{"id":1493,"date":"2017-06-21T19:00:50","date_gmt":"2017-06-22T00:00:50","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/telg1001\/?p=1493"},"modified":"2026-04-05T23:45:23","modified_gmt":"2026-04-06T04:45:23","slug":"transformada-fourier-tabla","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/algoritmos101\/ss-u05\/transformada-fourier-tabla\/","title":{"rendered":"5.4.2 Transformadas de Fourier - Tabla"},"content":{"rendered":"\n

Referencia<\/strong><\/em>: Lathi Tabla 7.1 p699. Shaum Hsu Tabla 5-2 p223. Oppenheim Tabla 4.2 p329 pdf357<\/p>\n\n\n\n

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

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

No<\/th>x(t)<\/th>X(\u03c9)<\/th> <\/th><\/tr>
1<\/td>e-at<\/sup> \u03bc (t)<\/td> \\frac{1}{a + j \\omega}<\/span><\/td>a>0<\/td><\/tr>
2<\/td>eat<\/sup> \u03bc (-t)<\/td> \\frac{1}{a - j \\omega}<\/span><\/td>a>0<\/td><\/tr>
3<\/td>e-a|t|<\/sup><\/td> \\frac{2a}{a^2+ \\omega ^2}<\/span><\/td>a>0<\/td><\/tr>
4<\/td>t e-at<\/sup> \u03bc (t)<\/td> \\frac{1}{(a+j \\omega)^2}<\/span><\/td>a>0<\/td><\/tr>
5<\/td>tn<\/sup>  e-at<\/sup> \u03bc (t)<\/td> \\frac{n!}{(a+j \\omega)^{n+1}}<\/span><\/td>a>0<\/td><\/tr>
6a<\/td>\u03b4(t)<\/td>1<\/td> <\/td><\/tr>
6b<\/td>\u03b4(t-t0<\/sub>)<\/td>e-j\u03c9t0<\/sub><\/sup><\/td> <\/td><\/tr>
7<\/td>1<\/td> 2\\pi \\delta (\\omega)<\/span><\/td> <\/td><\/tr>
8<\/td>ej\u03c90<\/sub>t<\/sup><\/td> 2\\pi \\delta (\\omega-\\omega_0)<\/span><\/td> <\/td><\/tr>
9<\/td>cos (\u03c90<\/sub> t)<\/td> \\pi [\\delta (\\omega - \\omega_0) +\\delta (\\omega + \\omega_0)] <\/span><\/td> <\/td><\/tr>
10<\/td>sin (\u03c90<\/sub> t)<\/td> \\pi [\\delta (\\omega + \\omega_0) -\\delta (\\omega - \\omega_0)] <\/span><\/td> <\/td><\/tr>
11a<\/td>\u03bc(t)<\/td> \\pi \\delta (\\omega ) +\\frac{1}{j \\omega } <\/span><\/td> <\/td><\/tr>
11b<\/td>\u03bc(-t)<\/td> \\pi \\delta (\\omega ) - \\frac{1}{j \\omega } <\/span><\/td> <\/td><\/tr>
12<\/td>sgn (t)<\/td>\\frac{2}{j \\omega} <\/span><\/td> <\/td><\/tr>
13<\/td>cos (\u03c90<\/sub> t) \u03bc(t)<\/td>\\frac{\\pi}{2} [\\delta (\\omega - \\omega_0) +\\delta (\\omega + \\omega_0)] + \\frac{j \\omega}{\\omega_0^2 - \\omega ^2}<\/span><\/td><\/tr>
14<\/td>sin (\u03c90<\/sub> t) \u03bc(t)<\/td>\\frac{\\pi}{2j} [\\delta (\\omega - \\omega_0) - \\delta (\\omega + \\omega_0)] + \\frac{\\omega_0}{\\omega_0^2 - \\omega ^2}<\/span><\/td><\/tr>
15<\/td>e-at<\/sup> sin (\u03c90<\/sub> t) \u03bc(t)<\/td> \\frac{\\omega_0}{(a+j\\omega)^2 + \\omega_0^2} <\/span><\/td>a>0<\/td><\/tr>
16<\/td>e-at<\/sup> cos (\u03c90<\/sub> t) \u03bc(t)<\/td> \\frac{a + j\\omega}{(a+j\\omega)^2 + \\omega_0^2} <\/span><\/td>a>0<\/td><\/tr>
17<\/td> rect \\Big(\\frac{1}{\\tau}\\Big) <\/span><\/td> \\tau sinc \\Big( \\frac{\\omega \\tau}{2} \\Big) <\/span><\/td> <\/td><\/tr>
18<\/td> \\frac{W}{\\pi} sinc (Wt) <\/span><\/td> rect \\Big(\\frac{\\omega}{2W} \\Big)<\/span><\/td> <\/td><\/tr>
19<\/td> \\Delta \\Big( \\frac{t}{\\tau} \\Big) <\/span><\/td> \\frac{\\tau}{2}sinc ^2 \\Big( \\frac{\\omega \\tau}{4} \\Big)<\/span><\/td> <\/td><\/tr>
20<\/td> \\frac{W}{2\\pi} sinc ^2 \\Big(\\frac{Wt}{2} \\Big) <\/span><\/td> \\Delta \\Big(\\frac{\\omega}{2W} \\Big)<\/span><\/td> <\/td><\/tr>
21<\/td> \\sum_{n=- \\infty}^{\\infty} \\delta(t-nT)<\/span><\/td> \\omega_0 \\sum_{n=-\\infty}^{\\infty} \\delta(\\omega-n \\omega_0)<\/span><\/td> \\omega_0 = \\frac{2 \\pi}{T} <\/span><\/td><\/tr>
22<\/td> \\frac{e^{-t^2}}{2 \\sigma ^2}<\/span><\/td> \\sigma \\sqrt{2 \\pi} e^{-\\sigma^2 \\omega^2 \/2}<\/span><\/td> <\/td><\/tr>
23<\/td> \\frac{1}{a^2 + t^2}<\/span><\/td> e ^{-a|\\omega|}<\/span><\/td> <\/td><\/tr>
24<\/td> e ^{-at^2}<\/span><\/td> \\sqrt{\\frac{\\pi}{a}}e ^{-\\omega^2 \/4a}<\/span><\/td>a>0<\/td><\/tr>
25<\/td> p_a(t) = \\begin{cases} 1 & |t|<a \\\\ 0 & |t|>a \\end{cases} <\/span><\/td> 2a\\frac{\\sin (\\omega a)}{(\\omega a)}<\/span><\/td> <\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

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

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

Referencia: Lathi Tabla 7.1 p699. Shaum Hsu Tabla 5-2 p223. Oppenheim Tabla 4.2 p329 pdf357 Transformada Fourier - Propiedades Series de Fourier de se\u00f1ales peri\u00f3dicas con Python No x(t) X(\u03c9)   1 e-at \u03bc (t) a>0 2 eat \u03bc (-t) a>0 3 e-a|t| a>0 4 t e-at \u03bc (t) a>0 5 tn  e-at \u03bc (t) […]<\/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-1493","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\/1493","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=1493"}],"version-history":[{"count":7,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/1493\/revisions"}],"predecessor-version":[{"id":24023,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/1493\/revisions\/24023"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/media?parent=1493"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/categories?post=1493"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/tags?post=1493"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}