{"id":1515,"date":"2017-06-20T20:00:00","date_gmt":"2017-06-21T01:00:00","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/telg1001\/?p=1515"},"modified":"2026-04-05T23:46:40","modified_gmt":"2026-04-06T04:46:40","slug":"transformada-fourier-tabla-de-propiedades","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/algoritmos101\/ss-u05\/transformada-fourier-tabla-de-propiedades\/","title":{"rendered":"5.4.1 Transformadas de Fourier - Tabla de Propiedades"},"content":{"rendered":"\n

Referencia<\/strong><\/em>: Schaum Hsu Tabla 5-1 p222. Lathi Tabla 7.2 p717, Oppenheim Tabla 4.1p328 pdf356<\/p>\n\n\n\n

Transformada Fourier - Tabla<\/a><\/p>\n\n\n\n

Series de Fourier de se\u00f1ales peri\u00f3dicas con Python<\/a><\/p>\n\n\n\n

Operaci\u00f3n<\/th>x(t)<\/th>X(\u03c9)<\/th><\/tr>
 <\/td>x(t)
x1<\/sub>(t)
x2<\/sub>(t)<\/td>		X(\u03c9)
X1<\/sub>(\u03c9)
X2<\/sub>(\u03c9)<\/td><\/tr>
Multiplicaci\u00f3n por escalar<\/td>k x(t)<\/td>k X(\u03c9)<\/td><\/tr>
Aditiva<\/td>x1<\/sub>(t) +x2<\/sub>(t)<\/td>X1<\/sub>(\u03c9) + X2<\/sub>(\u03c9)<\/td><\/tr>
Linealidad<\/td>a1<\/sub> x1<\/sub>(t) + a2<\/sub> x2<\/sub>(t)<\/td>a1<\/sub> X1<\/sub>(\u03c9) + a2<\/sub> X2<\/sub>(\u03c9)<\/td><\/tr>
Conjugada<\/td>x*<\/sup>(t)<\/td>X*<\/sup>(-\u03c9)<\/td><\/tr>
Inversi\u00f3n en tiempo<\/td>x(-t)<\/td>X(-\u03c9)<\/td><\/tr>
Dualidad<\/td>X(t)<\/td>2\u03c0 x(-\u03c9)<\/td><\/tr>
Escalamiento
(a Real)<\/td>		x(at)<\/td> \\frac{1}{|a|} X \\Big(\\frac{\\omega}{a} \\Big) <\/span><\/td><\/tr>
Desplazamiento en tiempo (t Real)<\/td>x(t-t0<\/sub>)<\/td>X(\u03c9) e-j\u03c9t0<\/sub><\/sup><\/td><\/tr>
Deplazamiento en frecuencia (\u03c90<\/sub> Real)<\/td>x(t)ej\u03c90<\/sub>t<\/sup><\/td>X(\u03c9-\u03c90<\/sub>)<\/td><\/tr>
Convoluci\u00f3n en tiempo<\/td> x_1(t) \\circledast x_2 (t)<\/span><\/td>X1<\/sub>(\u03c9)X2<\/sub>(\u03c9)<\/td><\/tr>
Convoluci\u00f3n en frecuencia<\/td>x1<\/sub>(t)x2<\/sub>(t)<\/td> \\frac{1}{2 \\pi}X_1(\\omega) \\circledast X_2 (\\omega)<\/span><\/td><\/tr>
Derivada en tiempo<\/td> \\frac{\\delta^n}{\\delta t^n}x(t)<\/span><\/td>(j\u03c9)n<\/sup> X(\u03c9)<\/td><\/tr>
Derivada en frecuencia<\/td>(-jt)x(t)<\/td> \\frac{\\delta}{\\delta \\omega}X(\\omega)<\/span><\/td><\/tr>
Integral en tiempo<\/td> \\int_{- \\infty}^{t}x(u) \\delta u<\/span><\/td>\\frac{X(\\omega)}{j \\omega} + \\pi X(0) \\delta (\\omega) <\/span><\/td><\/tr>
Se\u00f1al Real<\/td> x(t) = x_e(t) + x_o(t)<\/span><\/td> X(\\omega) = A(\\omega)+jB(\\omega) <\/span><\/td><\/tr>
componente par
componente impar<\/td>		 x_e(t) <\/span>
x_o(t) <\/span><\/td>		 Re[X(\\omega)] = A(\\omega) <\/span>
j Im[X(\\omega)] = j B(\\omega) <\/span><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Relaci\u00f3n de Parseval<\/p>\n\n\n \\int_{-\\infty}^{\\infty} x_1 (\\lambda) X_2 (\\lambda) \\delta \\lambda = \\int_{-\\infty}^{\\infty} X_1 (\\lambda) x_2 (\\lambda) \\delta \\lambda<\/span>\n\n\n \\int_{-\\infty}^{\\infty} x_1 (t) x_2 (t) \\delta t = \\frac{1}{2 \\pi}\\int_{-\\infty}^{\\infty} X_1 (\\omega) X_2 (-\\omega) \\delta \\omega <\/span>\n\n\n \\int_{-\\infty}^{\\infty} |x (t)|^2 \\delta t = \\frac{1}{2 \\pi} \\int_{-\\infty}^{\\infty} |X (\\omega) |^2 \\delta \\omega <\/span>\n\n\n\n

Transformada Fourier - Tabla<\/a><\/p>\n\n\n\n

Series de Fourier de se\u00f1ales peri\u00f3dicas con Python<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Referencia: Schaum Hsu Tabla 5-1 p222. Lathi Tabla 7.2 p717, Oppenheim Tabla 4.1p328 pdf356 Transformada Fourier - Tabla Series de Fourier de se\u00f1ales peri\u00f3dicas con Python Operaci\u00f3n x(t) X(\u03c9)   x(t)x1(t)x2(t) X(\u03c9)X1(\u03c9)X2(\u03c9) Multiplicaci\u00f3n por escalar k x(t) k X(\u03c9) Aditiva x1(t) +x2(t) X1(\u03c9) + X2(\u03c9) Linealidad a1 x1(t) + a2 x2(t) a1 X1(\u03c9) + a2 X2(\u03c9) […]<\/p>\n","protected":false},"author":8043,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"wp-custom-template-entrada-ss-unidades","format":"standard","meta":{"footnotes":""},"categories":[175],"tags":[],"class_list":["post-1515","post","type-post","status-publish","format-standard","hentry","category-ss-u05"],"_links":{"self":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/1515","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=1515"}],"version-history":[{"count":5,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/1515\/revisions"}],"predecessor-version":[{"id":24025,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/1515\/revisions\/24025"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/media?parent=1515"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/categories?post=1515"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/tags?post=1515"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}