{"id":3744,"date":"2011-08-23T19:28:25","date_gmt":"2011-08-23T11:28:25","guid":{"rendered":"http:\/\/www.andrewsun.net\/panta_rhei\/?p=3744"},"modified":"2020-02-04T23:52:12","modified_gmt":"2020-02-04T15:52:12","slug":"%e5%81%9a%e6%ad%a3%e5%bc%a6%e6%b3%a2%e6%8b%9f%e5%90%88%e9%9c%80%e8%a6%81%e4%ba%86%e8%a7%a3%e7%9a%84%e5%9f%ba%e7%a1%80%e7%9f%a5%e8%af%86","status":"publish","type":"post","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/3744","title":{"rendered":"\u505a\u6b63\u5f26\u6ce2\u62df\u5408\u9700\u8981\u4e86\u89e3\u7684\u57fa\u7840\u77e5\u8bc6"},"content":{"rendered":"<div class=\"kcite-section\" kcite-section-id=\"3744\">\n<p>\u6bd4\u8f83\u5168\u9762\u7684\u8d44\u6599\uff1aJulius Orion Smith III, <em><a href=\"https:\/\/ccrma.stanford.edu\/~jos\/sasp\/sasp.html\">SPECTRAL AUDIO SIGNAL PROCESSING<\/a><\/em>, Ch. <a href=\"https:\/\/ccrma.stanford.edu\/~jos\/sasp\/Spectrum_Analysis_Sinusoids.html\">Spectrum Analysis of Sinusoids<\/a>\u3002<\/p>\n<p>\u5178\u578b\u975e\u7ebf\u6027\u56de\u5f52\u95ee\u9898\u7684\u89e3\u6cd5<\/p>\n<ul>\n<li>Wikipedia.org\u6700\u5c0f\u4e8c\u4e58\u6cd5\uff08least square\uff09\u7684<a href=\"http:\/\/en.wikipedia.org\/wiki\/Least_squares\">\u4ecb\u7ecd<\/a><\/li>\n<li>Cleve Moler, <em><a href=\"http:\/\/www.mathworks.com\/moler\/chapters.html\">Numerical Computing with MATLAB<\/a><\/em>, <a href=\"http:\/\/www.mathworks.com\/moler\/leastsquares.pdf\">Ch.5<\/a><\/li>\n<li>Henri Gavin, <em><a href=\"http:\/\/www.duke.edu\/~hpgavin\/ce281\/lm.pdf\">Levenberg-Marquardt method: introduction and examples<\/a><\/em>, <a href=\"http:\/\/www.duke.edu\/~hpgavin\/ce281\/\">CE 281: Experimental Systems<\/a>, Duke University<\/li>\n<\/ul>\n<p>Peak-finding by parabolic interpolation<\/p>\n<ul>\n<li><a href=\"http:\/\/terpconnect.umd.edu\/~toh\/spectrum\/PeakFindingandMeasurement.htm\">MATLAB\u4ee3\u7801<\/a>\uff0c\u4f5c\u8005\uff1aTom O&#8217;Haver\u3002MATLAB Central rating: 4.7<\/li>\n<li><a href=\"http:\/\/www.mathworks.com\/matlabcentral\/fileexchange\/25500\">MATLAB\u4ee3\u7801<\/a>\uff0c\u4f5c\u8005\uff1aNate Yoder\u3002MATLAB Central rating: 4.9<\/li>\n<\/ul>\n<!-- kcite active, but no citations found -->\n<\/div> <!-- kcite-section 3744 -->","protected":false},"excerpt":{"rendered":"<p>\u6bd4\u8f83\u5168\u9762\u7684\u8d44\u6599\uff1aJulius Orion Smith III, SPECTRAL AUDIO SIGNAL PROCESSING, Ch. 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4.9<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[264,303],"tags":[],"class_list":["post-3744","post","type-post","status-publish","format-standard","hentry","category-264","category-rheo"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p1aPvF-Yo","jetpack-related-posts":[{"id":6606,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/6606","url_meta":{"origin":3744,"position":0},"title":"\u8ba9\u8bba\u6587\u4f5c\u56fe\u66f4\u7f8e\u89c2\u7684\u65b9\u6cd5","author":"Andrew","date":"2015\u5e744\u670817\u65e5","format":"aside","excerpt":"OriginPro\u80fd\u4f5c\u5f88\u591a\u79cd\u56fe\uff0c\u4f46\u662f\u989c\u8272\u5f88\u4e11\uff0c\u8981\u624b\u52a8\u6362\u81ea\u5b9a\u4e49\u7684\u989c\u8272\u53c8\u6781\u5176\u9ebb\u70e6\u3002\u6211\u65e9\u5c31\u60f3\u4e0d\u7528\u5b83\u3002\u968f\u7740\u6211\u7814\u7a76\u8bfe\u9898\u7684\u8f6c\u53d8\uff0c\u5f88\u591a\u5b9e\u9a8c\u6570\u636e\u90fd\u662f\u5728Matlab\u91cc\u6279\u91cf\u8ba1\u7b97\u548c\u5904\u7406\u7684\u3002\u7528Matlab\u4f5c\u7684\u56fe\u6709\u4e86\u53d8\u7f8e\u89c2\u7684\u53ef\u80fd\u3002 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&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":7088,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/7088","url_meta":{"origin":3744,"position":4},"title":"Rice\u5206\u5e03\u7684\u6570\u503c\u8ba1\u7b97","author":"Andrew","date":"2016\u5e747\u67088\u65e5","format":false,"excerpt":"[latexpage] \u6211\u5728\u6781\u5750\u6807\u4e0b\u7684\u4e8c\u7ef4\u65e0\u89c4\u884c\u8d70\u4e2d\u8ba8\u8bba\u5230Rice\u5206\u5e03\uff1a \\begin{equation}\\label{eq:1} p_R\\left(r\\right)=\\frac{r}{\\sigma^2}I_0\\left(\\frac{r\\mu_r}{\\sigma^2}\\right)\\exp\\left(-\\frac{r^2+\\mu_r^2}{2\\sigma^2}\\right) \\end{equation} \u5f53\u65e0\u89c4\u884c\u8d70\u53d1\u751f\u7684\u201c\u4f4d\u7f6e\u201d\uff08$\\mu_r$\uff09\u79bb\u539f\u70b9\u5f88\u8fdc\u65f6\uff0c$\\mu_r$\u503c\u5f88\u5927\uff0c\u800c\u5206\u5e03\u7684\u6781\u503c\u4e5f\u5927\u81f3\u5904\u4e8e$r=\\mu_r$\u5904\uff0c\u56e0\u6b64\uff0c\u80fd\u770b\u5230\u5206\u5e03\u4e3b\u8981\u7279\u5f81\u7684$r$\u8303\u56f4\u4e5f\u5728$\\mu_r$\u9644\u8fd1\u3002\u8fd9\u65f6\uff0c\u5f0f(\\ref{eq:1})\u4e2d\u7684\u7b2c\u4e00\u7c7b\u4fee\u6b63\u8d1d\u585e\u5c14\u51fd\u6570$I_0\\left(\\frac{r\\mu_r}{\\sigma^2}\\right)$\u7684\u503c\u4f1a\u5f88\u5927\uff0c\u800c\u81ea\u7136\u6307\u6570\u9879$\\exp\\left(-\\frac{r^2+\\mu_r^2}{2\\sigma^2}\\right)$\u4f1a\u5f88\u5c0f\uff0c\u4f46\u6574\u4e2a\u5f0f(\\ref{eq:1})\u7684\u503c\u4ecd\u7136\u662f\u9002\u4e2d\u7684\u3002\u5728MATLAB\u8f93\u5165\u4e0a\u5f0f\u8ba1\u7b97\u65f6\uff0c\u4f1a\u56e0\u4e3a\u8ba1\u7b97\u8fc7\u7a0b\u4e2d\u6d89\u53ca\u5230\u5f88\u5927\u7684\u548c\u5f88\u5c0f\u7684\u503c\uff0c\u6240\u4ee5\u5c3d\u7ba1\u6700\u7ec8\u7ed3\u679c\u7684\u503c\u662f\u9002\u4e2d\u7684\uff0c\u8ba1\u7b97\u4e5f\u4f1a\u6ea2\u51fa\u3002\u8fd9\u65f6\u53ef\u4ee5\u5229\u7528\u7b2c\u4e00\u7c7b\u4fee\u6b63\u8d1d\u585e\u5c14\u51fd\u6570\u7684\u6e10\u8fd1\u5c55\u5f00\u3002\u5f53$\\alpha$\u4e3a\u5b9a\u503c\u3001$\\left|z\\right|$\u5f88\u5927\u4e14$\\left|\\mathrm{arg}z\\right|","rel":"","context":"In &quot;\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0&quot;","block_context":{"text":"\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/category\/tagged"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":9108,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/9108","url_meta":{"origin":3744,"position":5},"title":"Leon B. Lucy","author":"Andrew","date":"2024\u5e7412\u670814\u65e5","format":false,"excerpt":"[latexpage] \u80cc\u666f \u5728\u6570\u503c\u8ba1\u7b97\u9886\u57df\u6709\u4e00\u4e2a\u6bd4\u8f83\u77e5\u540d\u7684\u53bb\u5377\u79ef\u8fed\u4ee3\u7b97\u6cd5\u2014\u2014Lucy--Richardson\u7b97\u6cd5\uff0c\u5b83\u88ab\u540e\u4e16\u96c6\u4e2d\u7528\u4e8e\u56fe\u50cf\u53bb\u566a\u3002\u4f8b\u5982\uff0cMATLAB\u7684Image Processing Toolbox\u6709\u4e00\u4e2adeconvlucy\u547d\u4ee4\uff0c\u58f0\u79f0\u5c31\u662f\u7528Lucy--Richardson\u7b97\u6cd5\u5bf9\u7ed9\u5b9a\u56fe\u7247\uff08\u50cf\u7d20\u77e9\u9635\uff09\u4f5c\u7ed9\u5b9a\u70b9\u6269\u6563\u51fd\u6570\u7684\u53bb\u566a\u3002 \u4f46\u662f\uff0cLucy\u7684\u539f\u6587\u6240\u9488\u5bf9\u7684\u95ee\u9898\uff0c\u6bd4\u73b0\u5728\u4e00\u822c\u5e94\u7528\u66f4\u5e7f\u4e49\u3002\u5047\u5b9a$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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