{"id":23278,"date":"2024-03-19T18:10:25","date_gmt":"2024-03-19T10:10:25","guid":{"rendered":"http:\/\/www.jdcui.com\/?p=23278"},"modified":"2025-05-03T21:34:05","modified_gmt":"2025-05-03T13:34:05","slug":"%e6%95%b0%e5%ad%a6-%e5%82%85%e9%87%8c%e5%8f%b6%e5%8f%98%e6%8d%a2%e5%85%ac%e5%bc%8f%e7%9a%84%e5%87%a0%e7%a7%8d%e5%bd%a2%e5%bc%8f-several-forms-of-fourier-transform-formulas","status":"publish","type":"post","link":"http:\/\/www.jdcui.com\/?p=23278","title":{"rendered":"[\u6570\u5b66][\u7b14\u8bb0] \u5085\u91cc\u53f6\u53d8\u6362\u516c\u5f0f\u7684\u51e0\u79cd\u5f62\u5f0f (Several Forms of Fourier Transform Formulas)"},"content":{"rendered":"<p><script id=\"MathJax-script\" async=\"\" src=\"http:\/\/www.jdcui.com\/wp-content\/MathJax_3_1_2\/MathJax-master\/es5\/tex-mml-chtml.js\"><\/script><\/p>\n<p><span style=\"color: #ff00ff; background-color: #ccffcc;\"><strong>\u5b9e\u5e72\u3001\u5b9e\u8df5\u3001\u79ef\u7d2f\u3001\u601d\u8003\u3001\u521b\u65b0\u3002<\/strong><\/span><\/p>\n<hr \/>\n<p># \u5085\u91cc\u53f6\u53d8\u6362\u516c\u5f0f\u7684\u51e0\u79cd\u5f62\u5f0f<\/p>\n<p>\u7814\u7a76\u632f\u52a8\u63a7\u5236\u3001\u968f\u673a\u632f\u52a8\u7b49\uff0c\u79bb\u4e0d\u5f00\u5085\u91cc\u53f6\u53d8\u6362\uff08Fourier transforms\uff09\u3002\u5bf9\u4e8e\u5085\u91cc\u53f6\u53d8\u6362\uff0c\u4e0d\u540c\u6587\u732e\u3001\u4e66\u7c4d\u6709\u65f6\u5019\u4f1a\u91c7\u7528\u4e0d\u540c\u5f62\u5f0f\u7684\u516c\u5f0f\uff0c\u521a\u5f00\u59cb\u770b\u7684\u65f6\u5019\u6709\u70b9\u51cc\u4e71\uff0c\u540e\u9762\u624d\u7406\u6e05\u695a\uff0c\u5176\u5b9e\u4e0d\u540c\u516c\u5f0f\u5f62\u5f0f\u672c\u8d28\u4e0a\u90fd\u662f\u7b49\u4ef7\u3002\u4e3a\u4e86\u4fbf\u4e8e\u540e\u7eed\u5b66\u4e60\uff0c\u4ee5\u4e0b\u603b\u7ed3\u51e0\u79cd\u5e38\u89c1\u7684\u5085\u91cc\u53f6\u53d8\u6362\u516c\u5f0f\u5f62\u5f0f\u3002PS.\u8fd9\u91cc\u5085\u91cc\u53f6\u53d8\u6362\uff0c\u6307\u7684\u662f\u975e\u5468\u671f\u51fd\u6570\uff08\u5468\u671f\u53ef\u4ee5\u7406\u89e3\u4e3a\u65e0\u9650\u957f\uff09\u7684\u5085\u91cc\u53f6\u53d8\u6362\uff0c\u4e0d\u662f\u5085\u91cc\u53f6\u7ea7\u6570\uff08Fourier series\uff09\uff0c\u5085\u91cc\u53f6\u7ea7\u6570\u662f\u9488\u5bf9\u5468\u671f\u51fd\u6570\u7684\u8bf4\u6cd5\u3002<\/p>\n<p><span style=\"background-color: #ccffff;\"><strong>## \u7b2c\u4e00\u79cd\u5f62\u5f0f<\/strong><\/span><\/p>\n<p>\u4e00\u79cd\u901a\u7528\u7684\u5f62\u5f0f\uff0c\\(\\Phi \\left( p \\right)\\)\u548c\\(F\\left( x \\right)\\)\u4e92\u4e3a\u5085\u91cc\u53f6\u53d8\u6362\u5bf9\uff1a<\/p>\n<p>$$\\Phi \\left( p \\right) \\Leftrightarrow F\\left( x \\right)$$<\/p>\n<p>$$\\Phi \\left( p \\right) = {1 \\over {2\\pi }}\\int_{ &#8211; \\infty }^{ + \\infty } {F\\left( x \\right)} \\;{e^{ipx}}dx$$<\/p>\n<p>$$F\\left( x \\right) = \\int_{ &#8211; \\infty }^{ + \\infty } {\\Phi \\left( p \\right)} \\;{e^{ &#8211; ipx}}dp$$<\/p>\n<p>\u5c06\u4e0a\u8ff0\u4e2d\u516c\u5f0f\u4e2d\u7684\u53d8\u91cf\\(x\\)\u66ff\u6362\u4e3a\\(t\\)\uff0c\\(p\\)\u66ff\u6362\u4e3a\\(f\\)\uff0c\u5219\u53d8\u4e3a\u7269\u7406\u4e2d\u4e60\u60ef\u7684\u7b26\u53f7\uff0c\u5176\u4e2d\\(t\\)\u4e3a\u65f6\u95f4\uff08time\uff09\uff0c\\(f\\)\u4e3a\u9891\u7387\uff08frequency\uff09\u3002<\/p>\n<p>$$\\Phi \\left( f \\right) \\Leftrightarrow F\\left( t \\right)$$<\/p>\n<p>$$\\Phi \\left( f \\right) = \\int_{ &#8211; \\infty }^{ + \\infty } {F\\left( t \\right)} \\;{e^{2\\pi ift}}dt$$<\/p>\n<p>$$F\\left( t \\right) = \\int_{ &#8211; \\infty }^{ + \\infty } {\\Phi \\left( f \\right)} \\;{e^{ &#8211; 2\\pi {\\rm{i}}ft}}df$$<\/p>\n<p>\u7531\u516c\u5f0f\u53ef\u89c1\uff0c\\(\\Phi \\left( f \\right)\\)\u548c\\(F\\left( t \\right)\\)\u57fa\u672c\u5bf9\u79f0\uff0c\u9664\u4e86\u81ea\u7136\u5bf9\u6570\u6307\u6570\u4e0a\u7684\u8d1f\u53f7\uff0c\u8d1f\u53f7\u53ef\u653e\u5728\\(\\Phi \\left( f \\right)\\)\uff0c\u4e5f\u53ef\u4ee5\u653e\u5728\\(F\\left( t \\right)\\)\uff0c\u552f\u4e00\u7684\u5dee\u522b\u662f\uff0c\u6307\u6570\u53d6\u6b63\u53f7\u548c\u53d6\u8d1f\u53f7\u6c42\u51fa\u7684\\(\\Phi \\left( f \\right)\\)\u5171\u8f6d\u3002<\/p>\n<p><span style=\"background-color: #ccffff;\"><strong>## \u7b2c\u4e8c\u79cd\u5f62\u5f0f<\/strong><\/span><\/p>\n<p>\u5728\u5f62\u5f0f\u4e00\u7684\u57fa\u7840\u4e0a\uff0c\u5c06\u9891\u7387 \u6539\u4e3a\u5706\u9891\u7387\uff08angular frequency\uff09\uff0c\u5373\\(w = 2\\pi f\\)\uff0c\\(df\\)\u6539\u4e3a\\({1 \\over {2\\pi }}dw = df\\)\uff0c\u5219\u516c\u5f0f\u53d8\u4e3a<\/p>\n<p>$$\\Phi \\left( w \\right) \\Leftrightarrow F\\left( t \\right)$$<\/p>\n<p>$$\\Phi \\left( w \\right) = \\int_{ &#8211; \\infty }^{ + \\infty } {F\\left( t \\right)} \\;{e^{iwt}}dt$$<\/p>\n<p>$$F\\left( t \\right) = {1 \\over {2\\pi }}\\int_{ &#8211; \\infty }^{ + \\infty } {\\Phi \\left( w \\right)} \\;{e^{ &#8211; iwt}}dw$$<\/p>\n<p>\u8fd9\u79cd\u5f62\u5f0f\u901a\u5e38\u5728\u4e00\u4e9b\u52a8\u529b\u5b66\u53ca\u6297\u9707\u4e66\u7c4d\u4e0a\u51fa\u73b0\uff0c\u6b64\u65f6\uff0c\u5728\u9006\u53d8\u6362\u516c\u5f0f\\(F\\left( t \\right)\\)\u4e2d\u591a\u4e86\u4e2a\\({1 \\over {2\\pi }}\\)\u3002<\/p>\n<p>\u53e6\u5916\uff0c\u8fd9\u4e2a\\({1 \\over {2\\pi }}\\)\u4e5f\u53ef\u4ee5\u653e\u5728\u6b63\u53d8\u6362\u4e00\u4fa7\\(\\Phi \\left( w \\right)\\)\uff0c\u5219\u516c\u5f0f\u53d8\u4e3a<\/p>\n<p>$$\\Phi \\left( w \\right) \\Leftrightarrow F\\left( t \\right)$$<\/p>\n<p>$$\\Phi \\left( w \\right) = {1 \\over {2\\pi }}\\int_{ &#8211; \\infty }^{ + \\infty } {F\\left( t \\right)} \\;{e^{iwt}}dt$$<\/p>\n<p>$$F\\left( t \\right) = \\int_{ &#8211; \\infty }^{ + \\infty } {\\Phi \\left( w \\right)} \\;{e^{ &#8211; iwt}}dw$$<\/p>\n<p>\u8fd8\u53ef\u4ee5\u5c06\\({1 \\over {2\\pi }}\\)\u5f00\u6839\u53f7\uff0c\u540c\u65f6\u653e\u5230\\(\\Phi \\left( w \\right)\\)\u548c\\(F\\left( t \\right)\\)\u4e2d\uff0c\u4fdd\u6301\u6b63\u53d8\u6362\u548c\u9006\u53d8\u6362\u516c\u5f0f\u7684\u5bf9\u79f0\u6027\uff0c\u5982\u4e0b\u6240\u793a<\/p>\n<p>$$\\Phi \\left( w \\right) \\Leftrightarrow F\\left( t \\right)$$<\/p>\n<p>$$\\Phi \\left( w \\right) = \\sqrt {{1 \\over {2\\pi }}} \\int_{ &#8211; \\infty }^{ + \\infty } {F\\left( t \\right)} \\;{e^{iwt}}dt$$<\/p>\n<p>$$F\\left( t \\right) = \\sqrt {{1 \\over {2\\pi }}} \\int_{ &#8211; \\infty }^{ + \\infty } {\\Phi \\left( w \\right)} \\;{e^{ &#8211; iwt}}dw$$<\/p>\n<ul style=\"list-style-type: square;\">\n<li><strong>\u76f8\u5173\u535a\u6587<span style=\"color: #0000ff;\">( Related Topics)<\/span><\/strong><\/li>\n<\/ul>\n<p><strong>[01] <a title=\"[\u7b14\u8bb0] \u968f\u673a\u8fc7\u7a0b\u4e2d\u7684\u5e73\u7a33\u4e0e\u5404\u6001\u5386\u7ecf (Stationarity and ergodicity in random processes)\" href=\"http:\/\/www.jdcui.com\/?p=23301\" target=\"_blank\" rel=\"noopener\">[\u7b14\u8bb0] \u968f\u673a\u8fc7\u7a0b\u4e2d\u7684\u5e73\u7a33\u4e0e\u5404\u6001\u5386\u7ecf (Stationarity and ergodicity in random processes)<\/a><\/strong><\/p>\n<p><strong>[02]\u00a0<span style=\"color: #ff0000;\"><a title=\"[\u632f\u52a8\u63a7\u5236] \u5e38\u89c1\u8d28\u91cf\u963b\u5c3c\u5668\u5206\u7c7b [Passive, semi-active, active and hybrid mass dampers]\" href=\"http:\/\/www.jdcui.com\/?p=22357\" target=\"_blank\" rel=\"noopener\">[\u632f\u52a8\u63a7\u5236] \u5e38\u89c1\u8d28\u91cf\u963b\u5c3c\u5668\u5206\u7c7b [Passive, semi-active, active and hybrid mass dampers]<\/a><\/span><\/strong><\/p>\n<p><strong>[03]\u00a0<a title=\"[\u52a8\u529b\u5b66][\u632f\u52a8\u63a7\u5236][\u8f6f\u4ef6] SDOF_FRE \u6848\u4f8b 2 \u2014\u2014 \u5730\u9707\u65f6\u7a0b\u54cd\u5e94\u5206\u6790 [SDOF_FRE Example 2: Earthquake Time History Analysis]\" href=\"http:\/\/www.jdcui.com\/?p=20090\" target=\"_blank\" rel=\"noopener\">[\u52a8\u529b\u5b66][\u632f\u52a8\u63a7\u5236][\u8f6f\u4ef6] SDOF_FRE \u6848\u4f8b 2 \u2014\u2014 \u5730\u9707\u65f6\u7a0b\u54cd\u5e94\u5206\u6790 [SDOF_FRE Example 2: Earthquake Time History Analysis]<\/a><\/strong><\/p>\n<p><strong>[04]\u00a0<a title=\"[\u52a8\u529b\u5b66][\u632f\u52a8\u63a7\u5236][\u7f16\u7a0b] SDOF_FRE: Dynamic Response Analysis of SDOF System using Frequency Domain Analysis Method [\u5355\u81ea\u7531\u5ea6\u4f53\u7cfb\u52a8\u529b\u54cd\u5e94\u9891\u57df\u5206\u6790\u7a0b\u5e8f]\" href=\"http:\/\/www.jdcui.com\/?p=18955\" target=\"_blank\" rel=\"noopener\">[\u52a8\u529b\u5b66][\u632f\u52a8\u63a7\u5236][\u7f16\u7a0b] SDOF_FRE: Dynamic Response Analysis of SDOF System using Frequency Domain Analysis Method [\u5355\u81ea\u7531\u5ea6\u4f53\u7cfb\u52a8\u529b\u54cd\u5e94\u9891\u57df\u5206\u6790\u7a0b\u5e8f]<\/a><\/strong><\/p>\n<p><strong>[05]\u00a0<a title=\"[\u52a8\u529b\u5b66][\u632f\u52a8\u63a7\u5236][\u7f16\u7a0b] SDOF_FRE \u6848\u4f8b1 \u2014\u2014 \u52a8\u529b\u65f6\u7a0b\u54cd\u5e94\u5206\u6790 [SDOF_FRE Example 1: Dynamic Force Time History Analysis]\" href=\"http:\/\/www.jdcui.com\/?p=20087\" target=\"_blank\" rel=\"noopener\">[\u52a8\u529b\u5b66][\u632f\u52a8\u63a7\u5236][\u7f16\u7a0b] SDOF_FRE \u6848\u4f8b1 \u2014\u2014 \u52a8\u529b\u65f6\u7a0b\u54cd\u5e94\u5206\u6790 [SDOF_FRE Example 1: Dynamic Force Time History Analysis]<\/a><\/strong><\/p>\n<p><strong>[06]\u00a0<a title=\"[\u7b14\u8bb0][\u6570\u5b66] \u8109\u51b2\u51fd\u6570\u516c\u5f0f\u63a8\u5bfc [Derivation of Delta Function]\" href=\"http:\/\/www.jdcui.com\/?p=20957\" target=\"_blank\" rel=\"noopener\">[\u7b14\u8bb0][\u6570\u5b66] \u8109\u51b2\u51fd\u6570\u516c\u5f0f\u63a8\u5bfc [Derivation of Delta Function]<\/a><\/strong><\/p>\n<p><strong>[07]\u00a0<a title=\"[Dynamics][\u52a8\u529b\u5b66][SAP2000] \u6881\u7684\u632f\u52a8\u5f62\u6001\u53ca\u632f\u578b\u8d28\u91cf (Vibration Modes and Modal Mass of Beams)\" href=\"http:\/\/www.jdcui.com\/?p=15984\" target=\"_blank\" rel=\"noopener\">[Dynamics][\u52a8\u529b\u5b66][SAP2000] \u6881\u7684\u632f\u52a8\u5f62\u6001\u53ca\u632f\u578b\u8d28\u91cf (Vibration Modes and Modal Mass of Beams)<\/a><\/strong><\/p>\n<p><strong>[08]\u00a0<a title=\"[\u8f6f\u4ef6][\u5730\u9707\u6ce2][\u6297\u9707] GMS_RESEARCH: Ground Motion Selection Program for Research [\u57fa\u4e8e\u76ee\u6807\u8c31\u5339\u914d\u6cd5\u5730\u9707\u6ce2\u9009\u6ce2\u5de5\u5177 \u79d1\u7814\u7248]\" href=\"http:\/\/www.jdcui.com\/?p=23253\" target=\"_blank\" rel=\"noopener\">[\u8f6f\u4ef6][\u5730\u9707\u6ce2][\u6297\u9707] GMS_RESEARCH: Ground Motion Selection Program for Research [\u57fa\u4e8e\u76ee\u6807\u8c31\u5339\u914d\u6cd5\u5730\u9707\u6ce2\u9009\u6ce2\u5de5\u5177 \u79d1\u7814\u7248]<\/a><\/strong><\/p>\n<p><strong>[09]\u00a0<a title=\"[\u8f6f\u4ef6][\u8bd5\u9a8c][\u7f16\u7a0b] NoiseRemoval: A Program for De-Noising of Experimental Data [\u8bd5\u9a8c\u6570\u636e\u964d\u566a\u4fee\u6b63\u5de5\u5177]\" href=\"http:\/\/www.jdcui.com\/?p=15046\" target=\"_blank\" rel=\"noopener noreferrer\">[\u8f6f\u4ef6][\u8bd5\u9a8c][\u7f16\u7a0b] NoiseRemoval: A Program for De-Noising of Experimental Data [\u8bd5\u9a8c\u6570\u636e\u964d\u566a\u4fee\u6b63\u5de5\u5177]<\/a><\/strong><\/p>\n<p><strong>[10]\u00a0<a title=\"[\u5de5\u5177][\u8bd5\u9a8c][\u66f4\u65b0] DataSmoothing v2022: A Program for Test Data Smoothing [\u8bd5\u9a8c\u6570\u636e\u66f2\u7ebf\u5e73\u6ed1+\u964d\u566a\u5de5\u5177]\" href=\"http:\/\/www.jdcui.com\/?p=18744\" target=\"_blank\" rel=\"noopener\">[\u5de5\u5177][\u8bd5\u9a8c][\u66f4\u65b0] DataSmoothing v2022: A Program for Test Data Smoothing [\u8bd5\u9a8c\u6570\u636e\u66f2\u7ebf\u5e73\u6ed1+\u964d\u566a\u5de5\u5177]<\/a><\/strong><\/p>\n<p><strong>[11]\u00a0<span style=\"color: #ff0000;\"><a title=\"[\u7f16\u7a0b][\u6570\u5b66][\u4fe1\u53f7\u5904\u7406] \u4e09\u5206\u4e4b\u4e00\u500d\u9891\u7a0b\u8c31\u5206\u6790 [1\/3 Octave Spectra Analysis]\" href=\"http:\/\/www.jdcui.com\/?p=20164\" target=\"_blank\" rel=\"noopener\">[\u7f16\u7a0b][\u6570\u5b66][\u4fe1\u53f7\u5904\u7406] \u4e09\u5206\u4e4b\u4e00\u500d\u9891\u7a0b\u8c31\u5206\u6790 [1\/3 Octave Spectra Analysis]<\/a><\/span><\/strong><\/p>\n<p><strong>[12]\u00a0<span style=\"color: #ff0000;\"><a title=\"[\u6570\u5b66][\u7f16\u7a0b] \u8499\u7279\u5361\u6d1b\u6a21\u62df\u6cd5\u6c42\u5706\u5468\u7387\u03c0 (Monte Carlo method to find PI)\" href=\"http:\/\/www.jdcui.com\/?p=17385\" target=\"_blank\" rel=\"noopener\">[\u6570\u5b66][\u7f16\u7a0b] \u8499\u7279\u5361\u6d1b\u6a21\u62df\u6cd5\u6c42\u5706\u5468\u7387\u03c0 (Monte Carlo method to find PI)<\/a><\/span><\/strong><\/p>\n<p><strong>[13] <span style=\"color: #ff0000;\"><a title=\"[\u6570\u5b66][\u7f16\u7a0b][\u6df7\u6c8c] \u866b\u53e3\u6a21\u578b\u7684\u6570\u503c\u6a21\u62df [Numerical simulation of insect population model]\" href=\"http:\/\/www.jdcui.com\/?p=17603\" target=\"_blank\" rel=\"noopener\">[\u6570\u5b66][\u7f16\u7a0b][\u6df7\u6c8c] \u866b\u53e3\u6a21\u578b\u7684\u6570\u503c\u6a21\u62df [Numerical simulation of insect population model]<\/a><\/span><\/strong><\/p>\n<p><strong>[14] <span style=\"color: #ff0000;\"><a title=\"[\u6570\u5b66][\u7b97\u6cd5][\u7f16\u7a0b\u8bad\u7ec3] \u6700\u5c0f\u4e8c\u4e58\u6cd5\u66f2\u7ebf\u62df\u5408( Least square curve fitting )\" href=\"http:\/\/www.jdcui.com\/?p=15600\" target=\"_blank\" rel=\"noopener\">[\u6570\u5b66][\u7b97\u6cd5][\u7f16\u7a0b\u8bad\u7ec3] \u6700\u5c0f\u4e8c\u4e58\u6cd5\u66f2\u7ebf\u62df\u5408( Least square curve fitting )<\/a><\/span><\/strong><\/p>\n<p><strong>[15] <span style=\"color: #ff0000;\"><a title=\"[\u7f16\u7a0b][\u6570\u5b66][\u51e0\u4f55] \u7f16\u7a0b\u8bad\u7ec3: \u62c9\u6885\u66f2\u7ebf |x|^n+|y|^n=1 \u53f7\u79f0200\u4e07\u7684\u5c0f\u7c73logo\u8f6e\u5ed3\u66f2\u7ebf (\u65b9\u4e0e\u5706\u7684\u8f6c\u53d8)\" href=\"http:\/\/www.jdcui.com\/?p=16029\" target=\"_blank\" rel=\"noopener\">[\u7f16\u7a0b][\u6570\u5b66][\u51e0\u4f55] \u7f16\u7a0b\u8bad\u7ec3: \u62c9\u6885\u66f2\u7ebf |x|^n+|y|^n=1 \u53f7\u79f0200\u4e07\u7684\u5c0f\u7c73logo\u8f6e\u5ed3\u66f2\u7ebf (\u65b9\u4e0e\u5706\u7684\u8f6c\u53d8)<\/a><\/span><\/strong><\/p>\n<p><strong>[16] <span style=\"color: #ff0000;\"><a title=\"[\u7f16\u7a0b\u8bad\u7ec3][\u6e38\u620f][\u6570\u5b66] \u7ea2\u9152\u676f\u4e0e\u767d\u9152\u676f\u91cc\u5230\u5e95\u6709\u591a\u5c11\u7ea2\u9152\u548c\u767d\u9152\uff1f\" href=\"http:\/\/www.jdcui.com\/?p=14118\" target=\"_blank\" rel=\"noopener\">[\u7f16\u7a0b\u8bad\u7ec3][\u6e38\u620f][\u6570\u5b66] \u7ea2\u9152\u676f\u4e0e\u767d\u9152\u676f\u91cc\u5230\u5e95\u6709\u591a\u5c11\u7ea2\u9152\u548c\u767d\u9152\uff1f<\/a><\/span><\/strong><\/p>\n<p><strong>[17] <span style=\"color: #ff0000;\"><a title=\"[\u6570\u5b66][\u6982\u7387] Buffon\u2019s Needle problem [\u84b2\u4e30\u6295\u9488\u95ee\u9898]\" href=\"http:\/\/www.jdcui.com\/?p=1301\" target=\"_blank\" rel=\"noopener\">[\u6570\u5b66][\u6982\u7387] Buffon\u2019s Needle problem [\u84b2\u4e30\u6295\u9488\u95ee\u9898]<\/a><\/span><\/strong><\/p>\n<p><strong>[18] <span style=\"color: #ff0000;\"><a title=\"[\u6570\u5b66] \u5085\u91cc\u53f6\u53d8\u6362\u516c\u5f0f\u7684\u51e0\u79cd\u5f62\u5f0f (Several Forms of Fourier Transform Formulas)\" href=\"http:\/\/www.jdcui.com\/?p=23278\" target=\"_blank\" rel=\"noopener\">[\u6570\u5b66] \u5085\u91cc\u53f6\u53d8\u6362\u516c\u5f0f\u7684\u51e0\u79cd\u5f62\u5f0f (Several Forms of Fourier Transform Formulas)<\/a><\/span><\/strong><\/p>\n<hr \/>\n<p style=\"text-align: center;\"><strong>\u7ed3\u6784|\u8d85\u9650|\u8f6f\u4ef6\u5f00\u53d1|\u7f16\u7a0b|\u53c2\u6570\u5316|\u4f18\u5316|\u7b97\u6cd5|\u632f\u52a8\u63a7\u5236|\u51cf\u9694\u9707|\u6709\u9650\u5143|\u6280\u672f\u57f9\u8bad<\/strong><\/p>\n<p style=\"text-align: center;\">\u8ffd\u6c42\u5353\u8d8a \u811a\u8e0f\u5b9e\u5730 \u81f4\u529b\u4e8e\u63a2\u7d22\u548c\u62d3\u5c55\u884c\u4e1a\u8bbe\u8ba1\u524d\u6cbf<\/p>\n<p style=\"text-align: center;\"><a href=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2017\/01\/QRCODE.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-3636 alignnone\" src=\"http:\/\/www.jdcui.com\/wp-content\/uploads\/2017\/01\/QRCODE.jpg\" alt=\"WeChat_QRCode\" width=\"250\" height=\"255\" \/><\/a><\/p>\n<p style=\"text-align: center;\">https:\/\/www.jdcui.com<\/p>\n<p style=\"text-align: center;\">\u5408\u4f5c\u53ca\u6280\u672f\u54a8\u8be2<\/p>\n<p style=\"text-align: center;\">COOPERATION &amp; CONTACT<\/p>\n<p style=\"text-align: center;\">E-mail\uff1ajidong_cui@163.com<\/p>\n<p style=\"text-align: center;\">WeChat &amp; Tel: 13450468449<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5b9e\u5e72\u3001\u5b9e\u8df5\u3001\u79ef\u7d2f\u3001\u601d\u8003\u3001\u521b\u65b0\u3002 # \u5085\u91cc\u53f6\u53d8\u6362\u516c\u5f0f\u7684\u51e0\u79cd\u5f62\u5f0f \u7814\u7a76\u632f\u52a8\u63a7\u5236\u3001\u968f\u673a\u632f\u52a8\u7b49\uff0c\u79bb\u4e0d\u5f00\u5085\u91cc\u53f6\u53d8\u6362\uff08Fourier transforms\uff09\u3002\u5bf9\u4e8e\u5085\u91cc\u53f6\u53d8\u6362\uff0c\u4e0d\u540c\u6587\u732e\u3001\u4e66\u7c4d\u6709\u65f6\u5019\u4f1a\u91c7\u7528\u4e0d\u540c\u5f62\u5f0f\u7684\u516c\u5f0f\uff0c\u521a\u5f00\u59cb\u770b\u7684\u65f6\u5019\u6709\u70b9\u51cc\u4e71\uff0c\u540e\u9762\u624d\u7406\u6e05\u695a\uff0c\u5176\u5b9e\u4e0d\u540c\u516c\u5f0f\u5f62\u5f0f\u672c\u8d28\u4e0a\u90fd\u662f\u7b49\u4ef7\u3002\u4e3a\u4e86\u4fbf\u4e8e\u540e\u7eed\u5b66\u4e60\uff0c\u4ee5\u4e0b\u603b\u7ed3\u51e0\u79cd\u5e38\u89c1\u7684\u5085\u91cc\u53f6\u53d8\u6362\u516c\u5f0f\u5f62\u5f0f\u3002PS.\u8fd9\u91cc\u5085\u91cc\u53f6\u53d8\u6362\uff0c\u6307\u7684\u662f\u975e\u5468\u671f\u51fd\u6570\uff08\u5468\u671f\u53ef\u4ee5\u7406\u89e3\u4e3a\u65e0\u9650\u957f\uff09\u7684\u5085\u91cc\u53f6\u53d8\u6362\uff0c\u4e0d\u662f\u5085\u91cc\u53f6\u7ea7\u6570\uff08Fourier series\uff09\uff0c\u5085\u91cc\u53f6\u7ea7\u6570\u662f\u9488\u5bf9\u5468\u671f\u51fd\u6570\u7684\u8bf4\u6cd5\u3002 ## \u7b2c\u4e00\u79cd\u5f62\u5f0f \u4e00\u79cd\u901a\u7528\u7684\u5f62\u5f0f\uff0c\\(\\Phi \\left( p \\right)\\)\u548c\\(F\\left( x \\right)\\)\u4e92\u4e3a\u5085\u91cc\u53f6\u53d8\u6362\u5bf9\uff1a $$\\Phi \\left( p \\right) \\Leftrightarrow F\\left( x \\right)$$ $$\\Phi \\left( p \\right) = {1 \\over {2\\pi &#8230;<\/p>\n","protected":false},"author":1,"featured_media":23338,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4,3164],"tags":[2260,2261,2280,4126,2258,4128,1951,4125,3573,135,2281,3304],"class_list":["post-23278","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-math-geometry","category--vibration-control","tag-dft","tag-discrete-fourier-transform","tag-fft","tag-fourier-series","tag-fourier-transform","tag-fourier-transform-pairs","tag-1951","tag-4125","tag-3573","tag-135","tag-2281","tag-3304"],"aioseo_notices":[],"views":2829,"_links":{"self":[{"href":"http:\/\/www.jdcui.com\/index.php?rest_route=\/wp\/v2\/posts\/23278","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.jdcui.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.jdcui.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.jdcui.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.jdcui.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=23278"}],"version-history":[{"count":0,"href":"http:\/\/www.jdcui.com\/index.php?rest_route=\/wp\/v2\/posts\/23278\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/www.jdcui.com\/index.php?rest_route=\/wp\/v2\/media\/23338"}],"wp:attachment":[{"href":"http:\/\/www.jdcui.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=23278"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.jdcui.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=23278"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.jdcui.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=23278"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}