{"id":1627,"date":"2026-10-30T19:00:00","date_gmt":"2026-10-30T10:00:00","guid":{"rendered":"https:\/\/quantumsea.net\/?p=1627"},"modified":"2026-10-27T19:16:20","modified_gmt":"2026-10-27T10:16:20","slug":"qs-gibbs-phenomenon-20261025","status":"publish","type":"post","link":"https:\/\/quantumsea.net\/?p=1627","title":{"rendered":"\u30ae\u30d6\u30b9\u73fe\u8c61\u3001\u9805\u6570\u3092\u5897\u3084\u3057\u3066\u3082\u6bb5\u5dee\u306e\u98db\u3073\u51fa\u3057\u304c\u6d88\u3048\u306a\u3044\u7406\u7531"},"content":{"rendered":"<p>\u6b63\u5f26\u6ce2\u3092\u305f\u304f\u3055\u3093\u8db3\u3057\u5408\u308f\u305b\u308b\u3068\u3001\u56db\u89d2\u3044\u6ce2\u5f62\u3092\u63cf\u3051\u307e\u3059\u3002\u8db3\u3059\u6ce2\u3092\u5897\u3084\u305b\u3070\u89d2\u3082\u92ed\u304f\u306a\u308a\u307e\u3059\u304c\u3001\u6bb5\u5dee\u306e\u8fd1\u304f\u306b\u306f\u3001\u5143\u306e\u9ad8\u3055\u3092\u5c11\u3057\u8d85\u3048\u308b\u5c71\u304c\u6b8b\u308a\u307e\u3059\u3002\u8a08\u7b97\u3092\u7d30\u304b\u304f\u3057\u305f\u306e\u306b\u3001\u306a\u305c\u3053\u306e\u98db\u3073\u51fa\u3057\u306f\u6d88\u3048\u306a\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<section class=\"influvetor-quick-summary\" aria-label=\"\u7c21\u5358\u306b\u307e\u3068\u3081\u308b\u3068\uff1f\">\n<p><strong>\u7c21\u5358\u306b\u307e\u3068\u3081\u308b\u3068\uff1f<\/strong><\/p>\n<ul>\n<li>\u30ae\u30d6\u30b9\u73fe\u8c61\u306f\u3001\u4e0d\u9023\u7d9a\u306a\u6bb5\u5dee\u3092\u30d5\u30fc\u30ea\u30a8\u7d1a\u6570\u306e\u9014\u4e2d\u307e\u3067\u306e\u548c\u3067\u8868\u3059\u3068\u3001\u305d\u306e\u8fd1\u304f\u306b\u98db\u3073\u51fa\u3057\u304c\u6b8b\u308b\u73fe\u8c61\u3067\u3059\u3002<\/li>\n<li>\u9805\u6570\u3092\u5897\u3084\u3059\u3068\u3001\u5c71\u306f\u6bb5\u5dee\u306e\u3059\u3050\u305d\u3070\u3078\u5bc4\u308a\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u5143\u306e\u5024\u304b\u3089\u306e\u98db\u3073\u51fa\u3057\u91cf\u306f\u3001\u6bb5\u5dee\u5168\u4f53\u306e\u9ad8\u3055\u306e\u7d049%\u3078\u8fd1\u3065\u304d\u307e\u3059\u3002<\/li>\n<li>\u6ce2\u5f62\u306e\u518d\u73fe\u6027\u3092\u898b\u308b\u3068\u304d\u306f\u3001\u5c71\u306e\u9ad8\u3055\u3068\u6bb5\u5dee\u304b\u3089\u306e\u8ddd\u96e2\u3092\u5206\u3051\u3066\u6bd4\u3079\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u7d30\u3044\u9818\u57df\u306b\u53ce\u307e\u308b\u3053\u3068\u3068\u3001\u6700\u5927\u306e\u8aa4\u5dee\u304c\u5c0f\u3055\u304f\u306a\u308b\u3053\u3068\u306f\u5225\u3067\u3059\u3002<\/li>\n<\/ul>\n<\/section>\n<h2>\u307e\u305a\u3001\u4f55\u3092\u8db3\u3057\u3066\u3044\u308b\u306e\u304b<\/h2>\n<p>\u3053\u3053\u3067\u306f\u3001\u4e0b\u5074\u304c\u22121\u3001\u4e0a\u5074\u304c\uff0b1\u306e\u7406\u60f3\u7684\u306a\u77e9\u5f62\u6ce2\u3092\u8003\u3048\u307e\u3059\u3002\u77e9\u5f62\u6ce2\u3068\u306f\u3001\u4e8c\u3064\u306e\u9ad8\u3055\u3092\u4ea4\u4e92\u306b\u53d6\u308b\u56db\u89d2\u3044\u6ce2\u5f62\u3067\u3059\u3002\u4f4d\u76f8\u3092\u8868\u3059\u6a2a\u8ef8\u3092 x \u3068\u3057\u3001\u2212\u03c0 &lt; x &lt; 0 \u3067\u306f\u22121\u30010 &lt; x &lt; \u03c0 \u3067\u306f\uff0b1\u3001\u305d\u308c\u3092\u5468\u671f2\u03c0\u3067\u7e70\u308a\u8fd4\u3059\u3082\u306e\u3068\u3057\u307e\u3059\u3002\u6bb5\u5dee\u306e\u9ad8\u3055\u306f\u30011\u2212(\u22121)\uff1d2\u3067\u3059\u3002<\/p>\n<p>\u3053\u306e\u6ce2\u5f62\u306f\u3001\u57fa\u672c\u306e\u6b63\u5f26\u6ce2\u306b\u30013\u500d\u30015\u500d\u30017\u500d\u2026\u2026\u306e\u7d30\u304b\u306a\u6b63\u5f26\u6ce2\u3092\u52a0\u3048\u308b\u3053\u3068\u3067\u8fd1\u4f3c\u3067\u304d\u307e\u3059\u3002\u305f\u3060\u3057\u3001\u7d30\u304b\u306a\u6ce2\u307b\u3069\u91cd\u307f\u3092\u5c0f\u3055\u304f\u3057\u307e\u3059\u3002\u4f8b\u3048\u3070\u6700\u521d\u306e3\u9805\u306a\u3089\u3001\u6b21\u306e\u548c\u3067\u3059\u3002<\/p>\n<p><strong>S\u2083(x)\uff1d(4\/\u03c0)\uff3bsin x \uff0b sin(3x)\/3 \uff0b sin(5x)\/5\uff3d<\/strong><\/p>\n<p>\u4ee5\u4e0b\u306e N \u306f\u3001\u3053\u3046\u3057\u3066\u8db3\u3059<strong>\u5947\u6570\u6b21\u306e\u6b63\u5f26\u6ce2\u306e\u672c\u6570<\/strong>\u3067\u3059\u3002N\uff1d5\u306a\u30891\u30013\u30015\u30017\u30019\u6b21\u307e\u3067\u3092\u4f7f\u3044\u307e\u3059\u3002\u6700\u9ad8\u6b21\u6570\u306e9\u3068\u3001\u9805\u6570\u306e5\u3092\u6df7\u540c\u3057\u306a\u3044\u3088\u3046\u306b\u3057\u307e\u3059\u3002\u5143\u306e\u4fc2\u6570\u3092\u5909\u3048\u305a\u306b\u9014\u4e2d\u3067\u8db3\u3057\u6b62\u3081\u308b\u3001\u666e\u901a\u306e\u30d5\u30fc\u30ea\u30a8\u7d1a\u6570\u306e\u90e8\u5206\u548c\u3092\u6271\u3044\u307e\u3059\u3002<\/p>\n<h2>125\u9805\u306b\u3057\u3066\u3082\u3001\u6700\u5927\u5024\u306f1\u3092\u8d85\u3048\u308b<\/h2>\n<p>\u3053\u306e\u548c\u3092\u72ec\u81ea\u306b\u8a08\u7b97\u3057\u3001\u6bb5\u5dee\u306e\u53f3\u5074\u306b\u3067\u304d\u308b\u6700\u521d\u306e\u5c71\u3092\u6bd4\u8f03\u3057\u307e\u3057\u305f\u3002\u5024\u3082\u4f4d\u76f8 x \u3082\u3001\u3053\u306e\u4f8b\u3067\u306f\u7121\u6b21\u5143\u3067\u3059\u3002x \u306f\u89d2\u5ea6\u3068\u3057\u3066\u30e9\u30b8\u30a2\u30f3\u3067\u8868\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n<figure><img loading=\"lazy\" decoding=\"async\" style=\"max-width:100%;height:auto\" width=\"1100\" height=\"1500\" src=\"https:\/\/quantumsea.net\/wp-content\/uploads\/2026\/10\/qs-gibbs-phenomenon-20261025-figure-6e63574e3545.png\" alt=\"\u5947\u6570\u6b21\u306e\u6b63\u5f26\u6ce2\u30925\u300125\u3001125\u9805\u8db3\u3057\u305f\u6ce2\u5f62\u3092\u540c\u3058\u8ef8\u3067\u6bd4\u8f03\u3002\u6bb5\u5dee\u306e\u53f3\u5074\u306e\u6700\u521d\u306e\u5c71\u306fx\u7d040.3142\u30010.0628\u30010.0126\u30e9\u30b8\u30a2\u30f3\u3078\u8fd1\u3065\u304f\u4e00\u65b9\u3001\u6700\u5927\u5024\u306f\u3044\u305a\u308c\u3082\u7d041.18\u3002\u4e0a\u5074\u306e\u5143\u306e\u5024\u306f1\u3002\" \/><figcaption>\u7406\u60f3\u7684\u306a\u77e9\u5f62\u6ce2\u306e\u30d5\u30fc\u30ea\u30a8\u90e8\u5206\u548c\u3092\u72ec\u81ea\u8a08\u7b97\u3002\u56f3\u306f\u6bb5\u5dee\u306e\u53f3\u5074\u306e\u307f\u3092\u793a\u3057\u3001\u6a2a\u8ef8\u30fb\u7e26\u8ef8\u306e\u7bc4\u56f2\u3092\u63c3\u3048\u305f\u3002\u5b9f\u6e2c\u5024\u3067\u306f\u306a\u3044\u3002<\/figcaption><\/figure>\n<table>\n<thead>\n<tr>\n<th>\u9805\u6570 N<\/th>\n<th>\u6700\u521d\u306e\u5c71\u306e x<\/th>\n<th>\u5c71\u306e\u9ad8\u3055<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>5<\/td>\n<td>0.3142 rad<\/td>\n<td>1.18233<\/td>\n<\/tr>\n<tr>\n<td>25<\/td>\n<td>0.0628 rad<\/td>\n<td>1.17911<\/td>\n<\/tr>\n<tr>\n<td>125<\/td>\n<td>0.0126 rad<\/td>\n<td>1.17899<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>5\u9805\u304b\u3089125\u9805\u306b\u5897\u3084\u3059\u3068\u3001\u5c71\u3068\u6bb5\u5dee\u3068\u306e\u8ddd\u96e2\u306f25\u5206\u306e1\u306b\u306a\u308a\u307e\u3059\u3002\u4e00\u65b9\u3001\u5c71\u306e\u9ad8\u3055\u306f\u7d041.18\u306e\u307e\u307e\u3067\u3059\u3002\u300c\u3088\u308a\u72ed\u3044\u3068\u3053\u308d\u306b\u53ce\u307e\u3063\u305f\u300d\u3068\u306f\u3044\u3048\u307e\u3059\u304c\u3001\u300c\u3069\u3053\u3092\u898b\u3066\u3082\u5143\u306e\u5024\u304b\u3089\u305a\u308c\u306a\u304f\u306a\u3063\u305f\u300d\u3068\u306f\u3001\u307e\u3060\u3044\u3048\u307e\u305b\u3093\u3002<\/p>\n<p>\u9805\u6570\u3092\u9650\u308a\u306a\u304f\u5897\u3084\u3057\u305f\u3068\u304d\u3001\u3053\u306e\u6700\u521d\u306e\u5c71\u306f\u7d041.17898\u3078\u8fd1\u3065\u304d\u307e\u3059\u3002\u4e0a\u5074\u306e\u50241\u304b\u3089\u306e\u8d85\u904e\u306f\u7d040.17898\u3067\u3059\u3002\u305d\u308c\u3092<strong>\u6bb5\u5dee\u5168\u4f53\u306e\u9ad8\u30552\u3067\u5272\u308b<\/strong>\u3068\u3001\u7d040.08949\u3001\u3064\u307e\u308a\u7d048.949%\u306b\u306a\u308a\u307e\u3059\u3002\u300c\u7d049%\u300d\u306f\u3053\u306e\u5272\u5408\u3067\u3059\u3002\u4e0a\u5074\u306e\u50241\u3092\u57fa\u6e96\u306b\u3059\u308b\u306a\u3089\u7d0418%\u306b\u5f53\u305f\u308a\u3001\u5206\u6bcd\u304c\u9055\u3044\u307e\u3059\u3002\u307e\u305f\u3001\u6709\u9650\u306e\u9805\u6570\u3067\u5e38\u306b\u3074\u3063\u305f\u308a9%\u306b\u306a\u308b\u308f\u3051\u3067\u3082\u3042\u308a\u307e\u305b\u3093\u3002<\/p>\n<h2>\u5c71\u304c\u6b8b\u308b\u5834\u6240\u3082\u3001\u9805\u6570\u3068\u3068\u3082\u306b\u52d5\u304f<\/h2>\n<p>\u3053\u306e\u4f8b\u3067\u306f\u3001\u6700\u521d\u306e\u5c71\u306e\u4f4d\u7f6e\u306f x\uff1d\u03c0\/(2N) \u3068\u6c42\u3081\u3089\u308c\u307e\u3059\u3002\u548c\u3092\u5fae\u5206\u3059\u308b\u3068\u3001\u6bb5\u5dee\u306e\u53f3\u5074\u3067\u6700\u521d\u306b\u50be\u304d\u304c\u6b63\u304b\u3089\u8ca0\u3078\u5909\u308f\u308b\u306e\u304c\u3053\u306e\u4f4d\u7f6e\u306b\u306a\u308b\u305f\u3081\u3067\u3059\u3002N\u30925\u500d\u306b\u3059\u308c\u3070\u3001\u5c71\u307e\u3067\u306e\u8ddd\u96e2\u306f5\u5206\u306e1\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u3053\u3053\u3067\u4e8c\u3064\u306e\u898b\u65b9\u3092\u5206\u3051\u308b\u3068\u3001\u7591\u554f\u304c\u307b\u3069\u3051\u307e\u3059\u3002\u4e00\u3064\u306f\u3001\u6bb5\u5dee\u304b\u3089\u96e2\u308c\u305f<strong>\u540c\u3058\u5834\u6240\u3092\u898b\u7d9a\u3051\u308b<\/strong>\u898b\u65b9\u3002\u4f8b\u3048\u3070 x\uff1d0.4 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href=\"https:\/\/dlmf.nist.gov\/6.16\">NIST Digital Library of Mathematical Functions, \u00a76.16(i) Gibbs\u2019 Phenomenon<\/a>\uff08Version 1.2.8\u30012026\u5e749\u670815\u65e5\u516c\u958b\uff09\u3002\u77e9\u5f62\u6ce2\u306e\u90e8\u5206\u548c\u3001\u6700\u521d\u306e\u6975\u5927\u306e\u4f4d\u7f6e\u3068\u6975\u9650\u5024\u3092\u53c2\u7167\u3002<\/li>\n<li><a href=\"https:\/\/ocw.mit.edu\/courses\/es-1803-differential-equations-spring-2024\/mites_1803_s24_topic_full.pdf\">MIT OpenCourseWare, ES.1803 Differential Equations, Spring 2024, Topic Notes<\/a>\uff08Jeremy Orloff\u3001\u00a722.6\u3001\u518a\u5b50202\u30da\u30fc\u30b8\uff09\u3002\u6bb5\u5dee\u5168\u4f53\u306b\u5bfe\u3059\u308b\u8d85\u904e\u7387\u3068\u90e8\u5206\u548c\u306e\u56f3\u3092\u53c2\u7167\u3002\u672c\u6587\u306e5\u30fb25\u30fb125\u9805\u306e\u6570\u5024\u3068\u56f3\u306f\u3001Quantum Sea\u306b\u3088\u308b\u72ec\u81ea\u8a08\u7b97\u3002<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u6b63\u5f26\u6ce2\u3092\u305f\u304f\u3055\u3093\u8db3\u3057\u5408\u308f\u305b\u308b\u3068\u3001\u56db\u89d2\u3044\u6ce2\u5f62\u3092\u63cf\u3051\u307e\u3059\u3002\u8db3\u3059\u6ce2\u3092\u5897\u3084\u305b\u3070\u89d2\u3082\u92ed\u304f\u306a\u308a\u307e\u3059\u304c\u3001\u6bb5\u5dee\u306e\u8fd1\u304f\u306b\u306f\u3001\u5143\u306e\u9ad8\u3055\u3092\u5c11\u3057\u8d85\u3048\u308b\u5c71\u304c\u6b8b\u308a\u307e\u3059\u3002\u8a08\u7b97\u3092\u7d30\u304b\u304f\u3057\u305f\u306e\u306b\u3001\u306a\u305c\u3053\u306e\u98db\u3073\u51fa\u3057\u306f\u6d88\u3048\u306a\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002 \u7c21\u5358\u306b\u307e\u3068\u3081\u308b\u3068 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