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Sci. Technol.\u3001AIP\u7684Rev. Sci. Instrum.\u7b49\uff0c\u591a\u6d4f\u89c8\u91cc\u9762\u7684\u8bba\u6587\uff0c\u53ef\u4ee5\u4e86\u89e3\u5230\u66f4\u591a\u7684\u201c\u5947\u6280\u6deb\u5de7\u201d\uff0c\u8fdb\u4e00\u6b65\u5f00\u6269\u4eea\u5668\u8bbe\u8ba1\u4e0a\u7684\u601d\u7ef4\uff0c\u5728\u79d1\u5b66\u7814\u7a76\u4e0a\u5c31\u80fd\u83b7\u5f97\u66f4\u5927\u7684\u81ea\u7531\u3002\u603b\u4e4b\uff0c\u6211\u7684\u6f14\u8bb2\u8fd8\u662f\u4e3b\u8981\u4ee5\u63d0\u9ad8\u91cd\u89c6\u3001\u5f00\u6269\u773c\u754c\u3001\u6253\u6d88\u6050\u60e7\u4e3a\u4e3b\uff0c\u7559\u5f85\u5b66\u751f\u81ea\u5b66\u76f8\u5173\u5177\u4f53\u5185\u5bb9\u3002\u79d1\u5b66\u8ba1\u7b97\uff08scientific computing\uff09\u4e3a\u4ec0\u4e48\u672c\u8eab\u5c31\u662f\u4e00\u4e2a\u7814\u7a76\u9886\u57df\u5df2\u7ecf\u65e0\u5eb8\u8d58\u8ff0\u3002\u5176\u5b9e\u6211\u4ecb\u7ecd\u7684\u5185\u5bb9\u4e3b\u8981\u662f\u6570\u503c\u65b9\u6cd5\u5728\u5b9e\u9a8c\u7269\u7406\u4e2d\u7684\u5e94\u7528\uff0c\u7ed3\u5408MATLAB\u7f16\u7a0b\u6765\u8bb2\u8ff0\u3002\u7531\u4e8e\u6570\u503c\u65b9\u6cd5\u548c\u7a0b\u5e8f\u8bbe\u8ba1\u5bf9\u5916\u884c\u6765\u8bf4\u6709\u4e00\u5b9a\u95e8\u69db\uff0c\u5e02\u9762\u4e0a\u7684\u6559\u6750\u8ddf\u79d1\u7814\u5e94\u7528\u53c8\u6709\u4e00\u5b9a\u8ddd\u79bb\uff0c\u56e0\u6b64\u662f\u9700\u8981\u4e00\u4e2a\u6709\u9488\u5bf9\u6027\u7684\u8bb2\u5ea7\u6765\u5e2e\u5b66\u751f\u6253\u6d88\u8fd9\u4e2a\u95e8\u69db\u7684\u3002\u6240\u5174\u5728MATLAB\u7684\u6559\u6750\u5f80\u5f80\u4f1a\u5e26\u6709\u6570\u503c\u65b9\u6cd5\u7684\u7b80\u4ecb\uff0c\u8fd9\u65b9\u9762\u6709\u5f88\u597d\u7684\u6559\u6750\u3002\u9996\u5148MATLAB\u7f51\u7ad9\u4e0a\u7684\u8fd9\u4e00\u7f51\u9875\u7684\u8d44\u6599\u5c31\u5f88\u597d\u3002\u6709\u4e00\u672c\u7ecf\u5178\u6559\u6750\u53eb\u300a\u901a\u8fc7MATLAB\u8fdb\u884c\u6570\u503c\u8ba1\u7b97\u300b\u3002\u79d1\u5b66\u4f5c\u56fe\u8fd9\u65b9\u9762\u7684\u4ecb\u7ecd\u4e5f\u662f\u9488\u5bf9\u6211\u5728\u7814\u7a76\u751f\u4e2d\u770b\u5230\u7684\u4e00\u4e9b\u95ee\u9898\u7684\u3002\u5b66\u751f\u4ece\u672c\u79d1\u5b66\u4e60\u9636\u6bb5\u5c31\u5df2\u7ecf\u4ece\u8bfe\u672c\u4e0a\u770b\u5230\u5f88\u591a\u56fe\u8868\uff0c\u66f4\u4e0d\u7528\u8bf4\u5230\u4e86\u7814\u7a76\u751f\u9636\u6bb5\u4ece\u8bba\u6587\u4e2d\u770b\u5230\u66f4\u591a\u7c7b\u578b\u7684\u56fe\u8868\u4e86\u3002\u6240\u4ee5\u4e00\u822c\u6765\u8bf4\u9762\u5bf9\u81ea\u5df1\u6d4b\u5f97\u7684\u6570\u636e\uff08data\uff09\uff0c\u5b66\u751f\u51ed\u76f4\u89c9\u80fd\u591f\u9009\u62e9\u6b63\u786e\u7684\u56fe\u8868\u7c7b\u578b\u53bb\u5c55\u793a\uff08illustrate\uff09\uff0c\u6216\u8005\u7528\u8fd1\u5e74\u6765\u7279\u522b\u6d41\u884c\u7684\u8bcd\u2014\u2014\u53ef\u89c6\u5316\uff08visualize\uff09\u3002\u4e8b\u5b9e\u4e0adata visualization\u4e5f\u662f\u4e00\u4e2a\u5b66\u672f\u7814\u7a76\u9886\u57df\u3002\u5f88\u591a\u79d1\u5b66\u4f5c\u56fe\u8f6f\u4ef6\u7684\u529f\u80fd\u662f\u878d\u5165\u4e86\u5f88\u591a\u65b0\u7684\u7814\u7a76\u6210\u679c\u7684\u3002\u56de\u5230\u5b66\u751f\u7684\u95ee\u9898\u4e0a\uff0c\u9996\u5148\u662f\u6709\u4e9b\u65f6\u5019\u5b66\u751f\u9009\u62e9\u4e86\u4e0d\u6070\u5f53\u7684\u7c7b\u578b\u7684\u56fe\u6765\u5c55\u793a\u81ea\u5df1\u7684\u6570\u636e\u3002\u90a3\u4e48\u5982\u4f55\u8df3\u51fa\u5177\u4f53\u7684\u9519\u8bef\u6848\u4f8b\uff1f\u80fd\u5426\u4e00\u822c\u6027\u5730\u544a\u8bc9\u5b66\u751f\u9009\u62e9\u6b63\u786e\u7c7b\u578b\u56fe\u8868\u7684\u539f\u5219\uff1f\u4e8b\u5b9e\u4e0a\u5f88\u591a\u4eba\u6ca1\u6709\u610f\u8bc6\u5230\u7684\u662f\uff0c\u6570\u636e\u3001\u56fe\u7684\u672c\u8d28\u662f\u51fd\u6570\u3002\u65e0\u8bba\u662f\u6570\u636e\u8868\u4e5f\u597d\u3001\u56fe\u4e5f\u597d\uff0c\u4f60\u8981\u544a\u8bc9\u8bfb\u8005\u7684\u603b\u662f\u4e00\u4e2a\u51fd\u6570\u5173\u7cfb\u3002\u90a3\u4e48\uff0c\u4f60\u8fd9\u4e2a\u51fd\u6570\uff0c\u662f\u6807\u91cf\u51fd\u6570\u8fd8\u662f\u77e2\u91cf\u51fd\u6570\uff1f\u662f\u6807\u91cf\u573a\u8fd8\u662f\u77e2\u91cf\u573a\uff1f\u662f\u591a\u5c11\u7ef4\u7a7a\u95f4\u7684\uff1f\u8fd9\u662f\u9996\u5148\u9700\u8981\u660e\u786e\u7684\u3002\u7136\u540e\u5c31\u53ef\u4ee5\u5411\u5b66\u751f\u7f57\u5217\uff0c\u4e0d\u540c\u7c7b\u578b\u7684\u51fd\u6570\u90fd\u53ef\u4ee5\u6709\u4ec0\u4e48\u76f8\u5e94\u7c7b\u578b\u7684\u53ef\u89c6\u5316\u65b9\u6cd5\u3002\u8fd9\u6837\u5c31\u4e0d\u4f1a\u4e71\u9009\u4e43\u81f3\u9009\u9519\u7c7b\u578b\u4e86\u3002\u5176\u6b21\uff0c\u5b66\u751f\u7ecf\u5e38\u6f0f\u6389\u6216\u8005\u9519\u8bef\u5730\u5904\u7406\u56fe\u4e2d\u7684\u5404\u4e2a\u5143\u7d20\uff08\u5ea7\u6807\u8f74\u6807\u7b7e\u3001\u56fe\u4f8b\u3001\u5355\u4f4d\u7b49\u7b49\uff09\u3002\u7b2c\u4e09\u5c31\u662f\u5982\u4f55\u4f7f\u56fe\u66f4\u7b80\u660e\u7f8e\u89c2\u7684\u95ee\u9898\uff0c\u8fd9\u5e76\u975e\u662f\u4e00\u4e2a\u7f8e\u672f\u95ee\u9898\uff0c\u800c\u662f\u6709\u5f88\u591a\u7814\u7a76\u7684\uff0c\u4f8b\u5982color schemes\u3001font families\/weights\u7b49\u65b9\u9762\u7ed9\u8bfb\u8005\u4ea7\u751f\u7684\u6548\u5e94\u4ee5\u53ca\u76f8\u5e94\u7684\u539f\u5219\u3002\u5f88\u591a\u5b66\u751f\u4e0d\u6ce8\u610f\u8fd9\u4e9b\u65b9\u9762\uff0c\u56fe\u5f88\u201c\u4e11\u201d\u3002\u6700\u540e\uff0c\u672a\u6765\u51e0\u5e74\u7684\u4e00\u4e2a\u53ef\u80fd\u7684\u8d8b\u52bf\u662f\u4ea4\u4e92\u6027\u7684\u6570\u636e\u56fe\uff0c\u4e00\u4e9b\u671f\u520a\u51fa\u7248\u5546\u5df2\u7ecf\u9f13\u52b1\u6295\u7a3f\u4eba\u652f\u6301\u8fd9\u6837\u7684\u529f\u80fd\uff0c\u6240\u4ee5\u4e5f\u53ef\u4ee5\u4f5c\u4e9b\u4ecb\u7ecd\u3002","rel":"","context":"In &quot;\u5173\u4e8e\u79d1\u7814\u7684\u6587\u7ae0&quot;","block_context":{"text":"\u5173\u4e8e\u79d1\u7814\u7684\u6587\u7ae0","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/category\/%e5%85%b3%e4%ba%8e%e7%a7%91%e7%a0%94%e7%9a%84%e6%96%87%e7%ab%a0"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":4792,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/4792","url_meta":{"origin":7224,"position":3},"title":"\u65f6\u6e29\u53e0\u52a0\u5f97\u5230\u7684\u677e\u5f1b\u65f6\u95f4\u662f\u4ec0\u4e48\u677e\u5f1b\u65f6\u95f4\uff1f","author":"Andrew","date":"2012\u5e747\u670814\u65e5","format":false,"excerpt":"\u8fd9\u4e2a\u95ee\u9898\u641e\u4e86\u6211\u4e00\u4e2a\u901a\u5bb5\uff0c\u8bb0\u5f55\u4e00\u4e0b\u3002 \u65f6\u6e29\u53e0\u52a0\u6027\u8d28\u662f\u6307\u4f53\u7cfb\u5728\u4e0d\u540c\u6e29\u5ea6\u6d4b\u91cf\u5f97\u5230\u7684\u76f8\u5173\u51fd\u6570\u6216\u54cd\u5e94\u51fd\u6570\u53ef\u5728\u65f6\u95f4\u8f74\u5e73\u79fb\u53e0\u52a0\u6210\u4e00\u6761\u4e3b\u66f2\u7ebf\u3002\u5e73\u79fb\u56e0\u5b50aT\u5e38\u5e38\u8ba4\u4e3a\u662f\u677e\u5f1b\u65f6\u95f4\u7684\u6bd4\u503c\uff1a \u4f46\u662f\uff0c\u5b9e\u9645\u6837\u54c1\u5f80\u5f80\u5177\u6709\u4e00\u4e2a\u8f83\u5bbd\u7684\u677e\u5f1b\u65f6\u95f4\u8c31\u3002\u90a3\u4e48\u4e0a\u5f0f\u4e2d\u7684\u677e\u5f1b\u65f6\u95f4\u5230\u5e95\u662f\u54ea\u4e2a\u503c\uff0c\u662f\u5e73\u5747\u503c\u8fd8\u662f\u6700\u5927\u503c\u8fd8\u662f\u4ec0\u4e48\uff1f \u73bb\u7483\u6001\u4f53\u7cfb\u7684\u76f8\u5173\u51fd\u6570\u6216\u54cd\u5e94\u51fd\u6570\u5e38\u5e38\u7b26\u5408Kohlrausch-Williams-Watts\uff08KWW\uff09\u5173\u7cfb\uff1a \u5982\u679c\u4f53\u7cfb\u53ea\u6709\u4e00\u4e2a\u677e\u5f1b\u65f6\u95f4\u503c\uff0c\u5219\u03b2 = 1\uff0c\u03c40\u5c31\u662f\u677e\u5f1b\u65f6\u95f4\u3002\u5982\u679c0 < \u03b2 < 1\uff0c\u5219\u53cd\u6620\u4f53\u7cfb\u6709\u4e00\u4e2a\u5bbd\u5206\u5e03\u7684\u677e\u5f1b\u65f6\u95f4\u8c31\u3002\u03c40\u53ea\u80fd\u662f\u4e00\u4e2a\u7528\u6765\u63cf\u8ff0\u76f8\u5173\u51fd\u6570\u6216\u54cd\u5e94\u51fd\u6570\u7684\u7279\u5f81\u65f6\u95f4\u3002\u65f6\u6e29\u53e0\u52a0\u5f97\u5230\u7684\u5c31\u662f\u03c40\u7684\u6bd4\u503c\u3002\u03c40\u8ddf\u677e\u5f1b\u65f6\u95f4\u8c31\u6709\u4ec0\u4e48\u5173\u7cfb\u5462\uff1f\u5b83\u662f\u4e0d\u662f\u5c31\u662f\u5e73\u5747\u677e\u5f1b\u65f6\u95f4<\u03c4>\u5462\uff1f \u4ee5\u5e94\u529b\u677e\u5f1b\u4e3a\u4f8b\uff0c\u5047\u8bbe\u6837\u54c1\u53ef\u8868\u793a\u6210\u65e0\u6570\u4e2aMaxwell\u6a21\u578b\u7684\u548c\uff1a \u5176\u4e2dg(\u03c4)\u662f\u677e\u5f1b\u65f6\u95f4\u5206\u5e03\u51fd\u6570\u3002\u5b83\u4e0e\u66f4\u5e38\u7528\u7684\u677e\u5f1b\u65f6\u95f4\u8c31\u7684\u5173\u7cfb\u662fH(\u03c4)=\u03c4g(\u03c4)\u3002\u7531\u4e8eG(t)\u7b26\u5408KWW\u65b9\u7a0b\uff0c\u5219\u6709 \u4ee4u=1\/\u03c4\uff0c\u4e0a\u5f0f\u5c31\u53d8\u6210\u4e00\u4e2aLaplace\u53d8\u6362\uff1a \u4e3a\u4e86\u5f97\u5230g(\u03c4)\uff0c\u987b\u8ba1\u7b97\u4ee5\u4e0b\u53cdLaplace\u53d8\u6362\uff1a g(\u03c4)\u7684n\u9636\u77e9<\u03c4n>\uff1a \u6240\u4ee5 \u5373\u5bf9\u4e8e\u4e00\u4e2a\u6ee1\u8db3KWW\u578b\u54cd\u5e94\u51fd\u6570G(t)\u7684\u4f53\u7cfb\uff0c\u5176\u5e73\u5747\u677e\u5f1b\u65f6\u95f4<\u03c4>\u4e0eKWW\u65b9\u7a0b\u7684\u7279\u5f81\u65f6\u95f4\u03c40\u6210\u6b63\u6bd4\uff0c\u56e0\u6b64\u5e73\u79fb\u56e0\u5b50aT\u786e\u5b9e\u662f\u5e73\u5747\u677e\u5f1b\u65f6\u95f4\u7684\u6bd4\u503c \u3002 \u66f4\u9ebb\u70e6\u7684\u95ee\u9898\u662f\uff0c\u505a\u52a8\u6001\u6d4b\u8bd5\u7684\u65f6\u5019\uff0cG' = G''\u5904\u6240\u5bf9\u5e94\u7684\u9891\u7387\u5012\u6570\u662f\u4ec0\u4e48\u65f6\u95f4\uff1f\u5f88\u591a\u5730\u65b9\u8bf4\u8fd9\u662f\u6700\u5927\u677e\u5f1b\u65f6\u95f4\uff08maximum relaxation time\uff09\u03c4m\uff0c\u5373\u5f53\u89c2\u5bdf\u65f6\u95f4\u65f6\u95f4\u8d85\u8fc7\u03c4m\uff0c\u5c31\u53ef\u4ee5\u770b\u5230\u6837\u54c1\u7684\u6d41\u52a8\u3002\u53ef\u662f\uff0c\u4e00\u4e2a\u54cd\u5e94\u51fd\u6570\u7b26\u5408KWW\u65b9\u7a0b\u7684\u6837\u54c1\uff0c\u662f\u5426\u5177\u6709\u786e\u5b9a\u7684\u6700\u5927\u677e\u5f1b\u65f6\u95f4\uff1f\u4e5f\u5c31\u662f\u8bf4\uff0c\u5176\u677e\u5f1b\u65f6\u95f4\u5206\u5e03\u51fd\u6570g(\u03c4)\u662f\u5426\u6709\u786e\u5b9a\u7684\u5b9a\u4e49\u57df\uff0c\u4f7f\u5f97\u5f53\u03c4>\u03c4m\u65f6g(\u03c4) = 0\uff1f\u8fd9\u4e2a\u90fd\u4e0d\u597d\u8bf4\u3002\u201c\u6700\u5927\u677e\u5f1b\u65f6\u95f4\u201d\u7684\u6982\u5ff5\u8ddf\u677e\u5f1b\u65f6\u95f4\u8c31\u7684\u5173\u7cfb\uff0c\u591a\u6570\u89c1\u4e8e\u4eba\u4e3a\u7ed9\u5b9a\u7684\u677e\u5f1b\u65f6\u95f4\u8c31\uff0c\u4f8b\u5982Wedge-Box distribution\u3001BSW distribution\u7b49\u7b49\u3002\u7ed9\u5b9ag(\u03c4)\uff0c\u5012\u662f\u53ef\u4ee5\u5206\u522b\u8ba1\u7b97G'\u548cG'' \u4ee4G' = G''\uff0c\u628a\u4e0a\u9762\u4e24\u5f0f\u8054\u8d77\u6765\u89e3\u51fa\u03c9\u6765\uff0c\u5c31\u80fd\u6c42\u5f97\u6240\u8c13\u7684\u201c\u6700\u5927\u677e\u5f1b\u65f6\u95f4\u201d\u662f\u5565\uff0c\u4f46\u8fd9\u4e2a\u592a\u96be\u4e86\u2026\u2026\u53c8\u636e\u8bf4\uff0cG' = G''\u65f6\u7684\u03c9\u4e5f\u5c31\u662fG''\u6700\u5927\u503c\u65f6\u7684\u03c9\u3002\u5219\u4e0a\u9762\u7b2c\u4e8c\u4e2a\u5f0f\u5b50\u6c42\u5bfc\uff0c\u5c31\u5269\u4e0b\u88ab\u79ef\u51fd\u6570\u4e86\u3002\u90a3\u5768\u4e1c\u897f\u4e2d\u53f3\u8fb9\u7684\u5206\u5f0f\u662f\u975e\u96f6\u7684\uff0c\u6240\u4ee5\u552f\u6709\u8ba9g(\u03c4)=0\u3002\u8fd9\u5c31\u53c8\u56de\u5230\u4e4b\u524d\u95ee\u7684\u90a3\u4e2a\u95ee\u9898\u4e86\uff1ag(\u03c4)\u662f\u5426\u6709\u786e\u5b9a\u7684\u5b9a\u4e49\u57df\uff0c\u4f7f\u5f97\u5f53\u03c4>\u03c4m\u65f6g(\u03c4) = 0\uff1f \u6709\u4eba\u7ed9\u51fa\uff08\u89c1\u53c2\u8003\u6587\u732e\uff09\u4e86g(\u03c4)\u7684\u8fd1\u4f3c\u8868\u8fbe\u5f0f\uff0c\u662f\u4e2a\u542bGamma\u51fd\u6570\u7684\u7ea7\u6570\u3002\u8981\u6211\u89e3g(\u03c4) = 0\u51e0\u4e4e\u662f\u4e0d\u53ef\u80fd\u7684\u2026\u2026 \u8fd8\u6709\u4e00\u4e2a\u53ef\u80fd\u7684\u89e3\u51b3\u65b9\u6cd5\uff0c\u5c31\u662f\u91c7\u7528\u677e\u5f1b\u65f6\u95f4\u8c31\u7684\u4e00\u4e9b\u8fd1\u4f3c\u7b97\u6cd5\u3002\u4f8b\u5982\uff1a \u8fd9\u5c31\u53ef\u76f4\u63a5\u4eceG(t)\u53bb\u8ba1\u7b97\u677e\u5f1b\u65f6\u95f4\u8c31H(\u03c4)=\u03c4g(\u03c4)\uff0c\u7136\u540e\u4ee3\u5165\u4e0a\u9762\u7684\u5f0f\u5b50\u7b97\u51faG'\u548cG''\uff0c\u89e3\u51fa\u201c\u6700\u5927\u677e\u5f1b\u65f6\u95f4\u201d\u6765\u3002\u4f46\u603b\u4e4b\u90a3\u4e24\u4e2a\u79ef\u5206\u8fd8\u662f\u5f88\u96be\u641e \u6211\u731c\u6d4b\u8ba1\u6700\u5927\u677e\u5f1b\u65f6\u95f4\u03c4m\u4e5f\u662f\u8ddf\u03c40\u548c\u03b2\u6709\u5173\uff0c\u4f46\u662f\u5426\u6b63\u6bd4\u4e8e\u03c40\u5c31\u4e0d\u77e5\u9053\u4e86\u3002\u771f\u7684\u4e0d\u884c\u7684\u8bdd\uff0c\u6211\u53ea\u80fd\u5728MATLAB\u6570\u503c\u7b97\u4e00\u4e0b\uff0c\u8003\u5bdf\u4e00\u4e0b\u4e0d\u540c\u03b2\u503c\u4e0b\u7684\u6700\u5927\u677e\u5f1b\u65f6\u95f4\u03c4m\u3001\u5e73\u5747\u677e\u5f1b\u65f6\u95f4<\u03c4>\u548cKWW\u7684\u7279\u5f81\u65f6\u95f4\u03c40\u4e4b\u95f4\u7684\u8868\u89c2\u5173\u7cfb\uff0c\u770b\u80fd\u5426\u8fd1\u4f3c\u8ba4\u4e3a\u03c4m\u8ddf\u03c40\u6210\u6b63\u6bd4\u3002\u5982\u679c\u80fd\uff0c\u5219\u65f6\u6e29\u53e0\u52a0\u5f97\u5230\u7684\u5e73\u79fb\u56e0\u5b50\uff0c\u540c\u65f6\u4e5f\u662f\u6700\u5927\u677e\u5f1b\u65f6\u95f4\u4e4b\u6bd4\uff1a \u53c2\u8003\u6587\u732e\uff1aJ. Chem. Phys. 73:3348\uff0cText. Res. J. 21:404","rel":"","context":"In &quot;\u5de5\u4f5c\u7b14\u8bb0&quot;","block_context":{"text":"\u5de5\u4f5c\u7b14\u8bb0","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/category\/personal\/%e5%b7%a5%e4%bd%9c%e7%ac%94%e8%ae%b0"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":9177,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/9177","url_meta":{"origin":7224,"position":4},"title":"\u5728\u7535\u5b50\u8ba1\u7b97\u673a\u4e4b\u524d\u7684Fourier\u5206\u6790","author":"Andrew","date":"2025\u5e743\u670830\u65e5","format":"aside","excerpt":"[latexpage] \u5982\u679c\u6211\u4eec\u8981\u5bf9\u4e00\u4e2a\u5468\u671f\u4fe1\u53f7\u8fdb\u884cFourier\u7ea7\u6570\u5206\u6790\uff0c\u90a3\u4e48\u6211\u4eec\u662f\u5047\u5b9a\u8be5\u4fe1\u53f7\u53ef\u4ee5\u8868\u793a\u6210\\[f\\left(x\\right)=\\sum_{n=-\\infty}^\\infty c_n e^{\\mathrm{i}2\\pi n x\/P}\\]\u5176\u4e2d\\[c_n=\\frac{1}{P}\\int_0^P f\\left(x\\right)e^{-\\mathrm{i} 2\\pi n x\/P}\\mathrm{d}x\\] \u5728\u4eca\u5929\uff0c\u6211\u4eec\u7684\u5b9e\u9a8c\u4fe1\u53f7\u57fa\u672c\u90fd\u5df2\u7ecf\u6570\u5b57\u5316\uff0c\u5728\u7535\u5b50\u8ba1\u7b97\u673a\u4e2d\u4e00\u79d2\u949f\u4e0d\u5230\u5c31\u505a\u5b8c\u4e86\u4e00\u4e2a\u5feb\u901fFourier\u53d8\u6362\u8ba1\u7b97\u3002\u4f46\u662f\u5728\u4e0a\u4e16\u7eaa50~60\u5e74\u4ee3\uff0c\u7535\u5b50\u8ba1\u7b97\u673a\u8fd8\u6ca1\u53d1\u660e\u4e4b\u524d\uff0c\u5b9e\u9a8c\u7ed3\u679c\u672c\u8eab\u5c31\u53ef\u80fd\u662f\u901a\u8fc7X-Y\u8bb0\u5f55\u4eea\u6216\u53cc\u7b14\u8bb0\u5f55\u4eea\u753b\u5728\u5750\u6807\u7eb8\u4e0a\u7684\u3002\u5f53\u65f6\u7684\u4eba\u662f\u600e\u6837\u5bf9\u8fd9\u4e48\u4e00\u6bb5\u58a8\u8ff9\u8fdb\u884cFourier\u7ea7\u6570\u5206\u6790\u7684\u5462\uff1f\u6211\u4eec\u53ef\u4ee5\u770b\u5230\uff0cFourier\u7ea7\u6570\u7684\u5404\u4e2a\u7cfb\u6570$c_n$\u662f\u4e00\u4e2a\u79ef\u5206\u3002\u5728\u90a3\u4e2a\u5e74\u4ee3\uff0c\u79ef\u5206\u53ef\u4ee5\u4f7f\u7528\u6b27\u62c9\u6cd5\u6570\u503c\u6c42\u89e3\u3002\u5728\u6b64\u4e4b\u524d\uff0c\u9700\u8981\u5c06\u88ab\u79ef\u51fd\u6570\u8fdb\u884c\u4eba\u5de5\u91c7\u6837\uff08sampling\uff09\u79bb\u6563\u5316\u3002\u56e0\u6b64\u8fd9\u662f\u4e00\u4e2a\u5f88\u7e41\u7410\u7684\u4efb\u52a1\u3002 \u5c0f\u91ce\u6728\u91cd\u6cbb\uff08Shigeharu Onogi\uff09\u53ef\u80fd\u662f\u65e5\u672c\u6700\u65e9\u5bf9\u975e\u7ebf\u6027\u7c98\u5f39\u6027\u6d41\u4f53\u7684\u6b63\u5f26\u632f\u8361\u6d4b\u8bd5\u7ed3\u679c\u4f5c\u8c10\u6ce2\u5206\u6790\u7684\u7814\u7a76\u8005\u3002\u4ed6\u5f53\u65f6\u4f30\u8ba1\u5c31\u662f\u8fd9\u4e48\u505a\u7684\u3002 \u5728\u7f8e\u56fd\uff0cW. Philippoff\u5f88\u65e9\u5c31\u5f00\u53d1\u5bbd\u9891\u8303\u56f4\u7684\u52a8\u6001\u6d4b\u8bd5\u4eea\u5668\u3002\u4ed6\u57281966\u5e74\u53d1\u8868\u7684\u6587\u7ae0\u4e2d\uff0c\u7528\u4e00\u4e2a\u7279\u522b\u6784\u5efa\u7684\u53ef\u8c03\u8282\u6a21\u62df\u8ba1\u7b97\u5668\uff0c\u53bb\u540c\u65f6\u751f\u6210\u4e00\u4e2a\u57fa\u9891\u548c3\u500d\u9891\u7684\u6b63\u5f26\u4fe1\u53f7\uff0c\u7136\u540e\u4f5c\u52a0\u548c\u3002\u4ed6\u901a\u8fc7\u8c03\u8282\u8fd9\u4e2a\u6a21\u62df\u8ba1\u7b97\u5668\uff0c\u51d1\u51fa\u4e0e\u5b9e\u9a8c\u7ed3\u679c\u5f62\u72b6\u76f8\u4f3c\u7684Lissajous\u66f2\u7ebf\uff0c\u4ece\u800c\u5f97\u77e5\u8be5\u66f2\u7ebf\u76843\u500d\u9891\u8c10\u6ce2\u5e45\u503c\u548c\u76f8\u4f4d\u3002 1960\u5e74\u4ee3\uff0c\u6070\u597d\u662f\u6a21\u62df\u6280\u672f\u7684\u98a0\u5cf0\u65f6\u671f\u3002\u6a21\u62df\u8ba1\u7b97\u7535\u8def\u80fd\u80fd\u505a\u5f88\u591a\u4e8b\u60c5\u3002\u7531\u6d41\u53d8\u4eea\u5f97\u51fa\u7684\u6ce2\u5f62\u4fe1\u53f7\uff0c\u53ef\u901a\u8fc7\u76f8\u5173\u5668\u4e0e\u7ed9\u5b9a\u7684\u6ce2\u5f62\u6bd4\u8f83\uff0c\u8f93\u51fa\u7684\u7ed3\u679c\u662f\u4e0e\u7ed9\u5b9a\u6ce2\u5f62\u7684\u5185\u79ef\u3002\u8fd9\u6837\u5c31\u53ef\u4ee5\u901a\u8fc7\u8bbe\u5b9a\u53c2\u8003\u6ce2\u5f62\u4fe1\u53f7\uff0c\u4ece\u539f\u59cb\u4fe1\u53f7\u4e2d\u63d0\u53d6\u76f8\u5e94\u7684\u5206\u91cf\uff0c\u4ece\u800c\u5b9e\u73b0\u8c10\u6ce2\u5206\u6790\u3002\u4f8b\u5982\uff0cQueen's Collage\u673a\u68b0\u5de5\u7a0b\u7cfb\u7684Harris\u548cBogie\u3002 1967\u5e74\uff0cBrenner\u7684\u6797\u80af\u5b9e\u9a8c\u5ba4\u62a5\u544a\u7ed9\u51fa\u4e86Cooley\u548cTukey\u7684\u5feb\u901fFourier\u53d8\u6362\u7684Fortran\u7a0b\u5e8f\u3002\u51ef\u65af\u897f\u50a8\u5927\u5b66\u5316\u5b66\u7cfb\u7684Dodge\u548cKrieger\u57281971\u5e74\u5c31\u7528\u4e0a\u8fd9\u4e2a\u65b9\u6cd5\u6765\u8fdb\u884c\u8c10\u6ce2\u5206\u6790\u4e86\uff0c\u6b63\u5f0f\u8fdb\u5165\u4e86\u6570\u5b57\u65f6\u4ee3\u3002","rel":"","context":"In &quot;\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0&quot;","block_context":{"text":"\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/category\/tagged"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":9108,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/9108","url_meta":{"origin":7224,"position":5},"title":"Leon B. Lucy","author":"Andrew","date":"2024\u5e7412\u670814\u65e5","format":false,"excerpt":"[latexpage] \u80cc\u666f \u5728\u6570\u503c\u8ba1\u7b97\u9886\u57df\u6709\u4e00\u4e2a\u6bd4\u8f83\u77e5\u540d\u7684\u53bb\u5377\u79ef\u8fed\u4ee3\u7b97\u6cd5\u2014\u2014Lucy--Richardson\u7b97\u6cd5\uff0c\u5b83\u88ab\u540e\u4e16\u96c6\u4e2d\u7528\u4e8e\u56fe\u50cf\u53bb\u566a\u3002\u4f8b\u5982\uff0cMATLAB\u7684Image Processing Toolbox\u6709\u4e00\u4e2adeconvlucy\u547d\u4ee4\uff0c\u58f0\u79f0\u5c31\u662f\u7528Lucy--Richardson\u7b97\u6cd5\u5bf9\u7ed9\u5b9a\u56fe\u7247\uff08\u50cf\u7d20\u77e9\u9635\uff09\u4f5c\u7ed9\u5b9a\u70b9\u6269\u6563\u51fd\u6570\u7684\u53bb\u566a\u3002 \u4f46\u662f\uff0cLucy\u7684\u539f\u6587\u6240\u9488\u5bf9\u7684\u95ee\u9898\uff0c\u6bd4\u73b0\u5728\u4e00\u822c\u5e94\u7528\u66f4\u5e7f\u4e49\u3002\u5047\u5b9a$X$\u662f\u4e00\u4e2a\u8fde\u7eed\u53d6\u503c\u968f\u673a\u53d8\u91cf\u3002\u5b83\u7406\u5e94\u6309\u7167\u5206\u5e03\u5bc6\u5ea6\u51fd\u6570$\\phi\\left(x\\right)$\u3002\u6211\u4eec\u60f3\u628a$\\phi\\left(x\\right)$\u89c6\u4e3a\u67d0\u79cd\u7b80\u5355\u5206\u5e03$P\\left(x\\middle|\\xi\\right)$\u6309\u6743\u91cd\u8c31$\\psi\\left(\\xi\\right)$\u7684\u53e0\u52a0\u7ed3\u679c\uff1a \\begin{equation}\\label{eq:original_phi_expression}\\phi\\left(x\\right)=\\int P\\left(x\\middle|\\xi\\right)\\psi\\left(\\xi\\right)\\mathrm{d}\\xi\\end{equation} \u800c\u6211\u4eec\u60f3\u5f97\u77e5\u7ed9\u5b9a\u5f62\u5f0f\u7684\u6838$P\\left(x\\middle|\\xi\\right)$\u6240\u5bf9\u5e94\u7684\u6743\u91cd\u8c31$\\psi\\left(\\xi\\right)$\u3002\u5728\u8fd9\u91cc\uff0c$\\xi$\u662f\u6838\u51fd\u6570$P$\u7684\u53c2\u6570\u3002\u6bd4\u5982\uff0c\u6211\u4eec\u5173\u5fc3\u9ad8\u65af\u6838\u51fd\u6570\u7684\u60c5\u51b5\uff0c\u90a3\u4e48$P\\left(x\\middle|\\xi\\right)$\u53ef\u80fd\u662f\u4ee5$\\xi$\u4e3a\u6807\u51c6\u5dee\u7684\u9ad8\u65af\u51fd\u6570 \\[P\\left(x\\middle|\\xi\\right)=\\frac{1}{\\sqrt{2\\pi\\xi^2}}\\exp\\left[-\\frac{\\left(x-\\mu\\right)^2}{2\\xi^2}\\right]\\] 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