{"id":788,"date":"2019-03-09T22:53:55","date_gmt":"2019-03-09T13:53:55","guid":{"rendered":"https:\/\/mell0w-5phere.net\/jaded5phere\/?p=788"},"modified":"2020-07-29T21:40:15","modified_gmt":"2020-07-29T12:40:15","slug":"fourier-visualize","status":"publish","type":"post","link":"https:\/\/mell0w-5phere.net\/jaded5phere\/2019\/03\/09\/fourier-visualize\/","title":{"rendered":"\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u3067\u5186\u3092\u30b0\u30eb\u30b0\u30eb\u3057\u3066\u56f3\u3092\u63cf\u3044\u3066\u904a\u3076"},"content":{"rendered":"<p> \u3000\u5186\u3092\u30b0\u30eb\u30b0\u30eb\u3057\u3066\u56f3\u5f62\u3092\u63cf\u3044\u3066\u307f\u3088\u3046\u3002<\/p>\n<hr \/>\n<p>\u3000<\/p>\n<h4>\u30fb\u3053\u3046\u3044\u3046\u3084\u3064<\/h4>\n<p>\u3000Twitter\u3067\u3053\u3093\u306a\u611f\u3058\u306e\u306e\u52d5\u753b\u3092\u898b\u305f\u3053\u3068\u304c\u3042\u308b\u3060\u308d\u3046\u304b\u3002<img loading=\"lazy\" src=\"https:\/\/mell0w-5phere.net\/jaded5phere\/wp-content\/uploads\/2019\/03\/fft_cy.gif\" alt=\"\" width=\"529\" height=\"546\" class=\"alignnone size-full wp-image-789\" \/><br \/>\n\u3000\u5186\u304c\u9023\u306a\u3063\u3066\u3001\u307e\u308b\u3067\u30ed\u30dc\u30c3\u30c8\u30a2\u30fc\u30e0\u306e\u3088\u3046\u306b\u56f3\u3092\u63cf\u304d\u51fa\u3057\u3066\u3044\u304f\u3002\u4eca\u56de\u306f\u3053\u308c\u3092\u4f5c\u3063\u3066\u3044\u304f\u3002<\/p>\n<p>\u3000<\/p>\n<h4>\u30fb\u539f\u7406<\/h4>\n<p>\u3000\u753b\u9762\u3092\u8907\u7d20\u5e73\u9762\u306b\u898b\u7acb\u3066\u308b\u3068\u3001\u753b\u9762\u4e0a\u306e\u70b9\u306f\u3042\u308b1\u3064\u306e\u8907\u7d20\u6570 \\(z\\) \u3068\u5bfe\u5fdc\u3055\u305b\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u3053\u308c\u3092\u6642\u523b \\(t\\) \u306b\u3088\u3063\u3066\u5909\u5316\u3059\u308b\u5b9f\u6570\u5909\u6570\u8907\u7d20\u95a2\u6570 \\(z=f[t]\\) \u3068\u307f\u306a\u3059\u3053\u3068\u3067\u3001\u96e2\u6563\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u306b\u3064\u3044\u3066\u306f<a href=\"https:\/\/mell0w-5phere.net\/jaded5phere\/2017\/12\/28\/speana-fft\/\">\u3053\u306e\u8a18\u4e8b<\/a>\u3067\u89e6\u308c\u3066\u3044\u308b\u306e\u3067\u53c2\u8003\u306b\u3055\u308c\u305f\u3044\u3002<br \/>\n\u3000\u5909\u63db\u306e\u7d50\u679c\u5f97\u3089\u308c\u305f\u3082\u306e\u3092 \\(F[k]\\) \u3068\u3059\u308b\u3068\u3001\u30d5\u30fc\u30ea\u30a8\u9006\u5909\u63db\u306e\u516c\u5f0f\u3088\u308a\u5143\u306e\u95a2\u6570\u306f\u6b21\u306e\u3088\u3046\u306b\u8868\u305b\u308b\u3002$$f[t]=\\sum^{N-1}_{k=0} F[k]e^{i\\frac{2\\pi k}{N}t}$$<br \/>\n\u3000\\(\\displaystyle e^{i\\frac{2\\pi k}{N}t}\\) \u306f\u3001\u89d2\u901f\u5ea6\\(\\displaystyle \\frac{2\\pi k}{N}\\) \u3067\u5358\u4f4d\u5186\u4e0a\u3092\u5468\u56de\u3059\u308b\u70b9\u3068\u307f\u306a\u3059\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u305d\u3053\u306b\\(F[k]\\)\u3092\u639b\u3051\u308b\u3068\u3044\u3046\u3053\u3068\u306f\u3001\u5358\u4f4d\u5186\u306e\u534a\u5f84\u3092 \\(r_k=|F[k]|\\) \u500d\u3057\u3001\u521d\u671f\u4f4d\u76f8\u3092\\(\\phi_k=\\arg F[k]\\)\u3060\u3051\u305a\u3089\u3059\u3053\u3068\u3068\u540c\u7b49\u3067\u3042\u308b\u304b\u3089\u3001\u4e0a\u306e\u5f0f\u306f<br \/>\n\u3000$$f[t]=\\sum^{N-1}_{k=0} r_ke^{i\\left(\\frac{2\\pi k}{N}t+\\phi_k\\right)}$$\u3068\u8868\u305b\u308b\u3002<br \/>\n<img loading=\"lazy\" src=\"https:\/\/mell0w-5phere.net\/jaded5phere\/wp-content\/uploads\/2019\/03\/invfft_expl.png\" alt=\"\" width=\"800\" height=\"465\" class=\"alignnone size-full wp-image-799\" srcset=\"https:\/\/mell0w-5phere.net\/jaded5phere\/wp-content\/uploads\/2019\/03\/invfft_expl.png 800w, https:\/\/mell0w-5phere.net\/jaded5phere\/wp-content\/uploads\/2019\/03\/invfft_expl-300x174.png 300w, https:\/\/mell0w-5phere.net\/jaded5phere\/wp-content\/uploads\/2019\/03\/invfft_expl-768x446.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><br \/>\n\u3000\u307e\u305f\u3001\u7dcf\u548c\u3092\u3068\u308b\u3068\u3044\u3046\u3053\u3068\u306f\u3001\u8907\u7d20\u5e73\u9762\u4e0a\u306b\u304a\u3044\u3066\u3001\\(k\\)\u756a\u76ee\u306e\u5186\u306e\u4e0a\u3092\u5468\u56de\u3059\u308b\u70b9\u3092\u4e2d\u5fc3\u3068\u3057\u3066\\(k+1\\)\u756a\u76ee\u306e\u5186\u3092\u63cf\u304d\u3001\u3055\u3089\u306b\u305d\u306e\u5186\u306e\u4e0a\u3092\u5468\u56de\u3059\u308b\u70b9\u3092\u4e2d\u5fc3\u3068\u3057\u3066\\(k+2\\)\u756a\u76ee\u306e\u5186\u3092\u63cf\u304d...\u3068\u3044\u3046\u3053\u3068\u3092\u884c\u3046\u306e\u3068\u540c\u7b49\u3067\u3042\u308b\u304b\u3089\u3001\u5186\u3092\u91cd\u306d\u308b\u3053\u3068\u3067\u30d5\u30fc\u30ea\u30a8\u9006\u5909\u63db\u304c\u3067\u304d\u3001\u5143\u306e\u95a2\u6570\u304c\u8868\u73fe\u3055\u308c\u308b\u3068\u3044\u3046\u308f\u3051\u3067\u3042\u308b\u3002<img loading=\"lazy\" src=\"https:\/\/mell0w-5phere.net\/jaded5phere\/wp-content\/uploads\/2019\/03\/fft_cy_1.gif\" alt=\"\" width=\"529\" height=\"546\" class=\"alignnone size-full wp-image-803\" \/><\/p>\n<p>\u3000<\/p>\n<h4>\u30fb\u56f3\u30922\u500b\u63cf\u304d\u305f\u3044<\/h4>\n<p>\u3000\u3055\u3066\u3001\u5186\u306e\u91cd\u306d\u5408\u308f\u305b\u3067\u56f3\u3092\u63cf\u3051\u308b\u3053\u3068\u304c\u308f\u304b\u3063\u305f\u306e\u3067\u3001\u5192\u982d\u306b\u793a\u3057\u305f\u52d5\u753b\u306e\u3088\u3046\u306b2\u3064\u306e\u56f3\u3092\u63cf\u304f\u65b9\u6cd5\u3092\u8003\u3048\u3088\u3046\u3002<br \/>\n<img loading=\"lazy\" src=\"https:\/\/mell0w-5phere.net\/jaded5phere\/wp-content\/uploads\/2019\/03\/invfft_double_fig.png\" alt=\"\" width=\"800\" height=\"600\" class=\"alignnone size-full wp-image-805\" srcset=\"https:\/\/mell0w-5phere.net\/jaded5phere\/wp-content\/uploads\/2019\/03\/invfft_double_fig.png 800w, https:\/\/mell0w-5phere.net\/jaded5phere\/wp-content\/uploads\/2019\/03\/invfft_double_fig-300x225.png 300w, https:\/\/mell0w-5phere.net\/jaded5phere\/wp-content\/uploads\/2019\/03\/invfft_double_fig-768x576.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/>\u3000<br \/>\n\u3000\u53f3\u4e0a\u306f1\u3064\u76ee\u306e\u56f3\u306e\u865a\u90e8\u30682\u3064\u76ee\u306e\u56f3\u306e\u5b9f\u90e8\u3092\u62c5\u5f53\u3057\u3001\u5de6\u4e0b\u306f1\u3064\u76ee\u306e\u56f3\u306e\u5b9f\u90e8\u30682\u3064\u76ee\u306e\u56f3\u306e\u865a\u90e8\u3092\u62c5\u5f53\u3057\u3066\u3044\u308b\u3053\u3068\u306b\u306a\u308b\u306e\u3067\u30012\u3064\u306e\u56f3\u306e\u5b9f\u90e8\u304b\u865a\u90e8\u3092\u4ea4\u63db\u3057\u3066\u3084\u3063\u3066\u304b\u3089\u96e2\u6563\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u3059\u308c\u3070\u3088\u3044\u3053\u3068\u306b\u306a\u308b\u3002<\/p>\n<p>\u3000<\/p>\n<h4>\u30fb\u5b9f\u88c5<\/h4>\n<p>\u3000\u30bd\u30fc\u30b9\u30b3\u30fc\u30c9\u306e\u307b\u3068\u3093\u3069\u304c\u63cf\u753b\u51e6\u7406\u306e\u6587\u306a\u306e\u3067\u30b3\u30fc\u30c9\u3092\u3059\u3079\u3066\u8f09\u305b\u308b\u3053\u3068\u306f\u3057\u306a\u3044\u304c\u3001\u4e2d\u5fc3\u7684\u306a\u90e8\u5206\u306b\u3064\u3044\u3066\u5c11\u3057\u8a00\u53ca\u3057\u3066\u304a\u304f\u3002<br \/>\n\u3000\u4e0a\u306e\u8aac\u660e\u3067\u306f\u5186\u3092\u8868\u3059\u3046\u3048\u3067\\(e^{i\\theta}\\)\u3068\u3044\u3046\u5f62\u3092\u4f7f\u3063\u305f\u304c\u3001\u5b9f\u969b\u306b\u5b9f\u88c5\u3059\u308b\u3068\u306a\u308b\u3068\u5b9f\u90e8\u30fb\u865a\u90e8\u3092\\(x\\)\u30fb\\(y\\)\u306b\u5bfe\u5fdc\u3055\u305b\u308b\u5fc5\u8981\u304c\u3042\u308b\u306e\u3067\u3001\u3053\u306e\u5f62\u3067\u306f\u4e0d\u4fbf\u3067\u3042\u308b\u3002\u305d\u3053\u3067\u3001\u30aa\u30a4\u30e9\u30fc\u306e\u7b49\u5f0f\\(e^{i\\theta}=\\cos \\theta+i\\sin \\theta\\)\u3092\u4f7f\u3046\u3068\u5b9f\u90e8\u30fb\u865a\u90e8\u3092\u5225\u3005\u306b\u51e6\u7406\u3067\u304d\u308b\u306e\u3067\u4fbf\u5229\u3067\u3042\u308b\u3002\u4e0b\u306bjava\u3067\u306e\u5b9f\u88c5(\u306e\u4e00\u90e8)\u3092\u8f09\u305b\u3066\u304a\u304f\u3002<\/p>\n<pre class=\"line-numbers\"><code class=\"language-java\">for (int k=0; k&lt;N; k++) {\r\n    Complex coef1 = spectrum[0][k];  \/\/F[k]\u306e\u5024\r\n    Complex coef2 = spectrum[1][k];\r\n    float th = 2 * PI * k * t \/ N;\r\n    float th1 = th + coef1.Phi(); \/\/\u4f4d\u76f8\u3092\u305a\u3089\u3059\r\n    float th2 = th + coef2.Phi();\r\n    float amp1 = coef1.Abs(); \/\/\u632f\u5e45(\u5186\u306e\u534a\u5f84)\r\n    float amp2 = coef2.Abs();\r\n\r\n    x1 += amp1 * cos(th1); \/\/\u5b9f\u90e8\r\n    y1 += amp2 * sin(th2); \/\/\u865a\u90e8\r\n\r\n    x2 += amp2 * cos(th2);\r\n    y2 += amp1 * sin(th1);\r\n}\r\n<\/code><\/pre>\n<hr \/>\n<p>\u3000\u3068\u3044\u3046\u308f\u3051\u3067\u5186\u3092\u3050\u308b\u3050\u308b\u3057\u3066\u56f3\u3092\u63cf\u304f\u3053\u3068\u304c\u3067\u304d\u305f(?)\u3002\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u306f\u697d\u3057\u3044\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u3000\u5186\u3092\u30b0\u30eb\u30b0\u30eb\u3057\u3066\u56f3\u5f62\u3092\u63cf\u3044\u3066\u307f\u3088\u3046\u3002 \u3000 \u30fb\u3053\u3046\u3044\u3046\u3084\u3064 \u3000Twitter\u3067\u3053\u3093\u306a\u611f\u3058\u306e\u306e\u52d5\u753b\u3092\u898b\u305f\u3053\u3068\u304c\u3042\u308b\u3060\u308d\u3046\u304b\u3002 \u3000\u5186\u304c\u9023\u306a\u3063\u3066\u3001\u307e\u308b\u3067\u30ed\u30dc\u30c3\u30c8\u30a2\u30fc\u30e0\u306e\u3088\u3046\u306b\u56f3\u3092\u63cf\u304d\u51fa\u3057\u3066\u3044\u304f\u3002\u4eca\u56de\u306f\u3053\u308c\u3092\u4f5c\u3063\u3066\u3044\u304f\u3002 \u3000 \u30fb<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[83],"tags":[29],"_links":{"self":[{"href":"https:\/\/mell0w-5phere.net\/jaded5phere\/wp-json\/wp\/v2\/posts\/788"}],"collection":[{"href":"https:\/\/mell0w-5phere.net\/jaded5phere\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mell0w-5phere.net\/jaded5phere\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mell0w-5phere.net\/jaded5phere\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mell0w-5phere.net\/jaded5phere\/wp-json\/wp\/v2\/comments?post=788"}],"version-history":[{"count":17,"href":"https:\/\/mell0w-5phere.net\/jaded5phere\/wp-json\/wp\/v2\/posts\/788\/revisions"}],"predecessor-version":[{"id":811,"href":"https:\/\/mell0w-5phere.net\/jaded5phere\/wp-json\/wp\/v2\/posts\/788\/revisions\/811"}],"wp:attachment":[{"href":"https:\/\/mell0w-5phere.net\/jaded5phere\/wp-json\/wp\/v2\/media?parent=788"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mell0w-5phere.net\/jaded5phere\/wp-json\/wp\/v2\/categories?post=788"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mell0w-5phere.net\/jaded5phere\/wp-json\/wp\/v2\/tags?post=788"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}