{"id":977,"date":"2022-01-21T20:02:22","date_gmt":"2022-01-21T12:02:22","guid":{"rendered":"http:\/\/www.wayln.com\/?p=977"},"modified":"2022-01-22T22:55:11","modified_gmt":"2022-01-22T14:55:11","slug":"%e7%ac%ac%e5%9b%9b%e7%ab%a0-%e9%a2%91%e7%8e%87%e5%9f%9f%e6%bb%a4%e6%b3%a2","status":"publish","type":"post","link":"https:\/\/www.wayln.com\/?p=977","title":{"rendered":"\u7b2c\u56db\u7ae0 \u9891\u7387\u57df\u6ee4\u6ce2"},"content":{"rendered":"<div id=\"toc_container\" class=\"toc_transparent no_bullets\"><p class=\"toc_title\">Contents<\/p><ul class=\"toc_list\"><li><a href=\"#42\"><span class=\"toc_number toc_depth_1\">1<\/span> 4.2 \u57fa\u672c\u6982\u5ff5<\/a><ul><li><a href=\"#421\"><span class=\"toc_number toc_depth_2\">1.1<\/span> 4.2.1 \u590d\u6570<\/a><\/li><li><a href=\"#422\"><span class=\"toc_number toc_depth_2\">1.2<\/span> 4.2.2 \u5085\u91cc\u53f6\u7ea7\u6570<\/a><\/li><li><a href=\"#423\"><span class=\"toc_number toc_depth_2\">1.3<\/span> 4.2.3 \u51b2\u6fc0\u53ca\u5176\u53d6\u6837\u7279\u5f81<\/a><\/li><li><a href=\"#424\"><span class=\"toc_number toc_depth_2\">1.4<\/span> 4.2.4 \u8fde\u7eed\u53d8\u91cf\u51fd\u6570\u7684\u5085\u91cc\u53f6\u53d8\u6362<\/a><\/li><\/ul><\/li><li><a href=\"#43\"><span class=\"toc_number toc_depth_1\">2<\/span> 4.3 \u53d6\u6837\u548c\u53d6\u6837\u51fd\u6570\u7684\u5085\u91cc\u53f6\u53d8\u6362<\/a><ul><li><a href=\"#431\"><span class=\"toc_number toc_depth_2\">2.1<\/span> 4.3.1 \u53d6\u6837<\/a><\/li><li><a href=\"#432\"><span class=\"toc_number toc_depth_2\">2.2<\/span> 4.3.2 \u53d6\u6837\u51fd\u6570\u7684\u5085\u91cc\u53f6\u53d8\u6362<\/a><\/li><li><a href=\"#432-2\"><span class=\"toc_number toc_depth_2\">2.3<\/span> 4.3.2 \u53d6\u6837\u5b9a\u7406<\/a><\/li><li><a href=\"#434\"><span class=\"toc_number toc_depth_2\">2.4<\/span> 4.3.4 \u6df7\u6dc6<\/a><\/li><\/ul><\/li><\/ul><\/div>\n<h1><span id=\"42\">4.2 \u57fa\u672c\u6982\u5ff5<\/span><\/h1>\n<h2><span id=\"421\">4.2.1 \u590d\u6570<\/span><\/h2>\n<p>\u590d\u6570\u5b9a\u4e49\uff1a<\/p>\n<div class=\"katex math multi-line no-emojify\">C=R+jI \\tag{4.2-1}\n<\/div>\n<p>R\u548cI\u662f\u5b9e\u6570\uff0cj\u662f\u4e00\u4e2a\u7b49\u4e8e-1\u7684\u5e73\u65b9\u6839\u865a\u6570\uff0c\u5373<span class=\"katex math inline\">\\sqrt{-1}<\/span>.\u5b9e\u6570\u662fI=0\u7684\u590d\u6570\u7684\u5b50\u96c6\u3002\u4e00\u4e2a\u590d\u6570C\u7684\u5171\u8f6d\u8868\u793a\u4e3a<span class=\"katex math inline\">C^*<\/span>,\u5176\u5b9a\u4e49\u4e3a\uff1a<\/p>\n<div class=\"katex math multi-line no-emojify\">C^*=R-jI \\tag{4.2-2}\n<\/div>\n<p>\u6781\u5750\u6807\uff1a<\/p>\n<div class=\"katex math multi-line no-emojify\">C=|C|(cos\\theta+jsin\\theta) \\tag{4.2-3}\n<\/div>\n<p>\u5176\u4e2d\uff0c<span class=\"katex math inline\">|C|=\\sqrt{R^2+I^2}<\/span><br \/>\n\u6b27\u62c9\u516c\u5f0f\uff1a<\/p>\n<div class=\"katex math multi-line no-emojify\">e^{j\\theta}=cos\\theta+jsin\\theta \\tag{4.2-4}\n<\/div>\n<p>\u5176\u4e2d\uff0ce=2.71828&#8230;,\u6240\u4ee5<span class=\"katex math inline\">C=|C|e^{j\\theta}<\/span><\/p>\n<h2><span id=\"422\">4.2.2 \u5085\u91cc\u53f6\u7ea7\u6570<\/span><\/h2>\n<p>\u5177\u6709\u5468\u671fT\u7684\u8fde\u7eed\u53d8\u6362t\u7684\u5468\u671f\u51fd\u6570f(t)\u53ef\u4ee5\u88ab\u63cf\u8ff0\u4e3a\u4e58\u4ee5\u9002\u5f53\u7cfb\u6570\u7684\u6b63\u5f26\u548c\u4f59\u5f26\u548c\uff0c\u6211\u4eec\u77e5\u9053\uff0c\u8fd9\u4e2a\u548c\u5c31\u662f<strong>\u5085\u91cc\u53f6\u7ea7\u6570<\/strong>\uff0c\u5b83\u5177\u6709\u5982\u4e0b\u5f62\u5f0f\uff1a<\/p>\n<div class=\"katex math multi-line no-emojify\">f(t)=\\sum_{n=-\\infty}^{\\infty}c_ne^{j\\frac{2\\pi n}{T}t}\n<\/div>\n<p>\u5176\u4e2d\uff0c<\/p>\n<div class=\"katex math multi-line no-emojify\">c_n=\\frac{1}{T}\\int_{-T\/2}^{T\/2}f(t)e^{-j\\frac{2\\pi n}{T}t}dt,n=0,\u00b11\uff0c\u00b12&#8230;\u662f\u7cfb\u6570\n<\/div>\n<h2><span id=\"423\">4.2.3 \u51b2\u6fc0\u53ca\u5176\u53d6\u6837\u7279\u5f81<\/span><\/h2>\n<p>\u7ebf\u6027\u7cfb\u7edf\u548c\u5085\u91cc\u53f6\u53d8\u6362\u7814\u7a76\u7684\u6838\u5fc3\u662f\u51b2\u6fc0\u53ca\u5176\u53d6\u6837\u7279\u6027\u3002\u8fde\u7eed\u53d8\u91cft\u5728t=0\u5904\u7684\u5355\u4f4d\u51b2\u6fc0\u8868\u793a\u4e3a<span class=\"katex math inline\">\\delta(t)<\/span>,\u5176\u5b9a\u4e49\u4e3a\uff1a<\/p>\n<div class=\"katex math multi-line no-emojify\">\\delta(t)=\\begin{cases}\\infty ,&amp;t=0 \\\\ 0,&amp;t\\neq 0 \\end{cases} \\tag{4.2-8a}\n<\/div>\n<p>\u5b83\u8fd8\u88ab\u9650\u5236\u4e3a\u6ee1\u8db3\u7b49\u5f0f<\/p>\n<div class=\"katex math multi-line no-emojify\">\\int_{-\\infty}^{\\infty}\\delta(t)dt=1  \\tag{4.2-8b}\n<\/div>\n<p>\u7269\u7406\u4e0a\uff0c\u6211\u4eec\u628at\u89e3\u91ca\u4e3a\u65f6\u95f4\uff0c\u90a3\u4e48\u4e00\u4e2a\u51b2\u6fc0\u53ef\u770b\u6210\u5e45\u5ea6\u65e0\u9650\u3001\u6301\u7eed\u65f6\u95f4\u4e3a0\u3001\u5177\u6709\u5355\u4f4d\u9762\u79ef\u7684\u5c16\u5cf0\u4fe1\u53f7\u3002\u4e00\u4e2a\u51b2\u6fc0\u5177\u6709\u5982\u4e0b\u79ef\u5206\u7684\u6240\u8c13\u53d6\u6837\u7279\u6027\uff1a<\/p>\n<div class=\"katex math multi-line no-emojify\">\\int_{-\\infty}^{\\infty}f(t)\\delta(t)dt=f(0) \\tag{4.2-9}\n<\/div>\n<p>\u53d6\u6837\u7279\u6027\u7684\u4e00\u79cd\u66f4\u4e3a\u4e00\u822c\u7684\u8bf4\u660e\u6d89\u53ca\u4f4d\u4e8e\u4efb\u4e00\u70b9<span class=\"katex math inline\">t_0<\/span>\u7684\u51b2\u6fc0\uff0c\u8868\u793a\u4e3a<span class=\"katex math inline\">\\delta(t-t_0)<\/span>\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u53d6\u6837\u7279\u6027\u53d8\u4e3a\uff1a<\/p>\n<div class=\"katex math multi-line no-emojify\">\\int_{-\\infty}^{\\infty}f(t)\\delta(t-t_0)dt=f(t_0) \\tag{4.2-10}\n<\/div>\n<p>\u4ee4x\u8868\u793a\u4e00\u4e2a\u79bb\u6563\u53d8\u91cf\uff0c\u5355\u4f4d\u79bb\u6563\u51b2\u6fc0<span class=\"katex math inline\">\\delta(x)<\/span>\u5728\u79bb\u6563\u7cfb\u7edf\u4e2d\u7684\u4f5c\u7528\u4e0e\u5904\u7406\u53d8\u91cf\u65f6\u51b2\u6fc0<span class=\"katex math inline\">\\delta(t)<\/span>\u7684\u4f5c\u7528\u76f8\u540c\uff0c\u5176\u5b9a\u4e49\u5982\u4e0b\uff1a<\/p>\n<div class=\"katex math multi-line no-emojify\">\\delta(x)=\\begin{cases} 1,x=0 \\\\0,x \\neq 0\\end{cases} \\tag{4.2-11a}\n<\/div>\n<p>\u548c\u660e\u663e\uff0c\u8be5\u5b9a\u4e49\u4e5f\u6ee1\u8db3(4.2-8b)\u7684\u79bb\u6563\u7b49\u6548\u5f62\u5f0f\uff1a<\/p>\n<div class=\"katex math multi-line no-emojify\">\\sum_{x=-\\infty}^{\\infty}\\delta(x)=1 \\tag{4.2-11b}<\/p>\n<\/div>\n<p>\u79bb\u6563\u53d8\u91cf\u7684\u53d6\u6837\u7279\u6027\u6709\u5982\u4e0b\u5f62\u5f0f<\/p>\n<div class=\"katex math multi-line no-emojify\">\\sum_{-\\infty}^{\\infty}f(x)\\delta(t)=f(0) \\tag{4.2-12}\n<\/div>\n<p>\u66f4\u4e00\u822c\u7684\u5730\u7528\u4f4d\u7f6e<span class=\"katex math inline\">x=x_0<\/span>\u5904\u7684\u79bb\u6563\u51b2\u6fc0\uff0c<\/p>\n<div class=\"katex math multi-line no-emojify\">\\sum_{-\\infty}^{\\infty}f(x)\\delta(t)=f(x_0) \\tag{4.2-13}\n<\/div>\n<p>\u672c\u8282\u540e\u9762\u611f\u5174\u8da3\u7684\u662f\u51b2\u6fc0\u4e32<span class=\"katex math inline\">S_{\\Delta T}(t)<\/span>,\u5b83\u5b9a\u4e49\u4e3a\u65e0\u9650\u591a\u4e2a\u5206\u79bb\u7684\u5468\u671f\u51b2\u6fc0\u5355\u5143<span class=\"katex math inline\">\\Delta T<\/span>\u4e4b\u548c\uff1a<\/p>\n<div class=\"katex math multi-line no-emojify\">S_{\\Delta T}(t)=\\sum_{n=-\\infty}^{\\infty}\\delta(t-n\\Delta T) \\tag{4.2-14}\n<\/div>\n<h2><span id=\"424\">4.2.4 \u8fde\u7eed\u53d8\u91cf\u51fd\u6570\u7684\u5085\u91cc\u53f6\u53d8\u6362<\/span><\/h2>\n<p>\u4e3a\u4e86\u65b9\u4fbf\uff0c<span class=\"katex math inline\">f(t)<\/span>\u7684\u5085\u91cc\u53f6\u53d8\u6362\u53ef\u5199\u6210\uff1a<\/p>\n<div class=\"katex math multi-line no-emojify\">F(\\mu)=\\int_{-\\infty}^{\\infty}f(t)e^{-j2\\pi\\mu t}dt \\tag{4.2-16}\n<\/div>\n<p>\u76f8\u53cd\uff0c\u7ed9\u5b9a<span class=\"katex math inline\">F(\\mu)<\/span>,\u901a\u8fc7\u5085\u91cc\u53f6\u53cd\u53d8\u6362\u53ef\u4ee5\u83b7\u5f97<span class=\"katex math inline\">f(t)<\/span>\uff0c\u5373\uff1a<\/p>\n<div class=\"katex math multi-line no-emojify\">f(t)=\\int_{-\\infty}^{\\infty}F(\\mu)e^{j2\\pi \\mu t} d\\mu  \\tag{4.2-17}\n<\/div>\n<p>(4.2-16)\u548c\uff084.2-17\uff09\u5408\u8d77\u6765\u79f0\u4e3a\u5085\u91cc\u53f6\u53d8\u6362\u5bf9\u3002<\/p>\n<p>\u7528\u6b27\u62c9\u516c\u5f0f\uff0c\u6211\u4eec\u628a\u5f0f\uff084.2-16\uff09\u8868\u793a\u4e3a<\/p>\n<div class=\"katex math multi-line no-emojify\">F(\\mu)=\\int_{-\\infty}^{\\infty}f(t)[cos(2 \\pi \\mu t)-jsin(2 \\pi \\mu t)]dt\n<\/div>\n<p>\u6211\u4eec\u770b\u5230\uff0c\u5982\u679cf(t)\u662f\u5b9e\u6570\uff0c\u90a3\u4e48\u5176\u53d8\u6362\u901a\u5e38\u662f\u590d\u6570\uff0c\u6ce8\u610f\uff0c\u5085\u91cc\u53f6\u53d8\u6362\u662ff(t)\u4e58\u4ee5\u6b63\u5f26\u9879\u7684\u5c55\u5f00\uff0c\u6b63\u5f26\u9879\u7684\u9891\u7387\u6709<span class=\"katex math inline\">\\mu<\/span>\u7684\u503c\u51b3\u5b9a\uff08\u5982\u65e9\u4e9b\u65f6\u5019\u63d0\u5230\u8fc7\u7684\uff0c\u53d8\u91cft\u88ab\u79ef\u5206\u8fc7\u4e86\uff09\u3002\u56e0\u4e3a\u79ef\u5206\u540e\u5de6\u8fb9\u5269\u4e0b\u7684\u552f\u4e00\u53d8\u91cf\u662f\u9891\u7387\uff0c\u6545\u6211\u4eec\u8bf4\u5085\u91cc\u53f6\u53d8\u6362\u57df\u662f\u9891\u7387\u57df\u3002t\u53ef\u4ee5\u8868\u793a\u4efb\u4f55\u8fde\u7eed\u53d8\u91cf\uff0c\u9891\u7387\u53d8\u91cf<span class=\"katex math inline\">\\mu<\/span>\u7684\u5355\u4f4d\u53d6\u51b3\u4e8et\u7684\u5355\u4f4d\u3002\u4f8b\u5982\uff0c\u5982\u679ct\u8868\u793a\u5355\u4f4d\u4e3a\u79d2\u7684\u65f6\u95f4\uff0c\u5219<span class=\"katex math inline\">\\mu<\/span>\u7684\u5355\u4f4d\u4e3a\u5468\/\u79d2\uff0c\u6216\u8005\u8d6b\u5179\u3002\u5982\u679ct\u8868\u793a\u7684\u662f\u4ee5\u7c73\u4e3a\u5355\u4f4d\u7684\u8ddd\u79bb\uff0c\u5219<span class=\"katex math inline\">\\mu<\/span>\u7684\u5355\u4f4d\u662f\u5468\/\u7c73\u3002\u9891\u7387\u57df\u7684\u5355\u4f4d\u662f\u72ec\u7acb\u4e8e\u8f93\u5165\u53d8\u91cf\u7684\u6bcf\u5355\u4f4d\u5468\u671f\u7684\u3002<\/p>\n<p>\u901a\u5e38\uff0c\u5085\u91cc\u53f6\u53d8\u6362\u5305\u542b\u590d\u6570\u9879\uff0c\u4e14\u4e3a\u663e\u793a\u76ee\u7684\uff0c\u901a\u5e38\u5904\u7406\u8be5\u53d8\u91cf\u7684\u5e45\u503c\uff0c\u8be5\u5e45\u503c\u6210\u4e3a\u5085\u91cc\u53f6\u8c31\u6216\u8005\u9891\u8c31\uff1a<\/p>\n<div class=\"katex math multi-line no-emojify\">|F(\\mu)|=AW|\\frac{sin(\\pi \\mu W)}{\\pi\\mu W}|\n<\/div>\n<p>\u7a7a\u95f4\u57df\u4e2d\u4e24\u4e2a\u51fd\u6570\u7684\u5377\u79ef\u7684\u5085\u91cc\u53f6\u53d8\u6362\u7b49\u4e8e\u4e24\u4e2a\u51fd\u6570\u7684\u5085\u91cc\u53f6\u53d8\u5316\u7684\u9891\u7387\u57df\u4e2d\u7684\u4e58\u79ef\u3002\u9891\u7387\u57df\u7684\u5377\u79ef\u7c7b\u4f3c\u4e8e\u7a7a\u95f4\u57df\u7684\u4e58\u79ef\u3002<\/p>\n<h1><span id=\"43\">4.3 \u53d6\u6837\u548c\u53d6\u6837\u51fd\u6570\u7684\u5085\u91cc\u53f6\u53d8\u6362<\/span><\/h1>\n<h2><span id=\"431\">4.3.1 \u53d6\u6837<\/span><\/h2>\n<p>\u6a21\u62df\u53d6\u6837\u7684\u4e00\u79cd\u65b9\u6cd5\u662f\u7528\u4e00\u4e2a<span class=\"katex math inline\">\\Delta T<\/span>\u5355\u4f4d\u95f4\u9694\u7684\u51b2\u6fc0\u4e32\u4f5c\u4e3a\u53d6\u6837\u51fd\u6570\u53bb\u4e58\u4ee5f(t)\uff1a<\/p>\n<div class=\"katex math multi-line no-emojify\">\\tilde{f}(t)=f(t)s_{\\Delta T}(t)=\\sum_{n=-\\infty}^{\\infty}f(t)\\delta(t-n\\Delta T) \\tag{4.3-1}\n<\/div>\n<p>\u5176\u4e2d<span class=\"katex math inline\">\\tilde{f}(t)<\/span>\u8868\u793a\u53d6\u6837\u540e\u51fd\u6570.\u6bcf\u4e2a\u53d6\u6837\u503c\u7531\u52a0\u6743\u540e\u7684\u51b2\u6fc0\u201c\u5f3a\u5ea6\u201d\u7ed9\u51fa\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u79ef\u5206\u5f97\u5230\u4ed6\uff0c\u5e8f\u5217\u4e2d\u4efb\u610f\u53d6\u6837\u503c<span class=\"katex math inline\">f_k<\/span>\u7531\u4e0b\u5f0f\u7ed9\u51fa\uff1a<\/p>\n<div class=\"katex math multi-line no-emojify\">f_k=\\int_{-\\infty}^{\\infty}f(t)\\delta(t-k\\Delta T)dt=f(k\\Delta T) \\tag{4.3-2}\n<\/div>\n<h2><span id=\"432\">4.3.2 \u53d6\u6837\u51fd\u6570\u7684\u5085\u91cc\u53f6\u53d8\u6362<\/span><\/h2>\n<p>\u4ee4<span class=\"katex math inline\">F(\\mu)<\/span>\u4ee3\u8868\u8fde\u7eed\u51fd\u6570<span class=\"katex math inline\">f(t)<\/span>\u7684\u5085\u91cc\u53f6\u53d8\u6362\u3002\u53d6\u6837\u540e\u7684\u76f8\u5e94\u51fd\u6570<span class=\"katex math inline\">\\tilde{f}(t)<\/span>\u662f<span class=\"katex math inline\">f(t)<\/span>\u4e0e\u4e00\u4e2a\u51b2\u6fc0\u4e32\u7684\u4e58\u79ef\u3002<\/p>\n<h2><span id=\"432-2\">4.3.2 \u53d6\u6837\u5b9a\u7406<\/span><\/h2>\n<p>\u5982\u679c\u4ee5\u8d85\u8fc7\u51fd\u6570\u6700\u9ad8\u9891\u7387\u7684\u4e24\u500d\u7684\u53d6\u6837\u7387\u6765\u83b7\u5f97\u6837\u672c\uff0c\u8fde\u7eed\u7684\u5e26\u9699\u51fd\u6570\u53ef\u4ee5\u5b8c\u5168\u5730\u4ece\u5b83\u7684\u6837\u672c\u96c6\u6765\u6062\u590d\u3002\u8fd9\u4e2a\u7ed3\u8bba\u5c31\u662f\u4f17\u6240\u5468\u77e5\u7684\u53d6\u6837\u5b9a\u7406\u3002<\/p>\n<h2><span id=\"434\">4.3.4 \u6df7\u6dc6<\/span><\/h2>\n","protected":false},"excerpt":{"rendered":"<p>Contents1 4.2 \u57fa\u672c\u6982\u5ff51.1 4.2.1 \u590d\u65701.2 4.2.2 \u5085\u91cc\u53f6\u7ea7\u65701.3 4.2.3  [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[43,17],"tags":[],"class_list":["post-977","post","type-post","status-publish","format-standard","hentry","category-43","category-17"],"_links":{"self":[{"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts\/977","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=977"}],"version-history":[{"count":7,"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts\/977\/revisions"}],"predecessor-version":[{"id":984,"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts\/977\/revisions\/984"}],"wp:attachment":[{"href":"https:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=977"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=977"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=977"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}