{"id":22047,"date":"2016-09-24T08:19:20","date_gmt":"2016-09-24T13:19:20","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/estg1003\/?p=812"},"modified":"2026-04-04T11:25:11","modified_gmt":"2026-04-04T16:25:11","slug":"2eva2009tii_t3-densidad-espectral-de-potencia","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/algoritmos101\/stp-evalua\/stp-2eva-fiec\/2eva2009tii_t3-densidad-espectral-de-potencia\/","title":{"rendered":"2Eva2009TII_T3 Densidad espectral de potencia"},"content":{"rendered":"\n

2da Evaluaci\u00f3n II T\u00e9rmino 2009-2010. Febrero 4, 2010 . FIEC03236<\/h2>\n\n\n\n

Tema 3<\/strong> (30 puntos). Un proceso aleatorio estacionario en sentido amplio X(t) con densidad espectral de potencia:<\/p>\n\n\n \\Im_{XX}(\\omega) = 50 \\pi \\delta(\\omega) + \\frac{3}{1+\\left(\\frac{\\omega}{2}\\right)^2} <\/span>\n\n\n\n

se aplica a una red con respuesta impulso<\/p>\n\n\n h(t) = 2 e^{-2t} \\mu (t) <\/span>\n\n\n\n

obteniendo luego de la red Y(t)<\/p>\n\n\n\n

Determine:<\/p>\n\n\n\n

a) Var[X(t)]<\/p>\n\n\n\n

b) La densidad espectral de potencia de la respuesta de Y(t)<\/p>\n\n\n\n

c) La potencia de Y(t)<\/p>\n\n\n\n

Pares de Transformadas de Fourier: <\/em><\/p>\n\n\n x(t) \\leftrightarrow X(\\omega) <\/span>\n\n\n 1 \\leftrightarrow 2 \\pi \\delta(\\omega)<\/span>\n\n\n e^{-at}\\mu (t) \\leftrightarrow \\frac{1}{a+j\\omega}<\/span>\n\n\n te^{-at}\\mu (t) \\leftrightarrow \\frac{1}{(a+j\\omega)^{2}}<\/span>\n\n\n t^{n}e^{-at}\\mu (t) \\leftrightarrow \\frac{n!}{(a+j\\omega)^{n+1}}<\/span>\n\n\n a>0 <\/span>\n","protected":false},"excerpt":{"rendered":"

2da Evaluaci\u00f3n II T\u00e9rmino 2009-2010. Febrero 4, 2010 . FIEC03236 Tema 3 (30 puntos). Un proceso aleatorio estacionario en sentido amplio X(t) con densidad espectral de potencia: se aplica a una red con respuesta impulso obteniendo luego de la red Y(t) Determine: a) Var[X(t)] b) La densidad espectral de potencia de la respuesta de Y(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":[209],"tags":[],"class_list":["post-22047","post","type-post","status-publish","format-standard","hentry","category-stp-2eva-fiec"],"_links":{"self":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/22047","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=22047"}],"version-history":[{"count":3,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/22047\/revisions"}],"predecessor-version":[{"id":22614,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/22047\/revisions\/22614"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/media?parent=22047"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/categories?post=22047"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/tags?post=22047"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}