{"id":479,"date":"2026-07-06T12:15:28","date_gmt":"2026-07-06T04:15:28","guid":{"rendered":"http:\/\/www.millscience.cn\/?p=479"},"modified":"2026-07-06T12:16:27","modified_gmt":"2026-07-06T04:16:27","slug":"dsjfkla","status":"publish","type":"post","link":"https:\/\/www.millscience.cn\/index.php\/dsjfkla\/","title":{"rendered":"1122"},"content":{"rendered":"\n<h1 class=\"wp-block-heading\">\u5176\u4ed6<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">\u5224\u65ad\u7ebf\u6027\u65f6\u4e0d\u53d8\u7cfb\u7edf<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\u4f8b\u9898 2\uff1a\u4ec0\u4e48\u6837\u7684\u624d\u662f\u771f\u6b63\u7684 LTI \u7cfb\u7edf\uff1f<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e3a\u4e86\u5bf9\u6bd4\uff0c\u6211\u4eec\u770b\u4e00\u4e2a\u6700\u7b80\u5355\u7684\u7eaf LTI \u7cfb\u7edf\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">y(n)=2x(n-1)<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u5224\u65ad\u7ebf\u6027<\/strong>\uff1a\u5148\u7ec4\u5408\u518d\u8fc7\u7cfb\u7edf\uff1ay_3(n)=2[ax_1(n-1)+bx_2(n-1)]\u5148\u8fc7\u7cfb\u7edf\u518d\u7ec4\u5408\uff1ay_4(n)=a[2x_1(n-1)]+b[2x_2(n-1)]\u663e\u7136y_3(n)=y_4(n)\uff0c\u662f<strong>\u7ebf\u6027<\/strong>\u7684\u3002<\/li>\n\n\n\n<li><strong>\u5224\u65ad\u65f6\u4e0d\u53d8\u6027<\/strong>\uff1a\u5148\u5ef6\u65f6\u518d\u8fc7\u7cfb\u7edf\uff08\u8f93\u5165\u53d8 x(n-k)\uff09\uff1a\u628a\u7cfb\u7edf\u91cc\u7684 x(\\cdot) \u91cc\u9762\u66ff\u6362\u6389\uff0c\u5916\u9762\u4e0d\u53d8\uff1ay_A(n)=2x((n-1)-k)=2x(n-k-1)\u5148\u8fc7\u7cfb\u7edf\u518d\u6574\u4f53\u5ef6\u65f6\uff08\u6240\u6709 n \u6362\u6210 n-k\uff09\uff1ay_B(n)=2x((n-k)-1)=2x(n-k-1)\u663e\u7136y_A(n)=y_B(n)\uff0c\u662f<strong>\u65f6\u4e0d\u53d8<\/strong>\u7684\u3002<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u4f8b\u9898 2 \u7ed3\u8bba<\/strong>\uff1a\u540c\u65f6\u6ee1\u8db3\uff0c\u6240\u4ee5\u662f\u7eaf\u6b63\u7684 LTI \u7cfb\u7edf\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u505a\u8fd9\u7c7b\u9898\uff0c\u6700\u5bb9\u6613\u7ffb\u8f66\u7684\u5730\u65b9\u5c31\u662f<strong>\u65f6\u4e0d\u53d8\u6027<\/strong>\u7684\u5224\u65ad\uff0c\u53ea\u8981\u7262\u8bb0\u201c<strong>\u66ff\u6362\u8c01<\/strong>\u201d\u7684\u533a\u522b\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u5148\u5ef6\u65f6\u540e\u8fc7\u7cfb\u7edf<\/strong>\uff1a\u53ea\u66ff\u6362 x() \u62ec\u53f7\u91cc\u9762\u7684\u53d8\u91cf\u3002<\/li>\n\n\n\n<li><strong>\u5148\u8fc7\u7cfb\u7edf\u540e\u5ef6\u65f6<\/strong>\uff1a\u7cfb\u7edf\u8868\u8fbe\u5f0f\u91cc<strong>\u6240\u6709<\/strong>\u51fa\u73b0 n \u7684\u5730\u65b9\uff0c\u5168\u90fd\u8981\u66ff\u6362\u6210 n-k\u3002<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">\u6c42\u4e00\u4e2a\u79bb\u6563\u65f6\u95f4\u5e8f\u5217\u7684\u5468\u671f<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\u4f8b\u9898 1-2 \u9010\u9898\u89e3\u6790<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">(1) f_1(k)=\\sin(\\frac{\\pi}{7}k+\\frac{\\pi}{6})<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u63d0\u53d6\u89d2\u9891\u7387<\/strong>\uff1a\u89c2\u5bdf\u81ea\u53d8\u91cf k \u524d\u9762\u7684\u7cfb\u6570\uff0c\u5f97\u51fa \\omega_0 = \\frac{\\pi}{7}\u3002<\/li>\n\n\n\n<li><strong>\u8ba1\u7b97\u6bd4\u503c<\/strong>\uff1a\\frac{2\\pi}{\\omega_0}=\\frac{2\\pi}{\\frac{\\pi}{7}}=14<\/li>\n\n\n\n<li><strong>\u7ed3\u8bba<\/strong>\uff1a\u56e0\u4e3a 14 \u662f\u4e00\u4e2a<strong>\u6574\u6570<\/strong>\uff08\u5bf9\u5e94\u7b2c\u4e00\u79cd\u60c5\u51b5\uff09\uff0c\u6240\u4ee5\u8be5\u5e8f\u5217\u662f\u5468\u671f\u5e8f\u5217\uff0c\u4e14\u6700\u5c0f\u6b63\u5468\u671f N_1 = 14\u3002<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">(2) f_2(k)=\\cos(\\frac{5\\pi}{6}k+\\frac{\\pi}{12})<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u63d0\u53d6\u89d2\u9891\u7387<\/strong>\uff1a\u5f97\u51fa \\omega_0 = \\frac{5\\pi}{6}\u3002<\/li>\n\n\n\n<li><strong>\u8ba1\u7b97\u6bd4\u503c<\/strong>\uff1a\\frac{2\\pi}{\\omega_0}=\\frac{2\\pi}{\\frac{5\\pi}{6}}=\\frac{12}{5}<\/li>\n\n\n\n<li><strong>\u7ed3\u8bba<\/strong>\uff1a\u56e0\u4e3a \\frac{12}{5} \u662f\u4e00\u4e2a<strong>\u6709\u7406\u5206\u6570<\/strong>\uff08\u5bf9\u5e94\u7b2c\u4e8c\u79cd\u60c5\u51b5\uff09\u3002\u4e3a\u4e86\u8ba9\u5468\u671f N \u6210\u4e3a\u4e00\u4e2a\u6574\u6570\uff0c\u6211\u4eec\u9700\u8981\u7ed9\u8fd9\u4e2a\u5206\u6570\u4e58\u4ee5\u4e00\u4e2a\u6700\u5c0f\u7684\u6574\u6570\uff08\u8fd9\u91cc\u662f\u5206\u6bcd 5\uff09\u6765\u628a\u5206\u6bcd\u6d88\u6389\u3002\u6240\u4ee5 N = \\frac{12}{5} \\times 5 = 12\u3002\u8be5\u5e8f\u5217\u662f\u5468\u671f\u5e8f\u5217\uff0c\u6700\u5c0f\u6b63\u5468\u671f N_2 = 12\u3002<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">(3) f_3(k)=\\cos(\\frac{1}{5}k+\\frac{\\pi}{3})<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u63d0\u53d6\u89d2\u9891\u7387<\/strong>\uff1a\u5f97\u51fa \\omega_0 = \\frac{1}{5}\u3002<\/li>\n\n\n\n<li><strong>\u8ba1\u7b97\u6bd4\u503c<\/strong>\uff1a\\frac{2\\pi}{\\omega_0}=\\frac{2\\pi}{\\frac{1}{5}}=10\\pi<\/li>\n\n\n\n<li><strong>\u7ed3\u8bba<\/strong>\uff1a\u56e0\u4e3a\u7ed3\u679c\u4e2d\u5305\u542b \\pi\uff0c\u6240\u4ee5 10\\pi \u662f\u4e00\u4e2a<strong>\u65e0\u7406\u6570<\/strong>\uff08\u5bf9\u5e94\u7b2c\u4e09\u79cd\u60c5\u51b5\uff09\u3002\u65e0\u8bba\u4f60\u4e58\u4ee5\u4ec0\u4e48\u6574\u6570\uff0c\u90fd\u65e0\u6cd5\u8ba9\u5b83\u53d8\u6210\u4e00\u4e2a\u6574\u6570\u5468\u671f\u3002\u56e0\u6b64\uff0c\u8be5\u5e8f\u5217<strong>\u4e0d\u662f\u5468\u671f\u5e8f\u5217<\/strong>\u3002<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u5982\u679c\u628a\u4e24\u4e2a\u4e0d\u540c\u5468\u671f\u7684\u5468\u671f\u5e8f\u5217\u76f8\u52a0\uff08\u6bd4\u5982 f_1(k) + f_2(k)\uff09\uff0c\u4f60\u6e05\u695a\u600e\u4e48\u6c42\u5b83\u4eec\u76f8\u52a0\u540e\u5f62\u6210\u7684\u65b0\u5e8f\u5217\u7684\u603b\u5468\u671f\u5417\uff1f<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">DFT\u7684\u8ba1\u7b97<\/h2>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.millscience.cn\/wp-content\/uploads\/2026\/07\/image-20260705180954623.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.millscience.cn\/wp-content\/uploads\/2026\/07\/image-20260705180954623.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"image-20260705180954623\"\/><\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u5f20\u56fe\u91cc\u7684\u8ba1\u7b97\u8fc7\u7a0b\u770b\u8d77\u6765\u5bc6\u5bc6\u9ebb\u9ebb\uff0c\u5168\u662f\u4e00\u5927\u4e32\u590d\u6742\u7684\u590d\u6307\u6570 e^{-j\\dots}\uff0c\u786e\u5b9e\u5f88\u5bb9\u6613\u8ba9\u4eba\u773c\u6655\u3002\u4f46\u8fd9\u5176\u5b9e\u662f\u4e00\u53ea\u201c\u7eb8\u8001\u864e\u201d\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u662f\u5728\u8ba1\u7b97 <strong>4 \u70b9\u79bb\u6563\u5085\u91cc\u53f6\u53d8\u6362 (DFT)<\/strong>\u3002\u4e66\u4e0a\u4e3a\u4e86\u5c55\u793a\u5b8c\u6574\u7684\u7406\u8bba\u63a8\u5bfc\uff0c\u628a\u516c\u5f0f\u5199\u6210\u4e86\u6700\u539f\u59cb\u3001\u6700\u7e41\u7410\u7684\u5f62\u5f0f\u3002\u53ea\u8981\u5f15\u5165\u4e00\u4e2a\u201c\u5316\u7b80\u795e\u5668\u201d\u2014\u2014<strong>\u65cb\u8f6c\u56e0\u5b50 W_N<\/strong>\uff0c\u8fd9\u4e2a\u8ba1\u7b97\u5c31\u4f1a\u53d8\u6210\u975e\u5e38\u7b80\u5355\u7684\u5c0f\u5b66\u52a0\u51cf\u6cd5\u548c\u57fa\u7840\u7684\u590d\u6570\u4e58\u6cd5\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e0b\u9762\u6211\u5e2e\u4f60\u628a\u8fd9\u4e00\u5927\u5768\u516c\u5f0f\u201c\u89e3\u538b\u7f29\u201d\uff0c\u6559\u4f60\u5982\u4f55\u7528\u6700\u5feb\u3001\u6700\u6e05\u6670\u7684\u65b9\u6cd5\u7b97\u51fa\u6765\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u4e00\u3001 \u7834\u89e3\u590d\u6742\u516c\u5f0f\u7684\u201c\u6838\u5fc3\u5bc6\u7801\u201d<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">DFT \u7684\u6807\u51c6\u8ba1\u7b97\u516c\u5f0f\u662f\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">X(k)=\\sum_{n=0}^{N-1}x(n)e^{-j\\frac{2\\pi}{N}nk}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u91cc\u9762\u6700\u5413\u4eba\u7684\u5c31\u662f\u90a3\u4e2a e \u7684\u6307\u6570\u90e8\u5206\u3002\u5728\u4fe1\u53f7\u5904\u7406\u4e2d\uff0c\u6211\u4eec\u7edf\u4e00\u5b9a\u4e49\u4e00\u4e2a\u7b26\u53f7\u53eb<strong>\u65cb\u8f6c\u56e0\u5b50 W_N<\/strong>\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">W_N=e^{-j\\frac{2\\pi}{N}}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u56e0\u4e3a\u8fd9\u9053\u9898\u662f <strong>4 \u70b9 DFT<\/strong>\uff0c\u6240\u4ee5 N=4\u3002\u6211\u4eec\u6765\u7b97\u4e00\u4e0b W_4 \u5230\u5e95\u662f\u4e2a\u4ec0\u4e48\u4e1c\u897f\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">W_4=e^{-j\\frac{2\\pi}{4}}=e^{-j\\frac{\\pi}{2}}=\\cos(\\frac{\\pi}{2})-j\\sin(\\frac{\\pi}{2})=-j<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u8bb0\u4f4f\u8fd9\u4e2a\u7ed3\u8bba\uff1a\u5728 4 \u70b9 DFT \u4e2d\uff0cW_4 \u7684\u672c\u8d28\u5c31\u662f\u4e00\u4e2a\u7b80\u5355\u7684 -j\u3002<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u57fa\u4e8e\u8fd9\u4e2a\u7ed3\u8bba\uff0c\u4e66\u4e0a\u90a3\u4e9b\u6781\u5176\u590d\u6742\u7684\u6307\u6570\u9879\uff0c\u5176\u5b9e\u53ea\u6709\u56db\u79cd\u7b80\u5355\u7684\u7ed3\u679c\uff0c\u5b83\u4eec\u662f\u5faa\u73af\u7684\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>W_4^0=1<\/li>\n\n\n\n<li>W_4^1=-j<\/li>\n\n\n\n<li>W_4^2=(-j)^2=-1<\/li>\n\n\n\n<li>W_4^3=(-j)^3=j<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u4e8c\u3001 \u7528\u5316\u7b80\u540e\u7684\u65b9\u6cd5\u91cd\u65b0\u8ba1\u7b97<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u73b0\u5728\uff0c\u6211\u4eec\u628a\u9898\u76ee\u7684\u5df2\u77e5\u6761\u4ef6\u5199\u4e0b\u6765\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8f93\u5165\u5e8f\u5217\uff1ax(0)=1+j,\\; x(1)=1-2j,\\; x(2)=1,\\; x(3)=-j<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u516c\u5f0f\u5316\u7b80\u4e3a\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">X(k)=\\sum_{n=0}^{3}x(n)W_4^{nk}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6211\u4eec\u9010\u4e2a\u6765\u770b\u4e66\u4e0a\u7684\u56db\u4e2a\u7ed3\u679c\u662f\u600e\u4e48\u7b97\u51fa\u6765\u7684\uff1a<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">1. \u8ba1\u7b97 X(0) \uff08\u6700\u7b80\u5355\u7684\u4e00\u9879\uff09<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">\u5f53 k=0 \u65f6\uff0c\u516c\u5f0f\u91cc\u7684 W_4^{n\\cdot 0} \u5168\u90e8\u53d8\u6210 W_4^0=1\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e5f\u5c31\u662f\u8bf4\uff0cX(0) <strong>\u5c31\u662f\u628a\u65f6\u57df\u7684\u56db\u4e2a\u6570\u5b57\u76f4\u63a5\u52a0\u8d77\u6765<\/strong>\uff0c\u6839\u672c\u4e0d\u7528\u4e58\u6307\u6570\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">X(0)=x(0)+x(1)+x(2)+x(3)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">X(0)=(1+j)+(1-2j)+1+(-j)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5408\u5e76\u5b9e\u90e8\u548c\u865a\u90e8\uff1a\u5b9e\u90e8 1+1+1=3\uff0c\u865a\u90e8 j-2j-j=-2j\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u7ed3\u679c\uff1a<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">X(0)=3-2j<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">2. \u8ba1\u7b97 X(1) \uff08\u4ed4\u7ec6\u770b\u590d\u6570\u4e58\u6cd5\uff09<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">\u5f53 k=1 \u65f6\uff0c\u6307\u6570\u9879\u7684\u89c4\u5f8b\u662f n\\cdot 1\uff0c\u5373 W_4^0, W_4^1, W_4^2, W_4^3\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5bf9\u5e94\u7684\u503c\u5206\u522b\u662f 1, -j, -1, j\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">X(1)=x(0)\\cdot(1)+x(1)\\cdot(-j)+x(2)\\cdot(-1)+x(3)\\cdot(j)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4ee3\u5165\u6570\u503c\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">X(1)=(1+j)\\cdot 1+(1-2j)\\cdot(-j)+1\\cdot(-1)+(-j)\\cdot j<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5c55\u5f00\u590d\u6570\uff08\u7262\u8bb0 j^2 = -1\uff09\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(1+j)\\cdot 1 = 1+j<\/li>\n\n\n\n<li>(1-2j)\\cdot(-j) = -j+2j^2 = -2-j<\/li>\n\n\n\n<li>1\\cdot(-1) = -1<\/li>\n\n\n\n<li>(-j)\\cdot j = -j^2 = 1<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u52a0\u5728\u4e00\u8d77\uff1a1+j-2-j-1+1<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u7ed3\u679c\uff1a<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">X(1)=-1<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">3. \u8ba1\u7b97 X(2)<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">\u5f53 k=2 \u65f6\uff0c\u6307\u6570\u9879\u89c4\u5f8b\u662f W_4^0, W_4^2, W_4^4, W_4^6\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5229\u7528\u5468\u671f\u6027\u5316\u7b80\uff08W_4^4=W_4^0=1\uff09\uff0c\u5bf9\u5e94\u7684\u503c\u53d8\u6210\u4e86\u4ea4\u66ff\u7684 1, -1, 1, -1\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">X(2)=x(0)\\cdot(1)+x(1)\\cdot(-1)+x(2)\\cdot(1)+x(3)\\cdot(-1)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4ee3\u5165\u6570\u503c\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">X(2)=(1+j)-(1-2j)+1-(-j)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">X(2)=1+j-1+2j+1+j<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u7ed3\u679c\uff1a<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">X(2)=1+4j<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">4. \u8ba1\u7b97 X(3)<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">\u5f53 k=3 \u65f6\uff0c\u6307\u6570\u9879\u89c4\u5f8b\u662f W_4^0, W_4^3, W_4^6, W_4^9\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5316\u7b80\u540e\u5bf9\u5e94\u7684\u503c\u662f 1, j, -1, -j\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">X(3)=x(0)\\cdot(1)+x(1)\\cdot(j)+x(2)\\cdot(-1)+x(3)\\cdot(-j)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4ee3\u5165\u6570\u503c\u5c55\u5f00\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">X(3)=(1+j)\\cdot 1+(1-2j)\\cdot j+1\\cdot(-1)+(-j)\\cdot(-j)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">X(3)=1+j+j-2j^2-1+j^2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">X(3)=1+j+j+2-1-1<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u7ed3\u679c\uff1a<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">X(3)=1+2j<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u603b\u7ed3<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e0b\u6b21\u5728\u8003\u8bd5\u6216\u505a\u9898\u9047\u5230\u8fd9\u79cd\u7b97 DFT \u7684\u9898\u76ee\uff0c<strong>\u5343\u4e07\u4e0d\u8981\u50cf\u4e66\u4e0a\u90a3\u6837\u53bb\u6284\u957f\u4e32\u7684 e^{-j\\dots}<\/strong>\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u76f4\u63a5\u5728\u8349\u7a3f\u7eb8\u4e0a\u5217\u51fa W_N \u7684\u51e0\u4e2a\u57fa\u672c\u503c\uff08\u901a\u5e38\u8003 4 \u70b9\u6216 8 \u70b9\uff09\uff0c\u7136\u540e\u76f4\u63a5\u628a\u5b83\u4eec\u5f53\u4f5c\u5e38\u6570\u4ee3\u5165\u5230\u4e58\u6cd5\u91cc\uff0c\u8fc7\u7a0b\u4f1a\u6e05\u6670\u4e14\u4e0d\u6613\u51fa\u9519\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u5706\u5468\u5706\u73af\u79fb\u4f4d<\/h2>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.millscience.cn\/wp-content\/uploads\/2026\/07\/image-20260705181233532.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.millscience.cn\/wp-content\/uploads\/2026\/07\/image-20260705181233532.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"image-20260705181233532\"\/><\/div><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">\u7b2c\u4e00\u6b65\uff1a\u7834\u89e3\u9898\u76ee\u7684\u201c\u9ed1\u8bdd\u201d<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u5728\u52a8\u624b\u7b97\u4e4b\u524d\uff0c\u6211\u4eec\u5148\u641e\u61c2\u9898\u76ee\u91cc\u8fd9\u4e9b\u7b26\u53f7\u5230\u5e95\u5728\u8bf4\u5565\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>x(n)=\\{1,2,3,4\\}<\/strong>\uff1a\u6570\u5b57 1 \u4e0b\u9762\u6709\u4e0b\u5212\u7ebf\uff0c\u610f\u601d\u662f\u5f53 n=0 \u65f6\uff0c\u503c\u4e3a 1\u3002\u539f\u6765\u7684\u5e8f\u5217\u53ea\u6709 4 \u4e2a\u6570\u3002<\/li>\n\n\n\n<li><strong>R_8(n)<\/strong>\uff1a\u8fd9\u4e2a\u53eb\u201c\u77e9\u5f62\u7a97\u201d\u3002\u4f60\u4e0d\u7528\u7ba1\u5b83\u590d\u6742\u7684\u5b9a\u4e49\uff0c\u5b83\u5728\u8fd9\u91cc\u7684\u610f\u601d\u4ec5\u4ec5\u662f\uff1a<strong>\u6211\u4eec\u7684\u7ed3\u679c\u53ea\u8981 n=0 \u5230 7 \u8fd9 8 \u4e2a\u6570\uff0c\u591a\u4f59\u7684\u4e0d\u8981\u3002<\/strong><\/li>\n\n\n\n<li><strong>((\\dots))_8<\/strong>\uff1a\u8fd9\u5c31\u662f\u6838\u5fc3\uff01\u5b83\u4ee3\u8868<strong>8\u70b9\u5faa\u73af\u79fb\u4f4d<\/strong>\uff08\u5bf9 8 \u53d6\u6a21\/\u6c42\u4f59\u6570\uff09\u3002<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u65e2\u7136\u8981\u5728 8 \u7684\u4e16\u754c\u91cc\u73a9\uff0c\u539f\u6765\u7684 x(n) \u53ea\u6709 4 \u4e2a\u6570\u4e0d\u591f\u600e\u4e48\u529e\uff1f<strong>\u672b\u5c3e\u8865 0 \u8865\u9f50 8 \u4e2a\uff01<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6240\u4ee5\uff0c\u6211\u4eec\u771f\u6b63\u8981\u64cd\u4f5c\u7684\u57fa\u7840\u5e8f\u5217\u5176\u5b9e\u662f\u8fd9\u6837\u7684\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">x(n) = \\{1, 2, 3, 4, 0, 0, 0, 0\\}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>(\u5bf9\u5e94\u4f4d\u7f6e\u5206\u522b\u662f n=0, 1, 2, 3, 4, 5, 6, 7)<\/em><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u7b2c\u4e8c\u6b65\uff1a\u9010\u4e2a\u51fb\u7834<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u505a\u5faa\u73af\u79fb\u4f4d\uff0c\u5c31\u628a\u8fd9 8 \u4e2a\u6570\u60f3\u8c61\u6210\u4e00\u4e2a\u9996\u5c3e\u76f8\u8fde\u7684\u5706\u73af\u3002\u79fb\u51fa\u53bb\u7684\u6570\uff0c\u4f1a\u50cf\u8d2a\u5403\u86c7\u7a7f\u5899\u4e00\u6837\u4ece\u53e6\u4e00\u8fb9\u94bb\u56de\u6765\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">1. x((n+2))_8 R_8(n)<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u542b\u4e49<\/strong>\uff1a+2 \u8868\u793a\u628a\u5e8f\u5217\u6574\u4f53\u5411<strong>\u5de6<\/strong>\u79fb\u52a8 2 \u683c\u3002<\/li>\n\n\n\n<li><strong>\u64cd\u4f5c<\/strong>\uff1a\u6700\u5de6\u8fb9\u7684 1 \u548c 2 \u88ab\u6324\u51fa\u53bb\u4e86\uff0c\u5b83\u4eec\u7ed5\u4e00\u5708\u4ece\u6700\u53f3\u8fb9\u8865\u8fdb\u6765\u3002<\/li>\n\n\n\n<li><strong>\u7ed3\u679c<\/strong>\uff1a\\{3, 4, 0, 0, 0, 0, 1, 2\\}<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">2. x((n-2))_8 R_8(n)<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u542b\u4e49<\/strong>\uff1a-2 \u8868\u793a\u628a\u5e8f\u5217\u6574\u4f53\u5411<strong>\u53f3<\/strong>\u79fb\u52a8 2 \u683c\u3002<\/li>\n\n\n\n<li><strong>\u64cd\u4f5c<\/strong>\uff1a\u6700\u53f3\u8fb9\u7684\u4e24\u4e2a 0 \u88ab\u6324\u51fa\u53bb\u4e86\uff0c\u7ed5\u4e00\u5708\u8865\u5230\u6700\u5de6\u8fb9\u3002<\/li>\n\n\n\n<li><strong>\u7ed3\u679c<\/strong>\uff1a\\{0, 0, 1, 2, 3, 4, 0, 0\\}<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">3. x((-n+2))_8 R_8(n)<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u542b\u4e49<\/strong>\uff1a\u4e00\u770b\u5230 -n\uff0c\u60c5\u51b5\u5c31\u7a0d\u5fae\u590d\u6742\u70b9\uff0c\u8fd9\u5305\u542b\u4e86<strong>\u65f6\u95f4\u7ffb\u8f6c<\/strong>\u3002\u505a\u8fd9\u79cd\u9898\uff0c\u6700\u7a33\u59a5\u7684\u529e\u6cd5\u5c31\u662f<strong>\u76f4\u63a5\u4ee3\u5165 n \u7b97\u5bf9\u5e94\u7684\u503c<\/strong>\uff0c\u53ea\u8981\u8bb0\u4f4f\u201c\u5bf9 8 \u6c42\u4f59\u6570\u201d\u5c31\u884c\u3002<\/li>\n\n\n\n<li><strong>\u64cd\u4f5c<\/strong>\uff08\u8ba9 n \u4ece 0 \u53d6\u5230 7\uff09\uff1a\n<ul class=\"wp-block-list\">\n<li>n=0\uff1a\u6c42 x(2) = 3<\/li>\n\n\n\n<li>n=1\uff1a\u6c42 x(1) = 2<\/li>\n\n\n\n<li>n=2\uff1a\u6c42 x(0) = 1<\/li>\n\n\n\n<li>n=3\uff1a\u6c42 x(-1)\uff0c\u5728 8 \u70b9\u5faa\u73af\u91cc\uff0c-1 \u7b49\u540c\u4e8e 7\uff08\u56e0\u4e3a -1+8=7\uff09\uff0c\u6240\u4ee5\u662f x(7) = 0<\/li>\n\n\n\n<li>n=4\uff1a\u6c42 x(-2)\uff0c\u5bf9\u5e94 x(6) = 0<\/li>\n\n\n\n<li>n=5\uff1a\u6c42 x(-3)\uff0c\u5bf9\u5e94 x(5) = 0<\/li>\n\n\n\n<li>n=6\uff1a\u6c42 x(-4)\uff0c\u5bf9\u5e94 x(4) = 0<\/li>\n\n\n\n<li>n=7\uff1a\u6c42 x(-5)\uff0c\u5bf9\u5e94 x(3) = 4<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u7ed3\u679c<\/strong>\uff1a\\{3, 2, 1, 0, 0, 0, 0, 4\\}<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">4. x((-n-2))_8 R_8(n)<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u542b\u4e49<\/strong>\uff1a\u540c\u6837\u7684\u65b9\u6cd5\uff0c\u5e26\u5165 n \u7b97\u7d22\u5f15\uff0c\u8d1f\u6570\u5c31\u52a0\u4e0a 8 \u627e\u5bf9\u5e94\u7684\u6b63\u6570\u4f4d\u7f6e\u3002<\/li>\n\n\n\n<li><strong>\u64cd\u4f5c<\/strong>\uff1a\n<ul class=\"wp-block-list\">\n<li>n=0\uff1a\u6c42 x(-2)\uff0c\u5373 x(6) = 0<\/li>\n\n\n\n<li>n=1\uff1a\u6c42 x(-3)\uff0c\u5373 x(5) = 0<\/li>\n\n\n\n<li>n=2\uff1a\u6c42 x(-4)\uff0c\u5373 x(4) = 0<\/li>\n\n\n\n<li>n=3\uff1a\u6c42 x(-5)\uff0c\u5373 x(3) = 4<\/li>\n\n\n\n<li>n=4\uff1a\u6c42 x(-6)\uff0c\u5373 x(2) = 3<\/li>\n\n\n\n<li>n=5\uff1a\u6c42 x(-7)\uff0c\u5373 x(1) = 2<\/li>\n\n\n\n<li>n=6\uff1a\u6c42 x(-8)\uff0c\u5373 x(0) = 1<\/li>\n\n\n\n<li>n=7\uff1a\u6c42 x(-9)\uff0c-9 \u52a0\u4e24\u4e2a 8 \u7b49\u4e8e 7\uff0c\u5373 x(7) = 0<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u7ed3\u679c<\/strong>\uff1a\\{0, 0, 0, 4, 3, 2, 1, 0\\}<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u6700\u7ec8\u586b\u7a7a\u7b54\u6848\u603b\u7ed3\uff1a<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\\{3, 4, 0, 0, 0, 0, 1, 2\\}<\/li>\n\n\n\n<li>\\{0, 0, 1, 2, 3, 4, 0, 0\\}<\/li>\n\n\n\n<li>\\{3, 2, 1, 0, 0, 0, 0, 4\\}<\/li>\n\n\n\n<li>\\{0, 0, 0, 4, 3, 2, 1, 0\\}<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\">\u8776\u5f62\u8fd0\u7b97<\/h2>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.millscience.cn\/wp-content\/uploads\/2026\/07\/image-20260705183349925.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.millscience.cn\/wp-content\/uploads\/2026\/07\/image-20260705183349925.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\"\/><\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u6ca1\u9519\uff0c\u8fd9\u6b63\u662f\u6570\u5b57\u4fe1\u53f7\u5904\u7406\u4e2d\u6700\u8457\u540d\u7684<strong>\u8776\u5f62\u8fd0\u7b97\uff08Butterfly Operation\uff09<\/strong>\uff01<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5177\u4f53\u6765\u8bf4\uff0c\u8fd9\u5f20\u56fe\u5c55\u793a\u7684\u662f\u4e00\u4e2a <strong>4 \u70b9\u57fa-2 \u9891\u7387\u62bd\u53d6\uff08DIF\uff09\u5feb\u901f\u5085\u91cc\u53f6\u53d8\u6362\uff08FFT\uff09<\/strong> \u7684\u4fe1\u53f7\u6d41\u56fe\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e0d\u7528\u89c9\u5f97\u5b83\u770b\u8d77\u6765\u50cf\u6bdb\u7ebf\u56e2\u4e00\u6837\u4e71\uff0c\u53ea\u8981\u638c\u63e1\u4e86\u5b83\u201c\u770b\u56fe\u8bf4\u8bdd\u201d\u7684\u4e24\u4e2a\u57fa\u672c\u89c4\u5219\uff0c\u7b97\u8d77\u6765\u6bd4\u4f20\u7edf\u7684\u7eaf\u4ee3\u6570\u516c\u5f0f\u7b80\u5355\u5f97\u591a\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83e\udd8b \u8776\u5f62\u56fe\u7684\u201c\u770b\u56fe\u89c4\u5219\u201d<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u5728\u770b\u61c2\u6574\u5f20\u56fe\u4e4b\u524d\uff0c\u6211\u4eec\u5148\u5355\u72ec\u62a0\u51fa\u4e00\u4e2a\u201c\u8774\u8776\u201d\u7684\u4ea4\u53c9\u70b9\u3002\u6bcf\u4e00\u4e2a\u57fa\u7840\u7684\u8776\u5f62\u8fd0\u7b97\u90fd\u9075\u5faa\u4ee5\u4e0b\u89c4\u5219\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u4e0a\u534a\u652f\u8def\u662f\u201c\u76f8\u52a0\u201d<\/strong>\uff1a\u4e24\u6761\u7ebf\u6c47\u805a\u5230\u4e0a\u9762\u90a3\u4e2a\u70b9\u65f6\uff0c\u76f4\u63a5\u628a\u4e24\u4e2a\u6570\u5b57\u52a0\u8d77\u6765\u3002<\/li>\n\n\n\n<li><strong>\u4e0b\u534a\u652f\u8def\u662f\u201c\u76f8\u51cf\u518d\u76f8\u4e58\u201d<\/strong>\uff1a\u7559\u610f\u4e0b\u534a\u652f\u8def\u6709\u4e00\u6839\u7ebf\u4e0a\u6807\u7740 <code>-1<\/code>\uff0c\u8fd9\u610f\u5473\u7740\u8981<strong>\u7528\u4e0a\u9762\u7684\u6570\u51cf\u53bb\u4e0b\u9762\u7684\u6570<\/strong>\u3002\u51cf\u5b8c\u4e4b\u540e\uff0c\u518d\u4e58\u4ee5\u524d\u65b9\u7bad\u5934\u5904\u6807\u6ce8\u7684<strong>\u65cb\u8f6c\u56e0\u5b50\uff08\u6bd4\u5982 W_4^0, W_4^1\uff09<\/strong>\u3002<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">\u638c\u63e1\u4e86\u8fd9\u4e2a\u89c4\u5219\uff0c\u6211\u4eec\u628a\u8fd9\u5f20\u56fe\u5206\u6210\u4e24\u7ea7\uff08\u4e24\u5217\uff09\u6765\u62c6\u89e3\u8ba1\u7b97\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u7b2c\u4e00\u7ea7\u8776\u5f62\u8fd0\u7b97\uff08\u770b\u5de6\u8fb9\u4e00\u534a\uff09<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u7b2c\u4e00\u7ea7\u662f\u4e24\u4e2a\u201c\u5927\u8de8\u5ea6\u201d\u7684\u8774\u8776\uff0c\u8de8\u5ea6\u4e3a 2\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6b64\u65f6\u7684\u8f93\u5165\u662f\u539f\u5e8f\u5217\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">x[0]=1, x[1]=2, x[2]=3, x[3]=4<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>1. \u7b2c\u4e00\u4e2a\u5927\u8774\u8776\uff08\u5904\u7406 x[0] \u548c x[2]\uff09\uff1a<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u4e0a\u534a\u652f\uff08\u7ea2\u8272 4\uff09<\/strong>\uff1a\u76f4\u63a5\u76f8\u52a0\u30021 + 3 = 4<\/li>\n\n\n\n<li><strong>\u4e0b\u534a\u652f\uff08\u7ea2\u8272 -2\uff09<\/strong>\uff1a\u76f8\u51cf\uff0c\u518d\u4e58\u4ee5 W_4^0\uff08\u56fe\u4e2d\u5df2\u7ed9\u51fa W_4^0=1\uff09\u3002(1 &#8211; 3) \\times 1 = -2<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>2. \u7b2c\u4e8c\u4e2a\u5927\u8774\u8776\uff08\u5904\u7406 x[1] \u548c x[3]\uff09\uff1a<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u4e0a\u534a\u652f\uff08\u7ea2\u8272 6\uff09<\/strong>\uff1a\u76f4\u63a5\u76f8\u52a0\u30022 + 4 = 6<\/li>\n\n\n\n<li><strong>\u4e0b\u534a\u652f\uff08\u7ea2\u8272 2j\uff09<\/strong>\uff1a\u76f8\u51cf\uff0c\u518d\u4e58\u4ee5 W_4^1\uff08\u56fe\u4e2d\u5df2\u7ed9\u51fa W_4^1=-j\uff09\u3002(2 &#8211; 4) \\times (-j) = -2 \\times (-j) = 2j<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u5230\u8fd9\u91cc\uff0c\u7b2c\u4e00\u7ea7\u7b97\u5b8c\u4e86\uff0c\u6211\u4eec\u5f97\u5230\u4e86\u56db\u4e2a\u4e2d\u95f4\u7ed3\u679c\uff0c\u4e5f\u5c31\u662f\u56fe\u4e2d\u4e2d\u95f4\u90a3\u5217\u7ea2\u8272\u7684\u6570\u5b57\uff1a<strong>4, 6, -2, 2j<\/strong>\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u7b2c\u4e8c\u7ea7\u8776\u5f62\u8fd0\u7b97\uff08\u770b\u53f3\u8fb9\u4e00\u534a\uff09<\/h3>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.millscience.cn\/wp-content\/uploads\/2026\/07\/image-20260705183349925.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.millscience.cn\/wp-content\/uploads\/2026\/07\/image-20260705183349925.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"image-20260705183349925\"\/><\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u7b2c\u4e8c\u7ea7\u53d8\u6210\u4e86\u4e24\u4e2a\u201c\u5c0f\u8de8\u5ea6\u201d\u7684\u8774\u8776\uff0c\u8de8\u5ea6\u4e3a 1\u3002\u5b83\u4eec\u5206\u522b\u5904\u7406\u521a\u624d\u7b97\u51fa\u6765\u7684\u90a3\u4e24\u7ec4\u7ea2\u8272\u7684\u4e2d\u95f4\u7ed3\u679c\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>(\u6ce8\uff1a\u7b2c\u4e8c\u7ea7\u7684\u65cb\u8f6c\u56e0\u5b50\u9ed8\u8ba4\u4e3a W_2^0=1\uff0c\u6240\u4ee5\u5728\u8fd9\u4e00\u7ea7\u53ea\u505a\u52a0\u51cf\u6cd5\uff0c\u4e0d\u6d89\u53ca\u590d\u6570\u4e58\u6cd5\u3002)<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>1. \u4e0a\u9762\u7684\u5c0f\u8774\u8776\uff08\u5904\u7406\u7ea2\u8272\u7684 4 \u548c 6\uff09\uff1a<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u4e0a\u534a\u652f<\/strong>\uff1a\u76f4\u63a5\u76f8\u52a0\u30024 + 6 = 10\uff08\u8fd9\u4e2a\u7ed3\u679c\u5bf9\u5e94 X[0]\uff09<\/li>\n\n\n\n<li><strong>\u4e0b\u534a\u652f<\/strong>\uff1a\u76f8\u51cf\u30024 &#8211; 6 = -2\uff08\u8fd9\u4e2a\u7ed3\u679c\u5bf9\u5e94 X[2]\uff09<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>2. \u4e0b\u9762\u7684\u5c0f\u8774\u8776\uff08\u5904\u7406\u7ea2\u8272\u7684 -2 \u548c 2j\uff09\uff1a<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u4e0a\u534a\u652f<\/strong>\uff1a\u76f4\u63a5\u76f8\u52a0\u3002-2 + 2j\uff08\u8fd9\u4e2a\u7ed3\u679c\u5bf9\u5e94 X[1]\uff09<\/li>\n\n\n\n<li><strong>\u4e0b\u534a\u652f<\/strong>\uff1a\u76f8\u51cf\u3002-2 &#8211; 2j\uff08\u8fd9\u4e2a\u7ed3\u679c\u5bf9\u5e94 X[3]\uff09<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u26a0\ufe0f \u8003\u70b9\u5927\u5751\uff1a\u8f93\u51fa\u7684\u201c\u5012\u4f4d\u5e8f\u201d<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u5982\u679c\u4f60\u4ed4\u7ec6\u770b\u6700\u53f3\u4fa7\u7684\u8f93\u51fa\u7ed3\u679c\uff0c\u4f1a\u53d1\u73b0\u5b83\u4eec\u7684\u4e0b\u6807\u987a\u5e8f\u662f\u4e71\u7684\uff1a\u4e0d\u662f 0, 1, 2, 3\uff0c\u800c\u662f <strong>0, 2, 1, 3<\/strong>\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u662f<strong>\u9891\u7387\u62bd\u53d6\u6cd5 (DIF)<\/strong> FFT \u7684\u4e00\u4e2a\u5178\u578b\u7279\u5f81\uff1a<strong>\u8f93\u5165\u662f\u81ea\u7136\u987a\u5e8f\uff0c\u8f93\u51fa\u662f\u5012\u4f4d\u5e8f\uff08Bit-Reversal\uff09<\/strong>\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5728\u5b9e\u9645\u5199\u6700\u7ec8\u7b54\u6848\u65f6\uff0c\u4f60\u9700\u8981\u624b\u52a8\u628a\u5b83\u4eec\u6309\u6b63\u786e\u7684\u4e0b\u6807\u91cd\u65b0\u6392\u597d\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>X[0] = 10<\/li>\n\n\n\n<li>X[1] = -2+2j<\/li>\n\n\n\n<li>X[2] = -2<\/li>\n\n\n\n<li>X[3] = -2-2j<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u6240\u4ee5\u6700\u7ec8\u7684 DFT \u5e8f\u5217\u7ed3\u679c\u5c31\u662f\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\{10, -2+2j, -2, -2-2j\\}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u548c\u4e0a\u4e00\u9898\u7528\u666e\u901a\u516c\u5f0f\u7b97\u51fa\u6765\u7684\u7ed3\u679c\u662f\u4e00\u6a21\u4e00\u6837\u7684\uff0c\u4f46\u901a\u8fc7\u8776\u5f62\u56fe\uff0c\u6211\u4eec\u5c06\u590d\u6742\u7684\u590d\u6570\u4e58\u52a0\u8fd0\u7b97\u62c6\u89e3\u6210\u4e86\u6700\u7b80\u5355\u7684\u8fde\u7ebf\u52a0\u51cf\u6cd5\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u753b\u6ee4\u6ce2\u5668\u56fe 1,2\u578b<\/h2>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.millscience.cn\/wp-content\/uploads\/2026\/07\/image-20260704220650343.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.millscience.cn\/wp-content\/uploads\/2026\/07\/image-20260704220650343.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"image-20260704220650343\"\/><\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u753b IIR \u6ee4\u6ce2\u5668\u7684<strong>\u76f4\u63a5 II \u578b\uff08\u5178\u8303\u578b\uff09*<em>\u7ed3\u6784\u56fe\uff0c\u5176\u5b9e\u5c31\u662f\u6839\u636e\u7cfb\u7edf\u51fd\u6570 H(z) \u8fdb\u884c\u201c\u586b\u7a7a\u201d\u3002\u8fd9\u4e2a\u8fc7\u7a0b\u975e\u5e38\u673a\u68b0\uff0c\u53ea\u8981\u8bb0\u4f4f\u4e00\u4e2a\u6838\u5fc3\u53e3\u8bc0\uff1a*<\/em>\u201c\u4e2d\u95f4\u4e32\u5ef6\u65f6\uff0c\u5de6\u8fb9\u753b\u5206\u6bcd\uff08\u9700\u53d8\u53f7\uff09\uff0c\u53f3\u8fb9\u753b\u5206\u5b50\uff08\u4e0d\u53d8\u53f7\uff09\u201d<\/strong>\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e0b\u9762\u4e3a\u4f60\u62c6\u89e3\u5177\u4f53\u7684\u4f5c\u56fe\u6b65\u9aa4\uff1a<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u7b2c\u4e00\u6b65\uff1a\u63d0\u53d6\u7cfb\u6570\u5e76\u786e\u8ba4\u7b26\u53f7\uff08\u6700\u5bb9\u6613\u51fa\u9519\u7684\u4e00\u6b65\uff09<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u89c2\u5bdf\u9898\u76ee\u7ed9\u51fa\u7684\u7cfb\u7edf\u51fd\u6570\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">H(z) = \\frac{8 &#8211; 4z^{-1} + 11z^{-2} &#8211; 2z^{-3}}{1 &#8211; \\frac{5}{4}z^{-1} + \\frac{3}{4}z^{-2} &#8211; \\frac{1}{8}z^{-3}}<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u53f3\u534a\u8fb9\uff08\u5206\u5b50\u7cfb\u6570 \/ \u524d\u9988\u5206\u652f\uff09<\/strong>\uff1a\u7cfb\u6570\u6309\u987a\u5e8f\u76f4\u63a5\u7167\u6284\uff0c<strong>\u7b26\u53f7\u4e0d\u53d8<\/strong>\u3002\n<ul class=\"wp-block-list\">\n<li>b_0 = 8<\/li>\n\n\n\n<li>b_1 = -4<\/li>\n\n\n\n<li>b_2 = 11<\/li>\n\n\n\n<li>b_3 = -2<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u5de6\u534a\u8fb9\uff08\u5206\u6bcd\u7cfb\u6570 \/ \u53cd\u9988\u5206\u652f\uff09<\/strong>\uff1a\u6ce8\u610f\u5206\u6bcd\u7684\u5e38\u6570\u9879\u5fc5\u987b\u662f 1\uff08\u9898\u76ee\u5df2\u6ee1\u8db3\uff09\u3002\u63d0\u53d6\u540e\u9762\u7684\u7cfb\u6570\u65f6\uff0c<strong>\u7b26\u53f7\u5fc5\u987b\u5168\u90e8\u53d6\u53cd<\/strong>\uff01\n<ul class=\"wp-block-list\">\n<li>\u539f\u5f0f\u662f -\\frac{5}{4}\uff0c\u753b\u56fe\u65f6\u7cfb\u6570\u4e3a \\frac{5}{4}<\/li>\n\n\n\n<li>\u539f\u5f0f\u662f +\\frac{3}{4}\uff0c\u753b\u56fe\u65f6\u7cfb\u6570\u4e3a -\\frac{3}{4}<\/li>\n\n\n\n<li>\u539f\u5f0f\u662f -\\frac{1}{8}\uff0c\u753b\u56fe\u65f6\u7cfb\u6570\u4e3a \\frac{1}{8}<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u7b2c\u4e8c\u6b65\uff1a\u642d\u5efa\u201c\u810a\u6881\u9aa8\u201d<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u89c2\u5bdf\u5230\u516c\u5f0f\u4e2d z \u7684\u6700\u9ad8\u6b21\u5e42\u662f -3\uff0c\u8fd9\u610f\u5473\u7740\u7cfb\u7edf\u662f\u4e09\u9636\u7684\uff0c\u9700\u8981\u7528\u5230 <strong>3 \u4e2a\u5ef6\u8fdf\u5355\u5143 (z^{-1})<\/strong>\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5728\u7eb8\u7684\u6b63\u4e2d\u95f4\uff0c\u4ece\u4e0a\u5230\u4e0b\u5782\u76f4\u753b 3 \u4e2a\u6807\u6709 z^{-1} \u7684\u65b9\u6846\uff0c\u7528\u7bad\u5934\u4e32\u8054\u8d77\u6765\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u7b2c\u4e09\u6b65\uff1a\u6309\u56fe\u7d22\u9aa5\u5b8c\u6210\u8fde\u7ebf<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u6309\u7167\u76f4\u63a5 II \u578b\u7684\u6807\u51c6\u753b\u6cd5\uff0c\u628a\u521a\u624d\u63d0\u53d6\u7684\u7cfb\u6570\u586b\u4e0a\u53bb\u3002\u6211\u7528\u5b57\u7b26\u753b\u4e3a\u4f60\u5c55\u793a\u6700\u7ec8\u7684\u7ed3\u6784\u56fe\u957f\u4ec0\u4e48\u6837\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Plaintext<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; x(n) \u2500\u2500\u25b6(\uff0b) \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u252c\u2500\u2500\u2500\u2500\u2500\u2500\u25b6 [  8 ] \u2500\u2500\u2500\u2500\u2500\u2500\u25b6(\uff0b)\u2500\u2500\u25b6 y(n)<br>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;  \u25b2 &nbsp; &nbsp; &nbsp; &nbsp;  \u2502 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; \u25b2<br>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;  \u2502 &nbsp; &nbsp; &nbsp;  [z^-1] &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;  \u2502<br>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;  \u2502 &nbsp; &nbsp; &nbsp; &nbsp;  \u2502 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; \u2502<br>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;  5\/4 \u2502 &nbsp; &nbsp; &nbsp; &nbsp;  \u2502 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; \u2502<br>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;  \u251c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2524\u2500\u2500\u2500\u2500\u2500\u2500\u25b6 [ -4 ] \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2524<br>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;  \u25b2 &nbsp; &nbsp; &nbsp; &nbsp;  \u2502 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; \u25b2<br>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;  \u2502 &nbsp; &nbsp; &nbsp;  [z^-1] &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;  \u2502<br>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;  \u2502 &nbsp; &nbsp; &nbsp; &nbsp;  \u2502 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; \u2502<br>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; -3\/4 \u2502 &nbsp; &nbsp; &nbsp; &nbsp;  \u2502 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; \u2502<br>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;  \u251c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2524\u2500\u2500\u2500\u2500\u2500\u2500\u25b6 [ 11 ] \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2524<br>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;  \u25b2 &nbsp; &nbsp; &nbsp; &nbsp;  \u2502 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; \u25b2<br>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;  \u2502 &nbsp; &nbsp; &nbsp;  [z^-1] &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;  \u2502<br>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;  \u2502 &nbsp; &nbsp; &nbsp; &nbsp;  \u2502 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; \u2502<br>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;  1\/8 \u2502 &nbsp; &nbsp; &nbsp; &nbsp;  \u2502 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; \u2502<br>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;  \u2514\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2534\u2500\u2500\u2500\u2500\u2500\u2500\u25b6 [ -2 ] \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2518<\/pre>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u7ed8\u56fe\u7ec6\u8282\u6838\u5bf9\u6e05\u5355\uff08\u8003\u8bd5\u753b\u5b8c\u540e\u81ea\u6211\u68c0\u67e5\uff09\uff1a<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u8f93\u5165\u8f93\u51fa<\/strong>\uff1a\u5de6\u4e0a\u89d2\u662f\u8f93\u5165 x(n)\uff0c\u53f3\u4e0a\u89d2\u662f\u8f93\u51fa y(n)\u3002<\/li>\n\n\n\n<li><strong>\u52a0\u6cd5\u5668 (\uff0b)<\/strong>\uff1a\u5de6\u4e0a\u89d2\u6709\u4e00\u4e2a\u52a0\u6cd5\u5668\u6c47\u603b\u53cd\u9988\u4fe1\u53f7\uff0c\u53f3\u4fa7\u6709\u4e00\u6392\u52a0\u6cd5\u5668\u6c47\u603b\u524d\u9988\u4fe1\u53f7\u3002<\/li>\n\n\n\n<li><strong>\u7bad\u5934\u65b9\u5411<\/strong>\uff1a\u6240\u6709\u7684\u4fe1\u53f7\u6d41\u52a8\u65b9\u5411\u90fd\u662f<strong>\u4ece\u4e0a\u5230\u4e0b\u3001\u4ece\u5de6\u5230\u53f3\u3001\u6216\u8005\u4ece\u4e0b\u5f80\u4e0a\u56de\u9988<\/strong>\uff0c\u7bad\u5934\u5343\u4e07\u4e0d\u8981\u753b\u53cd\u3002<\/li>\n\n\n\n<li><strong>\u53d8\u53f7\u68c0\u67e5<\/strong>\uff1a\u518d\u6b21\u76ef\u4f4f\u5de6\u8fb9\u90a3\u4e09\u4e2a\u4e58\u6cd5\u5668\u7cfb\u6570\uff08\\frac{5}{4}, -\\frac{3}{4}, \\frac{1}{8}\uff09\uff0c\u786e\u4fdd\u5b83\u4eec\u548c\u539f\u5206\u6bcd\u516c\u5f0f\u91cc\u7684\u7b26\u53f7\u6b63\u597d\u76f8\u53cd\u3002<\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.millscience.cn\/wp-content\/uploads\/2026\/07\/e34243d216c7b06d872aba2a5cb48bf.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.millscience.cn\/wp-content\/uploads\/2026\/07\/e34243d216c7b06d872aba2a5cb48bf.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"e34243d216c7b06d872aba2a5cb48bf\"\/><\/div><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">\u76f4\u63a5\u4e00\u578b\u753b\u6cd5<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u63d0\u53d6\u7cfb\u6570\u7684\u89c4\u5219\u548c\u521a\u624d\u4e00\u6a21\u4e00\u6837\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u5206\u5b50\uff08\u524d\u9988\uff0c\u5de6\u534a\u8fb9\uff09<\/strong>\uff1a\u76f4\u63a5\u7167\u6284\uff0c\u7b26\u53f7\u4e0d\u53d8\uff088, -4, 11, -2\uff09\u3002<\/li>\n\n\n\n<li><strong>\u5206\u6bcd\uff08\u53cd\u9988\uff0c\u53f3\u534a\u8fb9\uff09<\/strong>\uff1a\u9664\u4e86\u5e38\u6570\u9879 1 \u4e0d\u7ba1\uff0c\u5176\u4f59\u7cfb\u6570<strong>\u5fc5\u987b\u5168\u90e8\u53d8\u53f7<\/strong>\uff08\\frac{5}{4}, -\\frac{3}{4}, \\frac{1}{8}\uff09\u3002<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u7ed3\u6784\u56fe\u5c55\u793a<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u76f4\u63a5 I \u578b\u7684\u56fe\u770b\u8d77\u6765\u50cf\u4e00\u4e2a\u5de6\u53f3\u5bf9\u79f0\u7684\u5927\u9aa8\u67b6\uff1a\u5de6\u8fb9\u53ea\u5904\u7406\u8f93\u5165 x(n)\uff0c\u53f3\u8fb9\u53ea\u5904\u7406\u8f93\u51fa y(n)\uff0c\u7136\u540e\u5728\u4e2d\u95f4\u6c47\u5408\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Plaintext<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">&nbsp; &nbsp; &nbsp; &nbsp; x(n) &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; y(n)<br>&nbsp; &nbsp; &nbsp; &nbsp;  \u2502 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;  \u25b2<br>&nbsp; &nbsp; &nbsp; &nbsp;  \u251c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u25b6[  8 ]\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u25b6(\uff0b)\u25c0\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u252c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2524<br>&nbsp; &nbsp; &nbsp; &nbsp;  \u2502 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;  \u25b2 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; \u2502 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; \u2502<br>&nbsp; &nbsp; &nbsp;  [z^-1] &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; \u2502 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; \u2502 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; [z^-1]<br>&nbsp; &nbsp; &nbsp; &nbsp;  \u2502 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;  \u2502 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; \u2502 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; \u2502<br>&nbsp; &nbsp; &nbsp; &nbsp;  \u251c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u25b6[ -4 ]\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u25b6(\uff0b) &nbsp; &nbsp; &nbsp; &nbsp; \u2514\u2500\u2500\u2500\u2500\u2500[ 5\/4]\u25c0\u2500\u2500\u2500\u2524<br>&nbsp; &nbsp; &nbsp; &nbsp;  \u2502 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;  \u25b2 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; \u2502<br>&nbsp; &nbsp; &nbsp;  [z^-1] &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; \u2502 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; [z^-1]<br>&nbsp; &nbsp; &nbsp; &nbsp;  \u2502 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;  \u2502 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; \u2502<br>&nbsp; &nbsp; &nbsp; &nbsp;  \u251c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u25b6[ 11 ]\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u25b6(\uff0b) &nbsp; &nbsp; &nbsp; &nbsp; \u250c\u2500\u2500\u2500\u2500\u2500[-3\/4]\u25c0\u2500\u2500\u2500\u2524<br>&nbsp; &nbsp; &nbsp; &nbsp;  \u2502 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;  \u25b2 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; \u2502 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; \u2502<br>&nbsp; &nbsp; &nbsp;  [z^-1] &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; \u2502 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; \u2502 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; [z^-1]<br>&nbsp; &nbsp; &nbsp; &nbsp;  \u2502 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;  \u2502 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; \u2502 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; \u2502<br>&nbsp; &nbsp; &nbsp; &nbsp;  \u2514\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u25b6[ -2 ]\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u25b6(\uff0b)\u25c0\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2534\u2500\u2500\u2500\u2500\u2500[ 1\/8]\u25c0\u2500\u2500\u2500\u2518<\/pre>\n\n\n\n<h1 class=\"wp-block-heading\">\u5927\u9898<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">z\u53cd\u53d8\u6362<\/h2>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.millscience.cn\/wp-content\/uploads\/2026\/07\/P20260705-131508.jpg'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.millscience.cn\/wp-content\/uploads\/2026\/07\/P20260705-131508.jpg\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"P20260705-131508\"\/><\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u505a\u8fd9\u79cd\u9898\u7684\u6838\u5fc3\u76ee\u7684\u53ea\u6709\u4e00\u4e2a\uff1a<strong>\u628a\u4e00\u4e2a\u590d\u6742\u7684\u3001\u5728 Z \u53d8\u6362\u8868\u91cc\u67e5\u4e0d\u5230\u7684\u590d\u6742\u5206\u5f0f\uff0c\u62c6\u89e3\u6210\u51e0\u4e2a\u7b80\u5355\u7684\u3001\u80fd\u76f4\u63a5\u67e5\u8868\u79d2\u51fa\u7b54\u6848\u7684\u7b80\u5355\u5206\u5f0f\u76f8\u52a0\u3002<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6211\u4eec\u4e00\u6b65\u4e00\u6b65\u6765\u62c6\u89e3\u8fd9\u4e2a\u8fc7\u7a0b\uff1a<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u6838\u5fc3\u516c\u5f0f\u5bf9\u6bd4<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">X(z)=\\frac{1}{1+\\frac{1}{2}z^{-1}}, \\quad |z|&lt;\\frac{1}{2}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\frac{1}{1-az^{-1}} \\leftrightarrow a^nu(n) \\quad (|z|&gt;|a|)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5728\u67e5\u8868\u65f6\uff0c\u5bf9\u4e8e\u5206\u6bcd\u662f 1-az^{-1} \u7684\u8868\u8fbe\u5f0f\uff0c\u6709\u4e24\u5957\u5b8c\u5168\u76f8\u53cd\u7684\u89c4\u5219\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u5f53 |z|>|a| \u65f6<\/strong>\uff08\u5411\u5916\u53d1\u6563\uff09\uff1a\u5bf9\u5e94<strong>\u53f3\u8fb9\u5e8f\u5217<\/strong> a^nu(n)\u3002<\/li>\n\n\n\n<li><strong>\u5f53 |z|&lt;|a| \u65f6<\/strong>\uff08\u5411\u5185\u6536\u655b\uff09\uff1a\u5bf9\u5e94<strong>\u5de6\u8fb9\u5e8f\u5217<\/strong> -a^nu(-n-1)\u3002<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">\u7b2c\u4e00\u6b65\uff1a\u628a\u6b63\u6570\u6b21\u5e42\u53d8\u6210\u8d1f\u6570\u6b21\u5e42\uff08\u51d1\u6807\u51c6\u578b\uff09<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u9898\u76ee\u7ed9\u7684\u662f\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">X(z)=\\frac{z^2}{(z-1)(z-2)}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6211\u4eec\u5728\u67e5\u5e38\u7528\u7684 Z \u53d8\u6362\u8868\u65f6\uff0c\u516c\u5f0f\u5927\u591a\u662f\u5e26\u7740 z^{-1} \u7684\u3002\u6240\u4ee5\u6211\u4eec\u8981\u7ed9\u5206\u5b50\u5206\u6bcd\u540c\u65f6\u9664\u4ee5\u6700\u9ad8\u6b21\u5e42\uff08\u8fd9\u91cc\u662f z^2\uff09\uff0c\u628a\u5b83\u53d8\u6210\u8d1f\u6b21\u5e42\u7684\u5f62\u5f0f\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5206\u5b50\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">z^2 \\div z^2 = 1<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5206\u6bcd\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">(z-1)(z-2) = z^2-3z+2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uff0c\u9664\u4ee5 z^2 \u540e\u53d8\u6210<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1-3z^{-1}+2z^{-2}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uff0c\u518d\u5206\u89e3\u56e0\u5f0f\u5c31\u662f<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">(1-z^{-1})(1-2z^{-1})<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6240\u4ee5\u5f97\u5230\u4e86\u4e66\u4e0a\u7684\u7b2c\u4e00\u6b65\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">X(z)=\\frac{1}{(1-z^{-1})(1-2z^{-1})}<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u7b2c\u4e8c\u6b65\uff1a\u8bbe\u672a\u77e5\u6570\u62c6\u5206\uff08\u90e8\u5206\u5206\u5f0f\u5c55\u5f00\uff09<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u73b0\u5728\u5206\u6bcd\u6709\u4e24\u4e2a\u56e0\u5f0f\u76f8\u4e58\uff0c\u6211\u4eec\u8981\u628a\u5b83\u62c6\u6210\u4e24\u9879\u76f8\u52a0\u7684\u6837\u5b50\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">X(z)=\\frac{A}{1-z^{-1}}+\\frac{B}{1-2z^{-1}}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u73b0\u5728\u7684\u4efb\u52a1\u5c31\u662f\u6c42\u51fa A \u548c B \u5206\u522b\u662f\u591a\u5c11\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u7b2c\u4e09\u6b65\uff1a\u6c42 A \u548c B\uff08\u7559\u6570\u6cd5 \/ \u906e\u6321\u6cd5\uff09<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e66\u4e0a\u90a3\u4e00\u957f\u4e32\u516c\u5f0f\u5c31\u662f\u5728\u7b97\u8fd9\u4e2a\u3002\u8fd9\u91cc\u6559\u4f60\u4e00\u4e2a\u901a\u4fd7\u6613\u61c2\u7684\u201c\u906e\u6321\u6cd5\u201d\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>1. \u600e\u4e48\u6c42 A\uff1f<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A \u7684\u5206\u6bcd\u662f (1-z^{-1})\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4f60\u53bb\u770b\u603b\u5f0f\u5b50 X(z)=\\frac{1}{(1-z^{-1})(1-2z^{-1})}\uff0c\u628a\u548c A \u5206\u6bcd\u4e00\u6a21\u4e00\u6837\u7684\u90a3\u4e2a\u56e0\u5f0f <strong>(1-z^{-1}) \u906e\u4f4f\uff08\u5220\u6389\uff09<\/strong>\uff0c\u5269\u4e0b\u7684\u90e8\u5206\u5c31\u662f\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\frac{1}{1-2z^{-1}}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7136\u540e\uff0c\u8ba9\u88ab\u906e\u4f4f\u7684\u90a3\u90e8\u5206\u7b49\u4e8e 0\uff0c\u5373 1-z^{-1}=0\uff0c\u89e3\u5f97 z=1\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u628a z=1 \u4ee3\u5165\u5269\u4e0b\u7684\u90e8\u5206\u91cc\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A = \\frac{1}{1-2(1)^{-1}} = \\frac{1}{1-2} = -1<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u5c31\u548c\u4e66\u4e0a\u7b97\u51fa\u7684 A = -1 \u5bf9\u4e0a\u4e86\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>2. \u600e\u4e48\u6c42 B\uff1f<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u540c\u7406\uff0cB \u7684\u5206\u6bcd\u662f (1-2z^{-1})\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u56de\u5230\u603b\u5f0f\u5b50\uff0c\u628a <strong>(1-2z^{-1}) \u906e\u4f4f<\/strong>\uff0c\u5269\u4e0b\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\frac{1}{1-z^{-1}}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8ba9\u906e\u4f4f\u7684\u90e8\u5206\u7b49\u4e8e 0\uff0c\u5373 1-2z^{-1}=0\uff0c\u89e3\u5f97 2z^{-1}=1 \\Rightarrow z=2\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u628a z=2 \u4ee3\u5165\u5269\u4e0b\u7684\u90e8\u5206\u91cc\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B = \\frac{1}{1-(2)^{-1}} = \\frac{1}{1-0.5} = \\frac{1}{0.5} = 2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u5c31\u548c\u4e66\u4e0a\u7b97\u51fa\u7684 B = 2 \u5bf9\u4e0a\u4e86\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u7b2c\u56db\u6b65\uff1a\u5199\u51fa\u62c6\u89e3\u540e\u7684\u5b8c\u6574\u5f0f\u5b50<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u628a\u7b97\u51fa\u6765\u7684 A \u548c B \u4ee3\u56de\u53bb\uff0c\u770b\u7b2c\u4e8c\u5f20\u56fe\u7684\u6700\u4e0a\u9762\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">X(z)=\\frac{-1}{1-z^{-1}}+\\frac{2}{1-2z^{-1}}<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u7b2c\u4e94\u6b65\uff1a\u67e5\u8868\u5199\u7b54\u6848\uff08\u6ce8\u610f\u6536\u655b\u57df\uff09<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u4e00\u6b65\u8981\u7528\u5230\u9898\u76ee\u7ed9\u7684\u6761\u4ef6\uff1a<strong>\u6536\u655b\u57df |z| &gt; 2<\/strong>\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6536\u655b\u57df\u662f |z| &gt; \\text{\u67d0\u6570}\uff08\u5927\u4e8e\u53f7\uff09\uff0c\u8bf4\u660e\u8fd9\u662f\u4e00\u4e2a<strong>\u56e0\u679c\u5e8f\u5217\uff08\u53f3\u8fb9\u5e8f\u5217\uff09<\/strong>\uff0c\u5b83\u5728\u65f6\u57df\u91cc\u4e00\u5b9a\u4f1a\u4e58\u4e0a\u4e00\u4e2a\u9636\u8dc3\u5e8f\u5217 u(n)\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u56de\u5fc6\u4e00\u4e0b\u6700\u57fa\u7840\u7684 Z \u53d8\u6362\u5bf9\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\frac{1}{1-az^{-1}} \\leftrightarrow a^n u(n)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u73b0\u5728\u6211\u4eec\u5206\u522b\u5bf9\u62c6\u5f00\u7684\u4e24\u9879\u5957\u516c\u5f0f\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u7b2c\u4e00\u9879\uff1a\\frac{-1}{1-z^{-1}}\uff0c\u8fd9\u91cc\u7684 a=1\u3002\u53cd\u53d8\u6362\u5c31\u662f -1 \\cdot (1^n) u(n) = -u(n)\u3002<\/li>\n\n\n\n<li>\u7b2c\u4e8c\u9879\uff1a\\frac{2}{1-2z^{-1}}\uff0c\u8fd9\u91cc\u7684 a=2\u3002\u53cd\u53d8\u6362\u5c31\u662f 2 \\cdot (2^n) u(n)\u3002<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">\u628a\u5b83\u4eec\u52a0\u8d77\u6765\uff0c\u5c31\u662f\u6700\u7ec8\u7b54\u6848\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">x(n) = -u(n) + 2(2^n)u(n) = [2(2^n)-1]u(n)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u603b\u7ed3\u4e00\u4e0b\uff1a\u8fd9\u79cd\u9898\u5c31\u662f\u4e00\u5957\u6b7b\u6d41\u7a0b\uff1a<strong>\u5316\u8d1f\u6b21\u5e42 \\rightarrow \u8bbe A,B \\rightarrow \u906e\u6321\u6cd5\u6c42 A,B \\rightarrow \u5957\u516c\u5f0f\u51fa\u7ed3\u679c<\/strong>\u3002\u591a\u62ff\u7eb8\u7b14\u7ec3\u4e24\u6b21\uff0c\u4f60\u5c31\u80fd\u808c\u8089\u8bb0\u5fc6\u4e86\uff01<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">z\u53cd\u53d8\u6362\u4f8b\u98982<\/h2>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.millscience.cn\/wp-content\/uploads\/2026\/07\/P20260705-1406051.jpg'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.millscience.cn\/wp-content\/uploads\/2026\/07\/P20260705-1406051.jpg\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"P20260705-140605(1)\"\/><\/div><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">\u7b2c (3) \u9898\uff1a\u7ecf\u5178\u7684\u201c\u7559\u6570\u5c55\u5f00\u9898\u201d<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u9053\u9898\u7a0d\u5fae\u590d\u6742\u4e00\u70b9\uff0c\u4f46\u6d41\u7a0b\u548c\u6211\u4eec\u521a\u624d\u5b66\u7684\u201c\u906e\u6321\u6cd5\u201d\u4e00\u6a21\u4e00\u6837\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u9898\u76ee\uff1a<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">X(z)=\\frac{1-\\frac{1}{2}z^{-1}}{1+\\frac{3}{4}z^{-1}+\\frac{1}{8}z^{-2}}, \\quad |z|&gt;\\frac{1}{2}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u89e3\u9898\u6b65\u9aa4\uff1a<\/strong><\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u7b2c\u4e00\u6b65\uff1a\u628a\u5206\u6bcd\u56e0\u5f0f\u5206\u89e3<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">\u4f60\u9700\u8981\u628a\u5206\u6bcd\u7684\u4e8c\u6b21\u591a\u9879\u5f0f\u62c6\u6210\u4e24\u4e2a\u4e00\u6b21\u591a\u9879\u5f0f\u76f8\u4e58\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4ee4 y = z^{-1}\uff0c\u5206\u6bcd\u5c31\u662f 1+\\frac{3}{4}y+\\frac{1}{8}y^2\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7a0d\u5fae\u51d1\u4e00\u4e0b\u5341\u5b57\u76f8\u4e58\u6cd5\uff08\u6216\u8005\u6c42\u6839\u516c\u5f0f\uff09\uff0c\u53ef\u4ee5\u628a\u5b83\u5206\u89e3\u4e3a\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">(1+\\frac{1}{2}z^{-1})(1+\\frac{1}{4}z^{-1})<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>(\u68c0\u67e5\u4e00\u4e0b\uff1a1 + \\frac{1}{4}z^{-1} + \\frac{1}{2}z^{-1} + \\frac{1}{8}z^{-2} = 1 + \\frac{3}{4}z^{-1} + \\frac{1}{8}z^{-2}\uff0c\u6ca1\u95ee\u9898\uff01)<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6240\u4ee5\u73b0\u5728\u7684\u5f0f\u5b50\u53d8\u6210\u4e86\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">X(z)=\\frac{1-\\frac{1}{2}z^{-1}}{(1+\\frac{1}{2}z^{-1})(1+\\frac{1}{4}z^{-1})}<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u7b2c\u4e8c\u6b65\uff1a\u8bbe\u672a\u77e5\u6570\uff0c\u51c6\u5907\u62c6\u5206<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">\u628a\u5b83\u62c6\u6210\u4e24\u9879\u76f8\u52a0\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">X(z)=\\frac{A}{1+\\frac{1}{2}z^{-1}}+\\frac{B}{1+\\frac{1}{4}z^{-1}}<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u7b2c\u4e09\u6b65\uff1a\u7528\u201c\u906e\u6321\u6cd5\u201d\u6c42 A \u548c B<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u6c42 A<\/strong>\uff1a\u628a\u603b\u5f0f\u5b50\u91cc\u548c A \u5206\u6bcd\u4e00\u6837\u7684 (1+\\frac{1}{2}z^{-1}) \u906e\u4f4f\uff0c\u5269\u4e0b \\frac{1-\\frac{1}{2}z^{-1}}{1+\\frac{1}{4}z^{-1}}\u3002\u4ee4\u88ab\u906e\u4f4f\u7684\u90e8\u5206\u4e3a 0\uff0c\u5f97\u5230 z^{-1} = -2\u3002\u4ee3\u5165\u5269\u4e0b\u7684\u90e8\u5206\uff1aA=\\frac{1-\\frac{1}{2}(-2)}{1+\\frac{1}{4}(-2)}=\\frac{1+1}{1-0.5}=\\frac{2}{0.5}=4<\/li>\n\n\n\n<li><strong>\u6c42 B<\/strong>\uff1a\u628a\u603b\u5f0f\u5b50\u91cc\u548c B \u5206\u6bcd\u4e00\u6837\u7684 (1+\\frac{1}{4}z^{-1}) \u906e\u4f4f\uff0c\u5269\u4e0b \\frac{1-\\frac{1}{2}z^{-1}}{1+\\frac{1}{2}z^{-1}}\u3002\u4ee4\u88ab\u906e\u4f4f\u7684\u90e8\u5206\u4e3a 0\uff0c\u5f97\u5230 z^{-1} = -4\u3002\u4ee3\u5165\u5269\u4e0b\u7684\u90e8\u5206\uff1aB=\\frac{1-\\frac{1}{2}(-4)}{1+\\frac{1}{2}(-4)}=\\frac{1+2}{1-2}=\\frac{3}{-1}=-3<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u628a\u7b97\u51fa\u6765\u7684 A \u548c B \u586b\u56de\u53bb\uff0c\u62c6\u89e3\u6210\u529f\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">X(z)=\\frac{4}{1+\\frac{1}{2}z^{-1}}-\\frac{3}{1+\\frac{1}{4}z^{-1}}<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u7b2c\u56db\u6b65\uff1a\u67e5\u8868\u5199\u6700\u7ec8\u7ed3\u679c<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">\u89c2\u5bdf\u62c6\u51fa\u6765\u7684\u4e24\u9879\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u7b2c\u4e00\u9879\u7684\u6781\u70b9\u5728 z=-\\frac{1}{2}\uff0c\u516c\u5f0f\u91cc\u7684 a=-\\frac{1}{2}\u3002<\/li>\n\n\n\n<li>\u7b2c\u4e8c\u9879\u7684\u6781\u70b9\u5728 z=-\\frac{1}{4}\uff0c\u516c\u5f0f\u91cc\u7684 a=-\\frac{1}{4}\u3002\u9898\u76ee\u7ed9\u7684\u6536\u655b\u57df\u662f |z|>\\frac{1}{2}\u3002\u8fd9\u4e2a\u8303\u56f4\u5927\u4e8e\u4efb\u4f55\u4e00\u4e2a\u6781\u70b9\u7684\u7edd\u5bf9\u503c\uff08\\frac{1}{2} \u548c \\frac{1}{4}\uff09\uff0c\u8fd9\u610f\u5473\u7740<strong>\u62c6\u5206\u51fa\u6765\u7684\u4e24\u9879\u5168\u90fd\u662f\u53f3\u8fb9\u5e8f\u5217\uff08\u56e0\u679c\u5e8f\u5217\uff09<\/strong>\u3002<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u76f4\u63a5\u5957\u6807\u51c6\u516c\u5f0f\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u7b2c\u4e00\u9879\u53cd\u53d8\u6362\uff1a4(-\\frac{1}{2})^nu(n)<\/li>\n\n\n\n<li>\u7b2c\u4e8c\u9879\u53cd\u53d8\u6362\uff1a-3(-\\frac{1}{4})^nu(n)<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u76f8\u52a0\u5f97\u5230\u6700\u7ec8\u7b54\u6848\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">x(n)=4(-\\frac{1}{2})^nu(n)-3(-\\frac{1}{4})^nu(n)<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u753b\u8776\u5f62\u56fe<\/h2>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.millscience.cn\/wp-content\/uploads\/2026\/07\/P20260622-142249.jpg'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.millscience.cn\/wp-content\/uploads\/2026\/07\/P20260622-142249.jpg\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"P20260622-142249\"\/><\/div><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.millscience.cn\/wp-content\/uploads\/2026\/07\/P20260622-142400.jpg'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.millscience.cn\/wp-content\/uploads\/2026\/07\/P20260622-142400.jpg\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"P20260622-142400\"\/><\/div><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">1. \u57fa\u4e8e\u65f6\u95f4\u62bd\u53d6 (DIT) \u7684\u8776\u5f62\u56fe<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u5bf9\u5e94\u56fe\u7247\uff1a<strong>&#8220;1000020019.png&#8221;<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u6838\u5fc3\u53e3\u8bc0<\/strong>\uff1a<strong>\u5148\u4e58\u540e\u52a0\u51cf<\/strong>\u3002<\/li>\n\n\n\n<li><strong>\u753b\u56fe\u6b65\u9aa4\u4e0e\u89e3\u6790<\/strong>\uff1a\n<ul class=\"wp-block-list\">\n<li>\u753b\u4e00\u4e2a\u5927\u53c9\uff0c\u5de6\u8fb9\u4e24\u4e2a\u8f93\u5165\u7aef\u662f X_1(k) \u548c X_2(k)\u3002<\/li>\n\n\n\n<li>\u5c06\u65cb\u8f6c\u56e0\u5b50 W_N^k \u753b\u5728<strong>\u5de6\u4e0b\u65b9\u7684\u8f93\u5165\u652f\u8def<\/strong>\u4e0a\uff0c\u4f4d\u4e8e\u4ea4\u53c9\u70b9<strong>\u4e4b\u524d<\/strong>\u3002<\/li>\n\n\n\n<li>\u8fd9\u610f\u5473\u7740\u4e0b\u65b9\u7684\u8f93\u5165\u4fe1\u53f7 X_2(k) \u8981\u5148\u4e58\u4ee5 W_N^k \u624d\u80fd\u8fdb\u5165\u52a0\u51cf\u8fd0\u7b97\u3002<\/li>\n\n\n\n<li>\u4e0a\u534a\u652f\u8def\u7684\u8f93\u51fa\uff08\u524d\u534a\u90e8\u5206\uff09\u662f\u4e24\u8def\u4fe1\u53f7\u76f8\u52a0\uff1aX(k) = X_1(k) + W_N^k X_2(k)\u3002<\/li>\n\n\n\n<li>\u4e0b\u534a\u652f\u8def\u7684\u8f93\u51fa\uff08\u540e\u534a\u90e8\u5206\uff09\u662f\u4e0a\u534a\u8def\u51cf\u53bb\u4e0b\u534a\u8def\uff1aX(N\/2+k) = X_1(k) &#8211; W_N^k X_2(k)\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u8fd0\u7b97\u91cf\u8bf4\u660e<\/strong>\uff1a\u6839\u636e\u56fe\u793a\uff0c\u5b8c\u6210\u8fd9\u6837\u4e00\u4e2a\u8776\u5f62\u8fd0\u7b97\u9700\u8981 1 \u6b21\u590d\u4e58\uff0c2 \u6b21\u590d\u52a0\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">2. \u57fa\u4e8e\u9891\u7387\u62bd\u53d6 (DIF) \u7684\u8776\u5f62\u56fe<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u5bf9\u5e94\u56fe\u7247\uff1a<strong>&#8220;1000020017.png&#8221;<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u6838\u5fc3\u53e3\u8bc0<\/strong>\uff1a<strong>\u5148\u52a0\u51cf\u540e\u4e58<\/strong>\u3002<\/li>\n\n\n\n<li><strong>\u753b\u56fe\u6b65\u9aa4\u4e0e\u89e3\u6790<\/strong>\uff1a\n<ul class=\"wp-block-list\">\n<li>\u540c\u6837\u753b\u4e00\u4e2a\u5927\u53c9\uff0c\u5de6\u8fb9\u4e24\u4e2a\u8f93\u5165\u7aef\u4e3a x(n) \u548c x(n+N\/2)\u3002<\/li>\n\n\n\n<li>\u4ea4\u53c9\u70b9\u4e4b\u524d\u4e0d\u753b\u4efb\u4f55\u4e58\u6cd5\u7b26\u53f7\uff0c\u4e24\u8def\u8f93\u5165\u76f4\u63a5\u8fdb\u5165\u52a0\u51cf\u4ea4\u53c9\u70b9\u3002<\/li>\n\n\n\n<li>\u4e0a\u534a\u652f\u8def\u7684\u8f93\u51fa\u76f4\u63a5\u662f\u4e24\u8def\u8f93\u5165\u76f8\u52a0\uff1ax_1(n) = x(n) + x(n+N\/2)\u3002<\/li>\n\n\n\n<li>\u4e0b\u534a\u652f\u8def\u662f\u4e24\u8def\u8f93\u5165\u76f8\u51cf\u540e\uff0c<strong>\u518d<\/strong>\u6574\u4f53\u4e58\u4ee5\u65cb\u8f6c\u56e0\u5b50 W_N^n\u3002<\/li>\n\n\n\n<li>\u56e0\u6b64\uff0c\u65cb\u8f6c\u56e0\u5b50 W_N^n \u5fc5\u987b\u753b\u5728<strong>\u53f3\u4e0b\u65b9\u7684\u8f93\u51fa\u652f\u8def<\/strong>\u4e0a\uff0c\u4f4d\u4e8e\u76f8\u4ea4\u7684\u9ed1\u70b9<strong>\u4e4b\u540e<\/strong>\u3002\u4e0b\u65b9\u7684\u6700\u7ec8\u8f93\u51fa\u8868\u8fbe\u5f0f\u5199\u4e3a x_2(n) = [x(n) &#8211; x(n+N\/2)]W_N^n\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u8003\u8bd5\u901f\u8bb0\u9632\u6df7\u6dc6\u6307\u5357\uff1a<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u5728\u81ea\u5df1\u624b\u52a8\u753b\u5b8c\u6574\u7684 8 \u70b9\u6216 4 \u70b9 FFT \u6d41\u7a0b\u56fe\u65f6\uff0c\u53ea\u9700\u8bb0\u4f4f\u4ee5\u4e0b\u7279\u5f81\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u770b DIT (\u65f6\u95f4)<\/strong>\uff1a\u65cb\u8f6c\u56e0\u5b50\u5728<strong>\u4ea4\u53c9\u70b9\u5de6\u8fb9<\/strong>\uff08\u8fdb\u95e8\u524d\u5148\u4e58\uff09\u3002<\/li>\n\n\n\n<li><strong>\u770b DIF (\u9891\u7387)<\/strong>\uff1a\u65cb\u8f6c\u56e0\u5b50\u5728<strong>\u4ea4\u53c9\u70b9\u53f3\u8fb9<\/strong>\uff08\u51cf\u5b8c\u51fa\u95e8\u540e\u518d\u4e58\uff09\u3002<\/li>\n\n\n\n<li><strong>\u5171\u540c\u70b9<\/strong>\uff1a\u4e0d\u7ba1\u54ea\u79cd\u753b\u6cd5\uff0c\u4e0a\u534a\u652f\u8def\u7684\u4ea4\u53c9\u7ebf\u6c38\u8fdc\u4ee3\u8868<strong>\u76f8\u52a0<\/strong>\uff0c\u4e0b\u534a\u652f\u8def\u7684\u4ea4\u53c9\u7ebf\u6c38\u8fdc\u4ee3\u8868<strong>\u76f8\u51cf<\/strong>\u3002<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">\u6ee4\u6ce2\u5668\u7684\u8bbe\u8ba1<\/h2>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.millscience.cn\/wp-content\/uploads\/2026\/07\/image-20260705212026543.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.millscience.cn\/wp-content\/uploads\/2026\/07\/image-20260705212026543.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"image-20260705212026543\"\/><\/div><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.millscience.cn\/wp-content\/uploads\/2026\/07\/P20260705-2044321.jpg'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.millscience.cn\/wp-content\/uploads\/2026\/07\/P20260705-2044321.jpg\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"P20260705-204432(1)\"\/><\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u4e24\u9875\u7684\u6838\u5fc3\u5185\u5bb9\u662f\uff1a<strong>\u5982\u4f55\u8bbe\u8ba1\u4e00\u4e2a\u201c\u5df4\u7279\u6c83\u65af\u6a21\u62df\u4f4e\u901a\u6ee4\u6ce2\u5668 (Butterworth Analog Low-Pass Filter)\u201d<\/strong>\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5728\u6570\u5b57\u4fe1\u53f7\u5904\u7406\u4e2d\uff0c\u8981\u60f3\u8bbe\u8ba1\u4e00\u4e2a\u6570\u5b57\u6ee4\u6ce2\u5668\uff0c\u6211\u4eec\u901a\u5e38\u4f1a<strong>\u5148\u8bbe\u8ba1\u4e00\u4e2a\u6a21\u62df\u6ee4\u6ce2\u5668\uff0c\u7136\u540e\u518d\u628a\u5b83\u8f6c\u6362\u6210\u6570\u5b57\u7684<\/strong>\u3002\u800c\u201c\u5df4\u7279\u6c83\u65af\u201d\u662f\u6700\u7ecf\u5178\u7684\u4e00\u79cd\uff0c\u5b83\u7684\u7279\u70b9\u662f\u901a\u5e26\u975e\u5e38\u5e73\u5766\uff0c\u6ca1\u6709\u4efb\u4f55\u6ce2\u7eb9\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e66\u4e0a\u7684\u3010\u4f8b 6-1\u3011\u5176\u5b9e\u5c31\u662f\u624b\u628a\u624b\u6559\u4f60\u8fc7\u8fd9\u56db\u9053\u5173\u5361\uff0c\u6211\u4eec\u628a\u5b83\u201c\u7ffb\u8bd1\u201d\u6210\u4eba\u8bdd\uff1a<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u7b2c\u4e00\u6b65\uff1a\u660e\u786e\u7532\u65b9\u7684\u9700\u6c42 (\u6027\u80fd\u6307\u6807)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u8bbe\u8ba1\u6ee4\u6ce2\u5668\u5c31\u50cf\u505a\u5de5\u7a0b\uff0c\u9898\u76ee\uff08\u7532\u65b9\uff09\u4f1a\u7ed9\u4f60 4 \u4e2a\u786c\u6027\u6307\u6807\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\\Omega_p = 10000 \\text{ rad\/s}<\/strong>\uff1a\u901a\u5e26\u622a\u6b62\u9891\u7387\uff08\u5728\u8fd9\u4e2a\u9891\u7387\u4e4b\u524d\uff0c\u4fe1\u53f7\u5fc5\u987b\u65e0\u635f\u901a\u8fc7\uff09\u3002<\/li>\n\n\n\n<li><strong>A_p = 3 \\text{ dB}<\/strong>\uff1a\u901a\u5e26\u6700\u5927\u8870\u51cf\uff08\u5141\u8bb8\u4fe1\u53f7\u6700\u591a\u8870\u51cf\u591a\u5c11\uff09\u3002<\/li>\n\n\n\n<li><strong>\\Omega_s = 40000 \\text{ rad\/s}<\/strong>\uff1a\u963b\u5e26\u622a\u6b62\u9891\u7387\uff08\u5728\u8fd9\u4e2a\u9891\u7387\u4e4b\u540e\uff0c\u4fe1\u53f7\u5fc5\u987b\u88ab\u72e0\u72e0\u6390\u65ad\uff09\u3002<\/li>\n\n\n\n<li><strong>A_s = 35 \\text{ dB}<\/strong>\uff1a\u963b\u5e26\u6700\u5c0f\u8870\u51cf\uff08\u6390\u65ad\u7684\u529b\u5ea6\uff0c\u8d8a\u5927\u8d8a\u597d\uff09\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u7b2c\u4e8c\u6b65\uff1a\u8ba1\u7b97\u6ee4\u6ce2\u5668\u7684\u9636\u6570 N (\u51b3\u5b9a\u590d\u6742\u5ea6)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u6ee4\u6ce2\u5668\u7684\u9636\u6570 N \u51b3\u5b9a\u4e86\u4f60\u8981\u7528\u51e0\u4e2a\u7535\u5bb9\u7535\u611f\uff08\u6216\u8005\u51e0\u4e2a\u5ef6\u8fdf\u5355\u5143\uff09\u3002N \u8d8a\u5927\uff0c\u6ee4\u6ce2\u6548\u679c\u8d8a\u597d\uff0c\u4f46\u6210\u672c\u8d8a\u9ad8\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e66\u4e0a\u90a3\u4e2a\u770b\u8d77\u6765\u6781\u5176\u6050\u6016\u7684\u5e26\u6709 \\lg \u7684\u516c\u5f0f\uff0c\u5c31\u662f\u7528\u6765\u7b97 N \u7684\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u65e0\u8111\u4ee3\u5165<\/strong>\uff1a\u628a\u4e0a\u9762 4 \u4e2a\u6307\u6807\u585e\u8fdb\u516c\u5f0f\uff0c\u4e00\u987f\u6309\u8ba1\u7b97\u5668\uff0c\u7b97\u51fa N \\ge 2.9083\u3002<\/li>\n\n\n\n<li><strong>\u5411\u4e0a\u53d6\u6574<\/strong>\uff1a\u9636\u6570\u5fc5\u987b\u662f\u6574\u6570\uff0c\u6240\u4ee5\u6211\u4eec\u53d6 <strong>N = 3<\/strong>\u3002\u8fd9\u610f\u5473\u7740\u6211\u4eec\u9700\u8981\u4e00\u4e2a 3 \u9636\u7684\u6ee4\u6ce2\u5668\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u7b2c\u4e09\u6b65\uff1a\u8ba1\u7b97\u771f\u5b9e\u7684 3dB \u622a\u6b62\u9891\u7387 \\Omega_c<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u867d\u7136\u7532\u65b9\u7ed9\u4e86\u4e00\u4e2a\u901a\u5e26\u9891\u7387 \\Omega_p\uff0c\u4f46\u6211\u4eec\u6839\u636e\u516c\u5f0f\u53cd\u63a8\uff0c\u7b97\u51fa\u4e00\u4e2a\u66f4\u7cbe\u51c6\u7684\u7cfb\u7edf\u5185\u90e8\u4f7f\u7528\u7684\u622a\u6b62\u9891\u7387 \\Omega_c\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4ee3\u5165\u516c\u5f0f\u7b97\u51fa\u6765 <strong>\\Omega_c = 10441 \\text{ rad\/s}<\/strong>\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u7b2c\u56db\u6b65\uff1a\u5199\u51fa\u7cfb\u7edf\u51fd\u6570 H_a(s) (\u7ec8\u6781\u5927\u62db)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u662f\u6700\u5173\u952e\u7684\u4e00\u6b65\uff0c\u8981\u6c42\u51fa\u8fd9\u4e2a\u6ee4\u6ce2\u5668\u7684\u6570\u5b66\u8868\u8fbe\u5f0f H_a(s)\u3002\u4e66\u4e0a\u7ed9\u4e86\u4f60\u4e24\u79cd\u65b9\u6cd5\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u65b9\u6cd5 A\uff1a\u786c\u7b97\u6cd5\uff08\u6c42\u6781\u70b9\uff09<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5229\u7528\u516c\u5f0f\u786c\u7b97\u51fa 3 \u4e2a\u6781\u70b9 s_1, s_2, s_3\u3002\u56e0\u4e3a N=3\uff0c\u6781\u70b9\u5728\u590d\u5e73\u9762\u4e0a\u6b63\u597d\u662f\u4e00\u4e2a\u534a\u5706\u4e0a\u7684\u4e09\u4e2a\u70b9\u3002\u7136\u540e\u628a\u5b83\u4eec\u4e58\u8d77\u6765\u4f5c\u4e3a\u5206\u6bcd\u3002\u8fd9\u901a\u5e38\u5f88\u6298\u78e8\u4eba\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u65b9\u6cd5 B\uff1a\u67e5\u8868\u6cd5\uff08\u8003\u8bd5\u6700\u7231\u7528\uff0c\u4e5f\u5c31\u662f\u4e66\u4e0a\u5199\u7684\u201c\u53bb\u5f52\u4e00\u5316\u201d\uff09<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u524d\u4eba\u65e9\u5c31\u5e2e\u6211\u4eec\u7b97\u597d\u4e86\u57fa\u7840\u6a21\u677f\uff08\u5f52\u4e00\u5316\u7cfb\u7edf\u51fd\u6570\uff09\uff01<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u67e5\u8868<\/strong>\uff1a\u65e2\u7136\u7b97\u51fa\u6765 N=3\uff0c\u76f4\u63a5\u67e5\u4e66\u4e0a\u7684\u8868\uff0c\u627e\u5230 N=3 \u5bf9\u5e94\u7684\u57fa\u7840\u516c\u5f0f\u662f\uff1aG_a(p) = \\frac{1}{p^3 + 2p^2 + 2p + 1}<\/li>\n\n\n\n<li><strong>\u53bb\u5f52\u4e00\u5316\uff08\u66ff\u6362\u53d8\u5f62\uff09<\/strong>\uff1a\u628a\u57fa\u7840\u516c\u5f0f\u91cc\u7684\u5b57\u6bcd p\uff0c\u5168\u90e8\u66ff\u6362\u6210 <strong>\\frac{s}{\\Omega_c}<\/strong>\u3002<\/li>\n\n\n\n<li><strong>\u6574\u7406\u7ed3\u679c<\/strong>\uff1a\u628a \\Omega_c = 10441 \u4ee3\u5165\u8fdb\u53bb\uff0c\u5c55\u5f00\u5316\u7b80\uff0c\u5c31\u5f97\u5230\u4e86\u7b2c\u4e8c\u5f20\u56fe\u6700\u4e0a\u9762\u7684\u90a3\u4e00\u957f\u4e32\u6700\u7ec8\u7684\u7cfb\u7edf\u51fd\u6570 H_a(s)\u3002<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">\u7b2c\u4e8c\u5f20\u56fe (1000020024.jpg) \u4e0b\u534a\u90e8\u5206\u5728\u8bf4\u4ec0\u4e48\uff1f<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u4e2d\u95f4\u7684\u4ee3\u7801\u548c\u56fe<\/strong>\uff1a\u8fd9\u662f\u7528 MATLAB \u8f6f\u4ef6\u628a\u4f60\u521a\u624d\u624b\u5de5\u7b97\u51fa\u6765\u7684\u53c2\u6570\u753b\u4e86\u51fa\u6765\u3002\u56fe 6-5 \u5c31\u662f\u8fd9\u4e2a\u6ee4\u6ce2\u5668\u7684\u9891\u54cd\u66f2\u7ebf\uff0c\u4f60\u53ef\u4ee5\u770b\u5230\u5b83\u5728\u524d\u7aef\u975e\u5e38\u5e73\u7f13\uff08\u8fd9\u5c31\u662f\u5df4\u7279\u6c83\u65af\u7684\u7279\u8272\uff09\uff0c\u7136\u540e\u8fc5\u901f\u4e0b\u964d\u3002<\/li>\n\n\n\n<li><strong>\u6700\u5e95\u4e0b\u7684\u4e00\u6bb5\u8bdd<\/strong>\uff1a\u8fd9\u662f\u4e00\u4e2a<strong>\u9884\u544a<\/strong>\uff01\u5b83\u8bf4\uff0c\u65e2\u7136\u6211\u4eec\u73b0\u5728\u5df2\u7ecf\u5343\u8f9b\u4e07\u82e6\u6c42\u51fa\u4e86\u6a21\u62df\u6ee4\u6ce2\u5668\u7684 H_a(s)\uff0c\u4e0b\u4e00\u6b65\uff0c\u6211\u4eec\u5c31\u8981\u901a\u8fc7\u67d0\u79cd\u6620\u5c04\u6cd5\u5219\uff08\u6bd4\u5982\u628a S \u5e73\u9762\u7684\u865a\u8f74\u6620\u5c04\u5230 Z \u5e73\u9762\u7684\u5355\u4f4d\u5706\u4e0a\uff09\uff0c\u628a\u5b83\u53d8\u6210\u6570\u5b57\u6ee4\u6ce2\u5668 H(z)\u3002\u8fd9\u624d\u662f\u6211\u4eec\u8fd9\u95e8\u8bfe\u7684\u6700\u7ec8\u76ee\u7684\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u516c\u5f0f\u600e\u4e48\u67e5<\/h3>\n\n\n\n<h3 class=\"wp-block-heading\">\u7b2c\u4e00\u6b65\uff1a\u660e\u786e\u5f52\u4e00\u5316\u7cfb\u7edf\u51fd\u6570\u7684\u957f\u76f8<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u5bf9\u4e8e\u5df4\u7279\u6c83\u65af\u4f4e\u901a\u6ee4\u6ce2\u5668\uff0c\u5b83\u7684\u5f52\u4e00\u5316\u7cfb\u7edf\u51fd\u6570 G_a(p) \u6c38\u8fdc\u957f\u8fd9\u4e2a\u6837\u5b50\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">G_a(p) = \\frac{1}{B(p)}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5206\u5b50\u6c38\u8fdc\u662f 1\uff0c\u6211\u4eec\u9700\u8981\u62fc\u51d1\u7684\u4ec5\u4ec5\u662f<strong>\u5206\u6bcd B(p)<\/strong>\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u7b2c\u4e8c\u6b65\uff1a\u770b\u61c2\u8868\u5934\u7684\u516c\u5f0f<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u4ed4\u7ec6\u770b\u8868\u683c\u6700\u4e0a\u9762\u90a3\u884c\u516c\u5f0f\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B(p) = p^N + b_{N-1}p^{N-1} + b_{N-2}p^{N-2} + \\dots + b_1p + b_0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u4e2a\u516c\u5f0f\u544a\u8bc9\u4f60\u4e09\u4ef6\u4e8b\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u5206\u6bcd\u662f\u4e00\u4e2a\u5173\u4e8e p \u7684\u591a\u9879\u5f0f\u3002<\/li>\n\n\n\n<li>\u591a\u9879\u5f0f\u7684\u6700\u9ad8\u6b21\u5e42\u5c31\u662f\u4f60\u7b97\u51fa\u6765\u7684<strong>\u9636\u6570 N<\/strong>\uff0c\u800c\u4e14 p^N \u524d\u9762\u7684\u7cfb\u6570\u6c38\u8fdc\u662f 1\uff08\u6240\u4ee5\u8868\u91cc\u6ca1\u5199\uff09\u3002<\/li>\n\n\n\n<li>\u8868\u683c\u91cc\u586b\u7684 b_0, b_1, b_2 \\dots \u8fd9\u4e9b\u6570\u5b57\uff0c\u5c31\u662f p \u7684\u9010\u6e10\u964d\u7ea7\u7684\u6b21\u5e42\u524d\u9762\u7684<strong>\u7cfb\u6570<\/strong>\u3002<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">\u7b2c\u4e09\u6b65\uff1a\u5b9e\u6218\u62fc\u56fe\uff08\u4ee5\u524d\u4e00\u9898 N=3 \u4e3a\u4f8b\uff09<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u6211\u4eec\u5728\u4e0a\u4e00\u9898\u7b97\u51fa\u4e86\u6ee4\u6ce2\u5668\u7684\u9636\u6570 N=3\u3002\u73b0\u5728\u6211\u4eec\u6765\u67e5\u8868\u62fc\u516c\u5f0f\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u5b9a\u4f4d\u884c<\/strong>\uff1a\u5728\u6700\u5de6\u8fb9\u201c\u9636\u6570 N\u201d\u8fd9\u4e00\u5217\uff0c\u627e\u5230 <strong>3<\/strong> \u5bf9\u5e94\u7684\u90a3\u4e00\u884c\u3002<\/li>\n\n\n\n<li><strong>\u6284\u7cfb\u6570<\/strong>\uff1a\u987a\u7740\u8fd9\u4e00\u884c\u5f80\u53f3\u770b\uff0c\u6284\u4e0b\u5bf9\u5e94\u7684\u6570\u5b57\uff1a\n<ul class=\"wp-block-list\">\n<li>b_0 = 1.0000<\/li>\n\n\n\n<li>b_1 = 2.0000<\/li>\n\n\n\n<li>b_2 = 2.0000<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u62fc\u88c5\u5206\u6bcd B(p)<\/strong>\uff1a\u6700\u9ad8\u6b21\u5e42\u662f p^3\u3002\u7136\u540e\u628a\u7cfb\u6570\u4f9d\u6b21\u6392\u597d\uff1aB(p) = p^3 + b_2 p^2 + b_1 p^1 + b_0\u628a\u6570\u5b57\u4ee3\u8fdb\u53bb\uff1aB(p) = p^3 + 2.0000p^2 + 2.0000p + 1.0000<\/li>\n\n\n\n<li><strong>\u5199\u51fa\u5b8c\u6574\u6a21\u677f<\/strong>\uff1a\u52a0\u4e0a\u6c38\u8fdc\u4e3a 1 \u7684\u5206\u5b50\uff0c\u4f60\u5c31\u5f97\u5230\u4e86\u5b8c\u6574\u7684\u5f52\u4e00\u5316\u51fd\u6570\uff1aG_a(p) = \\frac{1}{p^3 + 2p^2 + 2p + 1}<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">\u4f60\u770b\uff0c\u8fd9\u4e2a\u7ed3\u679c\u662f\u4e0d\u662f\u548c\u4e0a\u4e00\u5f20\u56fe\u4e2d\u4e66\u672c\u4e0a\u7ed9\u51fa\u7684 G_a(p) \u4e00\u6a21\u4e00\u6837\uff01<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u518d\u6765\u7ec3\u4e00\u4e2a\uff1a\u5982\u679c N=4 \u600e\u4e48\u67e5\uff1f<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u627e N=4 \u90a3\u884c\u3002<\/li>\n\n\n\n<li>\u6284\u7cfb\u6570\uff1ab_0 = 1.0000, b_1 = 2.6131, b_2 = 3.4142, b_3 = 2.6131\u3002<\/li>\n\n\n\n<li>\u62fc\u88c5\u591a\u9879\u5f0f\uff08\u6700\u9ad8\u6b21\u662f p^4\uff09\uff1aB(p) = p^4 + 2.6131p^3 + 3.4142p^2 + 2.6131p + 1<\/li>\n\n\n\n<li>\u5b8c\u6574\u51fd\u6570\uff1aG_a(p) = \\frac{1}{p^4 + 2.6131p^3 + 3.4142p^2 + 2.6131p + 1}<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u6700\u540e\u4e00\u6b65\u7684\u4f7f\u547d\uff1a<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8bb0\u4f4f\uff0c\u67e5\u8868\u5f97\u5230\u7684 G_a(p) \u53ea\u662f\u4e00\u4e2a\u901a\u7528\u7684\u201c\u6a21\u677f\u201d\uff08\u5f52\u4e00\u5316\u7684\uff09\u3002\u5728\u771f\u6b63\u7684\u8003\u8bd5\u9898\u91cc\uff0c\u62ff\u5230\u8fd9\u4e2a\u5f0f\u5b50\u540e\uff0c\u4f60\u8fd8\u9700\u8981\u505a\u6700\u540e\u4e00\u6b65\u201c\u53bb\u5f52\u4e00\u5316\u201d\u2014\u2014\u5c31\u662f\u628a\u5f0f\u5b50\u91cc\u6240\u6709\u7684 p \u5f3a\u5236\u66ff\u6362\u6210 <strong>\\frac{s}{\\Omega_c}<\/strong>\uff08\\Omega_c \u662f\u4f60\u524d\u9762\u7b97\u51fa\u6765\u7684\u622a\u6b62\u9891\u7387\uff09\uff0c\u5316\u7b80\u540e\u624d\u80fd\u5f97\u5230\u6700\u7ec8\u7684\u6a21\u62df\u6ee4\u6ce2\u5668\u7cfb\u7edf\u51fd\u6570 H_a(s)\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u8109\u51b2\u54cd\u5e94\u4e0d\u53d8\u6cd5<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>p176<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u4e2a\u4f8b\u9898\uff08\u4f8b 6-3\uff09\u975e\u5e38\u7ecf\u5178\uff0c\u5b83\u6f14\u793a\u4e86\u5c06<strong>\u6a21\u62df\u6ee4\u6ce2\u5668<\/strong>\u8f6c\u6362\u4e3a<strong>\u6570\u5b57\u6ee4\u6ce2\u5668<\/strong>\u7684\u7b2c\u4e00\u79cd\u6838\u5fc3\u65b9\u6cd5\uff1a<strong>\u8109\u51b2\u54cd\u5e94\u4e0d\u53d8\u6cd5<\/strong>\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u4e2a\u65b9\u6cd5\u7684\u540d\u5b57\u542c\u8d77\u6765\u5f88\u9ad8\u7ea7\uff0c\u4f46\u5b83\u7684\u6838\u5fc3\u539f\u7406\u7528\u5927\u767d\u8bdd\u8bb2\u5c31\u662f\uff1a<strong>\u8ba9\u6570\u5b57\u6ee4\u6ce2\u5668\u7684\u5355\u4f4d\u8109\u51b2\u54cd\u5e94 h(n)\uff0c\u5b8c\u5168\u7b49\u4e8e\u6a21\u62df\u6ee4\u6ce2\u5668\u5355\u4f4d\u51b2\u6fc0\u54cd\u5e94 h_a(t) \u7684\u7b49\u95f4\u9694\u91c7\u6837<\/strong>\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u843d\u5b9e\u5230\u505a\u9898\u4e0a\uff0c\u8fd9\u4f9d\u7136\u662f\u4e00\u4e2a\u6781\u5176\u6b7b\u677f\u7684\u201c\u4e09\u6b65\u8d70\u201d\u5957\u8def\u3002\u6211\u5e26\u4f60\u4e00\u6b65\u6b65\u62c6\u89e3\u4e66\u4e0a\u7684\u8fc7\u7a0b\uff1a<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u7b2c\u4e00\u6b65\uff1a\u5c06 H_a(s) \u5c55\u5f00\u4e3a\u90e8\u5206\u5206\u5f0f\uff08\u8001\u670b\u53cb\u53c8\u6765\u4e86\uff09<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u9898\u76ee\u7ed9\u51fa\u7684\u6a21\u62df\u6ee4\u6ce2\u5668\u7cfb\u7edf\u51fd\u6570\u662f\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">H_a(s) = \\frac{3}{s^2 + 4s + 3}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6211\u4eec\u9700\u8981\u628a\u5b83\u62c6\u89e3\u6210\u4e00\u6b21\u9879\u76f8\u52a0\u7684\u5f62\u5f0f\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u56e0\u5f0f\u5206\u89e3\u5206\u6bcd<\/strong>\uff1as^2 + 4s + 3 = (s+1)(s+3)\u3002<\/li>\n\n\n\n<li><strong>\u8bbe\u672a\u77e5\u6570\u62c6\u5206<\/strong>\uff1a\u8bbe H_a(s) = \\frac{A}{s+1} + \\frac{B}{s+3}\u3002<\/li>\n\n\n\n<li><strong>\u7528\u201c\u906e\u6321\u6cd5\u201d\u6c42 A \u548c B<\/strong>\uff08\u8fd9\u62db\u4f60\u5df2\u7ecf\u4f1a\u4e86\uff01\uff09\uff1a\n<ul class=\"wp-block-list\">\n<li>\u6c42 A\uff1a\u906e\u4f4f (s+1)\uff0c\u5269\u4e0b \\frac{3}{s+3}\u3002\u4ee4 s = -1\uff0c\u4ee3\u5165\u5f97 A = \\frac{3}{-1+3} = \\frac{3}{2}\u3002<\/li>\n\n\n\n<li>\u6c42 B\uff1a\u906e\u4f4f (s+3)\uff0c\u5269\u4e0b \\frac{3}{s+1}\u3002\u4ee4 s = -3\uff0c\u4ee3\u5165\u5f97 B = \\frac{3}{-3+1} = -\\frac{3}{2}\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">\u628a\u516c\u56e0\u6570 \\frac{3}{2} \u63d0\u51fa\u6765\uff0c\u5c31\u5f97\u5230\u4e86\u4e66\u4e0a\u7684\u7b2c\u4e00\u6b65\u7ed3\u679c\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">H_a(s) = \\frac{3}{2} \\left( \\frac{1}{s+1} &#8211; \\frac{1}{s+3} \\right)<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u7b2c\u4e8c\u6b65\uff1a\u5957\u7528\u201c\u8109\u51b2\u54cd\u5e94\u4e0d\u53d8\u6cd5\u201d\u7684\u8f6c\u6362\u5b57\u5178<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u662f\u8fd9\u9053\u9898\u552f\u4e00\u7684\u201c\u65b0\u77e5\u8bc6\u70b9\u201d\u3002\u4f60\u9700\u8981\u8bb0\u4f4f\u4e00\u4e2a\u6b7b\u516c\u5f0f\uff08\u8f6c\u6362\u5b57\u5178\uff09\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u53ea\u8981\u5728 S \u57df\uff08\u6a21\u62df\uff09\u91cc\u770b\u5230 \\frac{1}{s &#8211; s_k}\uff0c\u5728 Z \u57df\uff08\u6570\u5b57\uff09\u91cc\u5c31\u76f4\u63a5\u66ff\u6362\u6210 \\frac{1}{1 &#8211; e^{s_k T} z^{-1}}<\/strong>\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>(T \u662f\u91c7\u6837\u5468\u671f\uff0c\u4e5f\u662f\u9898\u76ee\u4e2d\u8bbe\u5b9a\u7684\u5e38\u91cf)<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u73b0\u5728\u6211\u4eec\u5bf9\u7740\u5b57\u5178\u7ffb\u8bd1\u521a\u521a\u62c6\u597d\u7684\u5f0f\u5b50\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u7b2c\u4e00\u9879\uff1a\\frac{1}{s+1} = \\frac{1}{s &#8211; (-1)}\uff0c\u8fd9\u91cc s_k = -1\u3002\u7ffb\u8bd1\u8fc7\u6765\u5c31\u662f \\frac{1}{1 &#8211; e^{-T} z^{-1}}\u3002<\/li>\n\n\n\n<li>\u7b2c\u4e8c\u9879\uff1a\\frac{1}{s+3} = \\frac{1}{s &#8211; (-3)}\uff0c\u8fd9\u91cc s_k = -3\u3002\u7ffb\u8bd1\u8fc7\u6765\u5c31\u662f \\frac{1}{1 &#8211; e^{-3T} z^{-1}}\u3002<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u628a\u5b83\u4eec\u62fc\u56de\u53bb\uff0c\u6570\u5b57\u6ee4\u6ce2\u5668\u7684\u7cfb\u7edf\u51fd\u6570 H(z) \u5c31\u51fa\u6765\u4e86\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">H(z) = \\frac{3}{2} \\left( \\frac{1}{1 &#8211; e^{-T} z^{-1}} &#8211; \\frac{1}{1 &#8211; e^{-3T} z^{-1}} \\right)<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u7b2c\u4e09\u6b65\uff1a\u901a\u5206\u5316\u7b80\uff08\u7eaf\u4f53\u529b\u6d3b\uff09<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e66\u4e0a\u7d27\u63a5\u7740\u628a\u62ec\u53f7\u91cc\u7684\u4e24\u9879\u8fdb\u884c\u4e86\u901a\u5206\u76f8\u51cf\uff0c\u5408\u5e76\u6210\u4e86\u4e00\u4e2a\u5927\u5206\u5f0f\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u5206\u5b50<\/strong>\uff1a\u4ea4\u53c9\u76f8\u4e58\u76f8\u51cf\uff0c(1 &#8211; e^{-3T} z^{-1}) &#8211; (1 &#8211; e^{-T} z^{-1}) = (e^{-T} &#8211; e^{-3T}) z^{-1}\u3002<\/li>\n\n\n\n<li><strong>\u5206\u6bcd<\/strong>\uff1a\u4e24\u4e2a\u5206\u6bcd\u76f8\u4e58\uff0c\u5c55\u5f00\u540e\u5f97\u5230 1 &#8211; (e^{-T} + e^{-3T})z^{-1} + e^{-4T}z^{-2}\u3002<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u628a\u5916\u9762\u7684 \\frac{3}{2} \u4e58\u5230\u5206\u5b50\u4e0a\uff0c\u5c31\u5f97\u5230\u4e86\u4e66\u4e0a\u5316\u7b80\u540e\u7684\u6700\u7ec8\u516c\u5f0f\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">H(z) = \\frac{\\frac{3}{2} z^{-1} (e^{-T} &#8211; e^{-3T})}{1 &#8211; z^{-1}(e^{-T} + e^{-3T}) + z^{-2}e^{-4T}}<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u7b2c\u56db\u6b65\uff1a\u4ee3\u5165\u5177\u4f53\u7684\u91c7\u6837\u5468\u671f T<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u6700\u540e\uff0c\u4e66\u4e0a\u5206\u522b\u5047\u8bbe\u4e86 T=1s \u548c T=0.1s\uff0c\u7528\u8ba1\u7b97\u5668\u7b97\u51fa\u5177\u4f53\u7684\u6570\u503c\u4ee3\u5165\u516c\u5f0f\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5f53 T=1s \u65f6\uff0c\u7b97\u51fa\u6765 H_1(z) = \\frac{0.47714 z^{-1}}{1 &#8211; 0.41767 z^{-1} + 0.018316 z^{-2}}\u3002<\/li>\n\n\n\n<li>\u5f53 T=0.1s \u65f6\uff0c\u7b97\u51fa\u6765 H_2(z) = \\frac{0.24603 z^{-1}}{1 &#8211; 1.64566 z^{-1} + 0.67032 z^{-2}}\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83d\udca1 \u7075\u9b42\u62f7\u95ee\uff1a\u4e3a\u4ec0\u4e48\u8981\u7b97\u4e24\u4e2a\u4e0d\u540c\u7684 T\uff1f<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u7ffb\u5230\u7b2c\u4e8c\u5f20\u56fe\uff0c\u770b\u4e0b\u9762\u7684\u9891\u7387\u7279\u6027\u66f2\u7ebf\u56fe\uff0c\u8fd9\u624d\u662f\u51fa\u8fd9\u9053\u9898\u7684\u771f\u6b63\u76ee\u7684\uff01<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e66\u4e0a\u6307\u51fa\u4e86\u8109\u51b2\u54cd\u5e94\u4e0d\u53d8\u6cd5\u7684\u4e00\u4e2a<strong>\u81f4\u547d\u7f3a\u70b9<\/strong>\uff1a<strong>\u9891\u8c31\u6df7\u53e0\u5931\u771f<\/strong>\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u56e0\u4e3a\u9898\u76ee\u7ed9\u7684\u6a21\u62df\u6ee4\u6ce2\u5668 H_a(s) \u5e76\u4e0d\u662f\u4e00\u4e2a\u201c\u7edd\u5bf9\u5e26\u9650\u201d\u7684\u4fe1\u53f7\uff08\u5b83\u7684\u9ad8\u9891\u90e8\u5206\u6ca1\u6709\u5b8c\u5168\u8870\u51cf\u5230 0\uff09\uff0c\u6240\u4ee5\u5728\u8fdb\u884c\u6570\u5b57\u91c7\u6837\u65f6\uff0c\u5fc5\u7136\u4f1a\u53d1\u751f\u9ad8\u9891\u4fe1\u53f7\u6298\u53e0\u6df7\u53e0\u7684\u73b0\u8c61\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u4ece\u56fe (b) \u53ef\u4ee5\u660e\u663e\u770b\u51fa\uff0cT \u8d8a\u5927\uff08\u6bd4\u5982 T=1s\uff09\uff0c\u91c7\u6837\u9891\u7387\u8d8a\u4f4e\uff0c\u5931\u771f\u5c31\u8d8a\u4e25\u91cd\u3002<\/li>\n\n\n\n<li>\u5373\u4f7f\u628a T \u7f29\u5c0f\u5230 0.1s\uff0c\u5931\u771f\u867d\u7136\u51cf\u8f7b\u4e86\uff0c\u4f46\u4f9d\u7136\u5b58\u5728\u3002<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u6b63\u662f\u4e3a\u4e86\u514b\u670d\u8fd9\u4e2a\u8ba8\u538c\u7684\u201c\u9891\u8c31\u6df7\u53e0\u201d\uff0c\u5de5\u7a0b\u5e08\u4eec\u624d\u53d1\u660e\u4e86\u7b2c\u4e8c\u5f20\u56fe\u6700\u4e0b\u65b9\u6807\u9898\u6240\u5199\u7684\u2014\u2014<strong>\u53cc\u7ebf\u6027\u53d8\u6362\u6cd5<\/strong>\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e0d\u662f\u7684\uff01\u8fd9\u662f\u4e00\u4e2a\u5728\u521d\u5b66\u65f6\u975e\u5e38\u5bb9\u6613\u641e\u9519\u7684\u903b\u8f91\u9677\u9631\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u906e\u6321\u6cd5\uff08\u7559\u6570\u6cd5\uff09\u7684\u6838\u5fc3\u53e3\u8bc0\u662f\uff1a<strong>\u4ee4\u201c\u88ab\u906e\u4f4f\u7684\u5206\u6bcd\u201d\u7b49\u4e8e 0 \u6c42\u51fa\u6781\u70b9\uff0c\u7136\u540e\u4ee3\u5165\u201c\u5269\u4e0b\u7684\u5f0f\u5b50\u201d\u4e2d\u8fdb\u884c\u8ba1\u7b97\u3002<\/strong> \u7edd\u5bf9\u4e0d\u662f\u4ee4\u5269\u4e0b\u7684\u5f0f\u5b50\u7b49\u4e8e 0\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e3a\u4e86\u8ba9\u4f60\u5f7b\u5e95\u8bb0\u4f4f\uff0c\u4e14\u4e0d\u518d\u6b7b\u8bb0\u786c\u80cc\uff0c\u6211\u7ed9\u4f60\u62c6\u89e3\u4e00\u4e0b\u8fd9\u4e2a\u201c\u906e\u6321\u6cd5\u201d\u80cc\u540e\u7684\u6570\u5b66\u539f\u7406\u3002\u5b83\u5176\u5b9e\u6839\u672c\u4e0d\u662f\u4ec0\u4e48\u9b54\u672f\uff0c\u5c31\u662f\u5c0f\u5b66\u5b66\u8fc7\u7684<strong>\u7b49\u5f0f\u4e24\u8fb9\u540c\u4e58\u4e00\u4e2a\u6570<\/strong>\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u906e\u6321\u6cd5\u80cc\u540e\u7684\u771f\u6b63\u539f\u7406<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u6211\u4eec\u4ee5\u56fe\u7247\u91cc\u7684\u5f0f\u5b50\u4e3a\u4f8b\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\frac{3}{(s+1)(s+3)} = \\frac{A}{s+1} + \\frac{B}{s+3}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u73b0\u5728\u6211\u4eec\u7684\u76ee\u6807\u662f\u6c42\u51fa A\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e3a\u4e86\u628a A \u5355\u72ec\u201c\u5265\u79bb\u201d\u51fa\u6765\uff0c\u6211\u4eec\u5728<strong>\u7b49\u53f7\u5de6\u53f3\u4e24\u8fb9\uff0c\u540c\u65f6\u4e58\u4ee5 A \u7684\u5206\u6bcd\uff0c\u4e5f\u5c31\u662f (s+1)<\/strong>\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u7b49\u5f0f\u5de6\u8fb9<\/strong>\uff1a\u4e58\u4ee5 (s+1) \u540e\uff0c(s+1) \u88ab\u7ea6\u6389\u4e86\uff0c<strong>\u5269\u4e0b<\/strong>\uff1a \\frac{3}{s+3}<\/li>\n\n\n\n<li><strong>\u7b49\u5f0f\u53f3\u8fb9<\/strong>\uff1a\u4e24\u9879\u90fd\u8981\u4e58\u4ee5 (s+1)\uff0c\u53d8\u6210\u4e86\uff1a A + \\frac{B(s+1)}{s+3}<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u6240\u4ee5\u7b49\u5f0f\u53d8\u6210\u4e86\u8fd9\u6837\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\frac{3}{s+3} = A + \\frac{B(s+1)}{s+3}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u73b0\u5728\uff0c\u5173\u952e\u7684\u4e00\u6b65\u6765\u4e86\uff01\u6211\u4eec\u60f3\u7b49\u5f0f\u53f3\u8fb9\u53ea\u5269\u4e0b A\uff0c\u600e\u4e48\u628a\u5e26\u6709 B \u7684\u90a3\u4e00\u957f\u4e32\u76f4\u63a5\u6d88\u706d\u6389\uff1f<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5f88\u7b80\u5355\uff0c<strong>\u53ea\u8981\u8ba9 (s+1) = 0 \u5c31\u53ef\u4ee5\u4e86\uff01<\/strong> \u4e5f\u5c31\u662f\u4ee4 s = -1\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u628a s = -1 \u4ee3\u5165\u4e0a\u9762\u7684\u7b49\u5f0f\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u7b49\u5f0f\u53f3\u8fb9\u5e26\u6709 B \u7684\u9879\u56e0\u4e3a\u5206\u5b50\u662f 0\uff0c\u76f4\u63a5\u7070\u98de\u70df\u706d\uff0c\u53ea\u5269\u4e0b\u4e00\u4e2a\u5e72\u5e72\u51c0\u51c0\u7684 A\u3002<\/li>\n\n\n\n<li>\u7b49\u5f0f\u5de6\u8fb9\u628a s = -1 \u4ee3\u5165\u8fdb\u53bb\uff0c\u5c31\u53d8\u6210\u4e86 \\frac{3}{-1+3}\u3002<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u6240\u4ee5\uff0c A = \\frac{3}{-1+3} = \\frac{3}{2} \u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u603b\u7ed3\u201c\u906e\u6321\u6cd5\u201d\u7684\u52a8\u4f5c\u62c6\u89e3<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u4f60\u770b\uff0c\u8fd9\u5957\u4e25\u683c\u7684\u6570\u5b66\u63a8\u5bfc\uff0c\u5728\u505a\u9898\u65f6\u88ab\u524d\u8f88\u4eec\u7b80\u5316\u6210\u4e86\u6781\u5176\u201c\u65e0\u8111\u201d\u7684<strong>\u906e\u6321\u6cd5\u53e3\u8bc0<\/strong>\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u4f60\u8981\u627e\u8c01\u7684\u5206\u5b50\uff08\u6bd4\u5982 A\uff09\uff0c\u5c31\u770b<strong>\u8c01\u7684\u5206\u6bcd<\/strong>\uff08(s+1)\uff09\u3002<\/li>\n\n\n\n<li><strong>\u4ee4\u8fd9\u4e2a\u5206\u6bcd\u7b49\u4e8e 0<\/strong>\uff08\u4ee4 s+1=0\uff0c\u5f97\u5230 s=-1\uff09\u3002\u8fd9\u4e00\u6b65\u7684\u672c\u8d28\uff0c\u662f\u4e3a\u4e86\u5728\u7b49\u5f0f\u53f3\u8fb9\u6d88\u706d\u6389\u5176\u4ed6\u7684\u672a\u77e5\u6570\u3002<\/li>\n\n\n\n<li>\u53bb\u603b\u5f0f\u5b50\u91cc\uff0c\u628a\u8fd9\u4e2a\u5206\u6bcd<strong>\u7528\u624b\u6342\u4f4f\uff08\u906e\u6389\uff09<\/strong>\u3002\u8fd9\u4e00\u6b65\u7684\u672c\u8d28\uff0c\u662f\u7b49\u5f0f\u5de6\u8fb9\u7ea6\u5206\u62b5\u6d88\u7684\u8fc7\u7a0b\u3002<\/li>\n\n\n\n<li>\u628a\u521a\u521a\u6c42\u51fa\u6765\u7684 s=-1\uff0c<strong>\u4ee3\u5165\u5230\u6ca1\u6709\u88ab\u906e\u4f4f\u7684\u3001\u5269\u4e0b\u7684\u6240\u6709\u90e8\u5206\u91cc\u53bb\u7b97<\/strong>\u3002\u7b97\u51fa\u6765\u7684\u7ed3\u679c\u5c31\u662f\u6211\u4eec\u8981\u7684\u5206\u5b50\u3002<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">\u5343\u4e07\u522b\u628a\u201c\u5269\u4e0b\u7684\u5f0f\u5b50\u7b49\u4e8e 0\u201d\u548c\u201c\u906e\u4f4f\u7684\u5f0f\u5b50\u7b49\u4e8e 0\u201d\u641e\u53cd\u5566\uff01<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5176\u4ed6 \u5224\u65ad\u7ebf\u6027\u65f6\u4e0d\u53d8\u7cfb\u7edf \u4f8b\u9898 2\uff1a\u4ec0\u4e48\u6837\u7684\u624d\u662f\u771f\u6b63\u7684 LTI \u7cfb\u7edf\uff1f \u4e3a\u4e86\u5bf9\u6bd4\uff0c\u6211\u4eec\u770b\u4e00\u4e2a\u6700\u7b80\u5355\u7684\u7eaf LTI [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[20],"tags":[],"class_list":["post-479","post","type-post","status-publish","format-standard","hentry","category-others"],"_links":{"self":[{"href":"https:\/\/www.millscience.cn\/index.php\/wp-json\/wp\/v2\/posts\/479","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.millscience.cn\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.millscience.cn\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.millscience.cn\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.millscience.cn\/index.php\/wp-json\/wp\/v2\/comments?post=479"}],"version-history":[{"count":1,"href":"https:\/\/www.millscience.cn\/index.php\/wp-json\/wp\/v2\/posts\/479\/revisions"}],"predecessor-version":[{"id":491,"href":"https:\/\/www.millscience.cn\/index.php\/wp-json\/wp\/v2\/posts\/479\/revisions\/491"}],"wp:attachment":[{"href":"https:\/\/www.millscience.cn\/index.php\/wp-json\/wp\/v2\/media?parent=479"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.millscience.cn\/index.php\/wp-json\/wp\/v2\/categories?post=479"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.millscience.cn\/index.php\/wp-json\/wp\/v2\/tags?post=479"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}