd-rectangular-triangular","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/algoritmos101\/stp-u02eva\/psd-rectangular-triangular\/","title":{"rendered":"PSD - Rectangular y Triangular"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">1. PSD Rectangular<\/h2>\n\n\n\n<p><em><strong>Referencia<\/strong><\/em>: Problema Le\u00f3n Garc\u00eda 10.2 p.635<\/p>\n\n\n\n<figure class=\"wp-block-image alignright\"><a href=\"https:\/\/blog.espol.edu.ec\/algoritmos101\/estg1003\/files\/2018\/01\/rectangular01.png\"><img loading=\"lazy\" decoding=\"async\" width=\"214\" height=\"109\" src=\"https:\/\/blog.espol.edu.ec\/algoritmos101\/estg1003\/files\/2018\/01\/rectangular01.png\" alt=\"\" class=\"wp-image-1567\" \/><\/a><\/figure>\n\n\n\n<p>Sea p(x) una funci\u00f3n rectangular. \u00bf R<sub>X<\/sub>(\u03c4) = p(\u03c4\/T) es una funci\u00f3n de autocorrelaci\u00f3n? <\/p>\n\n\n\n<p><em><strong>Soluci\u00f3n propuesta<\/strong><\/em>:<\/p>\n\n\n\n<p>T=2, es funci\u00f3n rectangular es el ancho de la base.<\/p>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> S_Y(f) = F\\Big[ \\prod \\Big(\\frac{\\tau}{T} \\Big) \\Big] <\/span>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> = 2AT \\frac {Sen(2\\pi f \\tau)}{2\\pi fT} <\/span>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> = AT Sa (\\pi f\\tau) <\/span>\n\n\n\n<p>La funci\u00f3n S<sub>X<\/sub>(f) es negativa para algunos rangos de f. Dado que la densidad espectral de potencia es no negativa, la funci\u00f3n rectangular en el tiempo no es una funci\u00f3n de autocorrelac\u00f3n v\u00e1lida.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\" \/>\n\n\n\n<h2 class=\"wp-block-heading\">2. PSD Triangular<\/h2>\n\n\n\n<p>&nbsp;<em><strong>Referencia<\/strong><\/em>: Problema Le\u00f3n Garc\u00eda 10.1 p.635<\/p>\n\n\n\n<figure class=\"wp-block-image alignright size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"244\" height=\"132\" src=\"http:\/\/blog.espol.edu.ec\/algoritmos101\/files\/2018\/02\/triangular01.png\" alt=\"triangular01\" class=\"wp-image-22636\" \/><\/figure>\n\n\n\n<p>Sea g(x) una funci\u00f3n triangular.<\/p>\n\n\n\n<p>amplitud = A<br>T = 1 , en triangulares T es la mitad de la base del tri\u00e1ngulo.<\/p>\n\n\n\n<p>a) Encuentre la densidad espectral de potencia correspondiente a R<sub>X<\/sub>(\u03c4) = g(\u03c4\/T)<\/p>\n\n\n\n<p>b) Encuentre la autocorrelaci\u00f3n correspondiente a la densidad espectral de potencia S<sub>X<\/sub>(f) = g(f\/W)<\/p>\n\n\n\n<p><em><strong>Soluci\u00f3n propuesta<\/strong><\/em>:<br>a)<\/p>\n\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> S_x(f) = F\\Big[ g \\Big(\\frac{\\tau}{T} \\Big) \\Big]<\/span>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> = AT \\Big(\\frac{sin\\frac{\\omega T}{2}}{\\frac{\\omega T}{2}} \\Big)^2 <\/span>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> = AT \\big[Sa(\\pi f T) \\big]^2 <\/span>\n\n\n\n<p>b)<\/p>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> S_x(f) = F\\Big[ g \\Big(\\frac{f}{W} \\Big) \\Big]<\/span>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> R_X (\\tau) = AW \\Big(\\frac{sin\\frac{W \\tau}{2}}{\\frac{W \\tau}{2}} \\Big)^2 <\/span>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> = AW \\big[Sa(\\pi f \\tau) \\big]^2 <\/span>\n\n\n\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>1. PSD Rectangular Referencia: Problema Le\u00f3n Garc\u00eda 10.2 p.635 Sea p(x) una funci\u00f3n rectangular. \u00bf RX(\u03c4) = p(\u03c4\/T) es una funci\u00f3n de autocorrelaci\u00f3n? Soluci\u00f3n propuesta: T=2, es funci\u00f3n rectangular es el ancho de la base. La funci\u00f3n SX(f) es negativa para algunos rangos de f. Dado que la densidad espectral de potencia es no negativa, [&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-22025","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\/22025","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=22025"}],"version-history":[{"count":2,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/22025\/revisions"}],"predecessor-version":[{"id":23259,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/22025\/revisions\/23259"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/media?parent=22025"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/categories?post=22025"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/tags?post=22025"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}