{"id":68712,"date":"2026-01-30T15:25:14","date_gmt":"2026-01-30T07:25:14","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/68712.html"},"modified":"2026-01-30T15:25:14","modified_gmt":"2026-01-30T07:25:14","slug":"iir%e6%bb%a4%e6%b3%a2%e5%99%a8%e6%a0%b8%e5%bf%83%e5%8e%9f%e7%90%86%e6%b7%b1%e5%8c%96%ef%bc%9a%e4%bb%8e%e5%b7%ae%e5%88%86%e6%96%b9%e7%a8%8b%e5%88%b0%e5%b7%a5%e4%b8%9a%e7%ba%a7%e5%ae%9e%e7%8e%b0","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/68712.html","title":{"rendered":"IIR\u6ee4\u6ce2\u5668\u6838\u5fc3\u539f\u7406\u6df1\u5316\uff1a\u4ece\u5dee\u5206\u65b9\u7a0b\u5230\u5de5\u4e1a\u7ea7\u5b9e\u73b0"},"content":{"rendered":"

\u5d4c\u5165\u5f0fDSP\u5f00\u53d1\u8005\u548c\u7535\u5b50\u4fe1\u606f\u5b66\u4e60\u8005\u5e38\u9047\u8fd9\u7c7b\u75db\u70b9：\u4f20\u611f\u5668\u4fe1\u53f7\u6df7\u6742\u566a\u58f0\u65f6，\u57fa\u7840\u6ee4\u6ce2\u6548\u679c\u6709\u9650；\u60f3\u7528\u4e0aIIR\u6ee4\u6ce2\u5668，\u5374\u88ab\u5dee\u5206\u65b9\u7a0b\u3001\u5b9e\u73b0\u7ed3\u6784\u3001\u7cfb\u6570\u8bbe\u8ba1\u7b49\u95ee\u9898\u96be\u4f4f，\u7167\u642c\u4ee3\u7801\u6548\u679c\u5dee\u4e14\u96be\u6392\u67e5\u3002\u5176\u5b9eIIR\u6ee4\u6ce2\u5668\u6838\u5fc3\u662f\u201c\u9012\u63a8\u6ee4\u6ce2+\u53cd\u9988\u8865\u507f\u201d，\u638c\u63e1\u5dee\u5206\u65b9\u7a0b\u3001\u5b9e\u73b0\u7ed3\u6784\u3001\u7cfb\u6570\u8bbe\u8ba1\u4e09\u5927\u8981\u70b9\u5373\u53ef\u843d\u5730\u5de5\u4e1a\u7ea7\u5e94\u7528\u3002\u672c\u6587\u4ece\u539f\u7406\u5230\u5b9e\u6218\u5c42\u5c42\u62c6\u89e3：\u6df1\u5316N\u9636IIR\u5dee\u5206\u65b9\u7a0b\u4e0e\u9012\u63a8\u903b\u8f91，\u5bf9\u6bd4\u76f4\u63a5I\/II\u578b\u5dee\u5f02\u53ca\u5185\u5b58\u4f18\u52bf，\u6f14\u793aPython\u5de5\u4e1a\u7ea7\u7cfb\u6570\u8bbe\u8ba1，\u843d\u5730C\u8bed\u8a00\u5b9e\u73b0\u4e0e\u5b9e\u6218\u9a8c\u8bc1，\u5e2e\u4f60\u638c\u63e1IIR\u7684\u8bbe\u8ba1\u4e0e\u5de5\u7a0b\u5316\u5e94\u7528！<\/p>\n

\u4e00\u3001\u539f\u7406\u62c6\u89e3：N\u9636IIR\u6ee4\u6ce2\u5668\u7684\u6838\u5fc3\u903b\u8f91<\/h3>\n

IIR（\u65e0\u9650\u957f\u5355\u4f4d\u51b2\u6fc0\u54cd\u5e94）\u6ee4\u6ce2\u5668\u7684\u6838\u5fc3\u7279\u5f81\u662f\u8f93\u51fa\u4f9d\u8d56\u5f53\u524d\/\u5386\u53f2\u8f93\u5165\u53ca\u5386\u53f2\u8f93\u51fa，\u8fd9\u4e0e\u4ec5\u4f9d\u8d56\u8f93\u5165\u7684FIR\u6ee4\u6ce2\u5668\u5f62\u6210\u5173\u952e\u533a\u522b\u3002\u53cd\u9988\u73af\u8282\u4f7f\u5176\u80fd\u4ee5\u66f4\u4f4e\u9636\u6570\u5b9e\u73b0\u5f3a\u9891\u7387\u9009\u62e9\u7279\u6027，\u76f8\u540c\u6027\u80fd\u4e0b\u66f4\u7701\u8ba1\u7b97\u8d44\u6e90，\u9002\u914d\u5d4c\u5165\u5f0f\u8d44\u6e90\u7d27\u5f20\u573a\u666f\u3002<\/p>\n

1. \u4ece\u4e00\u9636\u5230N\u9636：\u5dee\u5206\u65b9\u7a0b\u7684\u6f14\u53d8<\/h4>\n

\u7406\u89e3N\u9636IIR\u53ef\u4ece\u4e00\u9636\u5165\u624b，\u5176\u5dee\u5206\u65b9\u7a0b\u76f4\u89c2\u6613\u61c2：<\/p>\n

y(n) = a\u2080x(n) + a\u2081x(n-1) – b\u2081y(n-1)<\/p>\n

\u5404\u7b26\u53f7\u542b\u4e49：x(n)\u4e3a\u5f53\u524d\u8f93\u5165\u3001x(n-1)\u4e3a\u524d\u4e00\u65f6\u523b\u8f93\u5165；y(n)\u4e3a\u5f53\u524d\u8f93\u51fa\u3001y(n-1)\u4e3a\u524d\u4e00\u65f6\u523b\u8f93\u51fa；a\u2080\u3001a\u2081\u4e3a\u8f93\u5165（\u524d\u9988）\u7cfb\u6570，b\u2081\u4e3a\u8f93\u51fa（\u53cd\u9988）\u7cfb\u6570\u3002\u516c\u5f0f\u76f4\u63a5\u4f53\u73b0IIR\u7684\u53cd\u9988\u7279\u6027\u2014\u2014\u8f93\u51fa\u5173\u8054\u8f93\u5165\u4e0e\u8f93\u51fa\u7684\u5386\u53f2\u4fe1\u606f\u3002<\/p>\n

\u63a8\u5e7f\u5230N\u9636，\u6807\u51c6\u5dee\u5206\u65b9\u7a0b\u4e3a：<\/p>\n

y(n) = \u03a3（\u4ecek=0\u5230N）a\u2096x(n-k) – \u03a3（\u4ecek=1\u5230N）b\u2096y(n-k)<\/p>\n

\u5173\u952e\u7ec6\u8282：\u8f93\u5165\u7cfb\u6570a\u2096\u5171N+1\u4e2a（k=0N），\u8f93\u51fa\u7cfb\u6570b\u2096\u5171N\u4e2a（k=1<\/sub>N，b\u2080\u5f52\u4e00\u5316\u4e3a1）\u3002\u8be5\u65b9\u7a0b\u662fIIR\u8bbe\u8ba1\u4e0e\u5b9e\u73b0\u7684\u6838\u5fc3，\u6240\u6709\u5de5\u7a0b\u5316\u5b9e\u73b0\u5747\u57fa\u4e8e\u6b64\u9012\u63a8\u3002<\/p>\n

\u9012\u63a8\u6838\u5fc3\u903b\u8f91：\u83b7\u53d6y(n)\u9700\u4e09\u7c7b\u4fe1\u606f\u2014\u2014\u5f53\u524d\/\u5386\u53f2\u8f93\u5165x(n)x(n-N)\u3001\u5386\u53f2\u8f93\u51fay(n-1)<\/sub>y(n-N)\u3001\u9884\u8bbe\u7cfb\u6570a\u2080a\u2099\u4e0eb\u2081<\/sub>b\u2099\u3002<\/p>\n

\u4e3e\u4e2a\u5177\u4f53\u4f8b\u5b50，\u4e8c\u9636IIR\u6ee4\u6ce2\u5668\u7684\u5dee\u5206\u65b9\u7a0b\u4e3a：<\/p>\n

y(n) = a\u2080x(n) + a\u2081x(n-1) + a\u2082x(n-2) – b\u2081y(n-1) – b\u2082y(n-2)<\/p>\n

\u4ee5\u4e8c\u9636\u4e3a\u4f8b，\u9012\u63a8\u6d41\u7a0b\u4e3a：1. \u7f13\u5b58x(n-1)\u3001x(n-2)\u4e0ey(n-1)\u3001y(n-2)；2. \u8f93\u5165x(n)\u540e\u4ee3\u5165\u65b9\u7a0b\u8ba1\u7b97y(n)；3. \u66f4\u65b0\u7f13\u5b58（\u65b0\u8f93\u5165\/\u8f93\u51fa\u8986\u76d6\u65e7\u6570\u636e），\u4e3a\u4e0b\u4e00\u6b21\u8ba1\u7b97\u51c6\u5907\u3002\u8fd9\u662f\u5d4c\u5165\u5f0f\u5b9e\u73b0IIR\u7684\u6838\u5fc3\u6d41\u7a0b\u3002<\/p>\n

\u4e8c\u3001\u5de5\u7a0b\u5316\u5206\u6790：\u76f4\u63a5I\u578b\u4e0e\u76f4\u63a5II\u578b\u7684\u5b9e\u73b0\u5dee\u5f02<\/h3>\n

\u76f4\u63a5I\u578b\u4e0e\u76f4\u63a5II\u578b\u662fIIR\u6700\u5e38\u7528\u7684\u4e24\u79cd\u5b9e\u73b0\u7ed3\u6784，\u6838\u5fc3\u5dee\u5f02\u5728\u4e8e\u5ef6\u8fdf\u5355\u5143\u6570\u91cf\u4e0e\u590d\u7528\u903b\u8f91，\u76f4\u63a5\u51b3\u5b9a\u5185\u5b58\u5360\u7528\u2014\u2014\u5d4c\u5165\u5f0fRAM\u8d44\u6e90\u7d27\u5f20，\u9009\u578b\u5bf9\u8d44\u6e90\u5229\u7528\u7387\u81f3\u5173\u91cd\u8981\u3002<\/p>\n

1. \u76f4\u63a5I\u578b：\u76f4\u89c2\u4f46\u5185\u5b58\u5360\u7528\u9ad8<\/h4>\n

\u76f4\u63a5I\u578b\u4e3a\u201c\u76f4\u8bd1\u5f0f\u201d\u7ed3\u6784，\u5bf9\u5e94\u5dee\u5206\u65b9\u7a0b\u903b\u8f91，\u542b\u4e24\u6761\u72ec\u7acb\u5ef6\u8fdf\u94fe：\u4e00\u6761\u7f13\u5b58\u5386\u53f2\u8f93\u5165x(n-k)，\u53e6\u4e00\u6761\u7f13\u5b58\u5386\u53f2\u8f93\u51fay(n-k)\u3002<\/p>\n

N\u9636\u76f4\u63a5I\u578b\u97002N\u4e2a\u5ef6\u8fdf\u5355\u5143（N\u4e2a\u5b58\u8f93\u5165\u3001N\u4e2a\u5b58\u8f93\u51fa），\u4f18\u52bf\u662f\u903b\u8f91\u76f4\u89c2\u3001\u6613\u8c03\u8bd5，\u9002\u5408\u5165\u95e8；\u7f3a\u70b9\u662f\u5185\u5b58\u5360\u7528\u9ad8，\u9ad8\u9636\u6ee4\u6ce2\u5668\u572851\u5355\u7247\u673a\u3001\u5c0f\u578bSTM32\u7b49\u8d44\u6e90\u7d27\u5f20\u573a\u666f\u9002\u7528\u6027\u5dee\u3002<\/p>\n

2. \u76f4\u63a5II\u578b：\u5185\u5b58\u4f18\u5316\u7684\u6838\u5fc3\u9009\u62e9<\/h4>\n

\u76f4\u63a5II\u578b\u901a\u8fc7z\u57df\u53d8\u6362\u4e0e\u7ed3\u6784\u91cd\u6392，\u5c06\u4e24\u6761\u5ef6\u8fdf\u94fe\u5408\u5e76\u4e3a\u4e00\u6761，\u5b9e\u73b0\u5ef6\u8fdf\u5355\u5143\u5171\u4eab\u590d\u7528，\u5927\u5e45\u964d\u4f4e\u5185\u5b58\u5360\u7528\u3002<\/p>\n

N\u9636\u76f4\u63a5II\u578b\u4ec5\u9700N\u4e2a\u5ef6\u8fdf\u5355\u5143，\u5185\u5b58\u5360\u7528\u51cf\u534a！\u4ee58\u9636float\u578b\u6ee4\u6ce2\u5668\u4e3a\u4f8b，\u76f4\u63a5I\u578b\u970064\u5b57\u8282（16\u4e2a\u5355\u5143），\u76f4\u63a5II\u578b\u4ec5\u970032\u5b57\u8282（8\u4e2a\u5355\u5143），\u8d44\u6e90\u8282\u7701\u6548\u679c\u663e\u8457\u3002<\/p>\n

\u9009\u578b\u5efa\u8bae：\u5d4c\u5165\u5f0f\u573a\u666f\u4f18\u5148\u9009\u76f4\u63a5II\u578b，\u5c24\u5176\u8d44\u6e90\u7d27\u5f20\u6216\u9ad8\u9636\u6ee4\u6ce2\u573a\u666f；\u4ec5\u4f4e\u9636（1~2\u9636）\u3001\u8c03\u8bd5\u521d\u671f\u9700\u76f4\u89c2\u9a8c\u8bc1\u903b\u8f91\u65f6，\u53ef\u8003\u8651\u76f4\u63a5I\u578b\u3002<\/p>\n

\u4e09\u3001\u5173\u952e\u6b65\u9aa4：\u7528Python\u8bbe\u8ba1\u5de5\u4e1a\u7ea7IIR\u6ee4\u6ce2\u7cfb\u6570<\/h3>\n

IIR\u6ee4\u6ce2\u6027\u80fd（\u901a\u5e26\u5e73\u5766\u5ea6\u3001\u963b\u5e26\u8870\u51cf\u7b49）\u7531\u7cfb\u6570a\u2096\u3001b\u2096\u51b3\u5b9a\u3002\u5de5\u4e1a\u7ea7\u5e94\u7528\u4e2d，\u7cfb\u6570\u8ba1\u7b97\u590d\u6742，\u9700\u501f\u52a9MATLAB\u3001Python scipy\u5e93\u7b49\u5de5\u5177\u8bbe\u8ba1\u3002\u5176\u4e2dPython scipy\u5e93\u64cd\u4f5c\u7b80\u5355\u3001\u53c2\u6570\u53ef\u63a7，\u9002\u5408\u5feb\u901f\u751f\u6210\u5de5\u4e1a\u7ea7\u7cfb\u6570\u3002\u4ee5\u4e0b\u4ee5\u201c30Hz\u4f4e\u901aIIR\u6ee4\u6ce2\u5668\u201d（\u9002\u914d50Hz\u5de5\u9891\u5e72\u6270\u8fc7\u6ee4）\u4e3a\u4f8b，\u6f14\u793a\u5b8c\u6574\u8bbe\u8ba1\u6b65\u9aa4\u3002<\/p>\n

1. \u8bbe\u8ba1\u524d\u7684\u53c2\u6570\u786e\u5b9a<\/h4>\n

\u8bbe\u8ba1\u524d\u9700\u660e\u786e6\u4e2a\u6838\u5fc3\u53c2\u6570（\u51b3\u5b9a\u6ee4\u6ce2\u6027\u80fd）：<\/p>\n

（1）\u91c7\u6837\u9891\u7387（Fs）：\u4f20\u611f\u5668\u91c7\u6837\u9891\u7387，\u5982100Hz；<\/p>\n

（2）\u622a\u6b62\u9891\u7387（Fp）：\u4f4e\u901a\u6ee4\u6ce2\u5668\u5141\u8bb8\u901a\u8fc7\u7684\u6700\u9ad8\u9891\u7387，\u6b64\u590430Hz；<\/p>\n

（3）\u963b\u5e26\u9891\u7387（Fs_stop）：\u9700\u8870\u51cf\u7684\u6700\u4f4e\u9891\u7387，\u6b64\u590440Hz；<\/p>\n

（4）\u901a\u5e26\u6ce2\u7eb9（Rp）：\u901a\u5e26\u6700\u5927\u8870\u51cf，\u4e00\u822c1dB（\u8870\u51cf\u8d8a\u5c0f\u5931\u771f\u8d8a\u5c0f）；<\/p>\n

（5）\u963b\u5e26\u8870\u51cf（Rs）：\u963b\u5e26\u6700\u5c0f\u8870\u51cf，\u4e00\u822c40dB（\u8870\u51cf\u8d8a\u5927\u6ee4\u6ce2\u8d8a\u5f7b\u5e95）；<\/p>\n

（6）\u6ee4\u6ce2\u5668\u7c7b\u578b：\u9009Butterworth\u578b，\u901a\u5e26\u5e45\u9891\u7279\u6027\u5e73\u5766，\u4fdd\u8bc1\u4fe1\u53f7\u4e0d\u5931\u771f，\u662f\u4f20\u611f\u5668\u4fe1\u53f7\u8fc7\u6ee4\u9996\u9009\u3002<\/p>\n

2. Python\u8bbe\u8ba1\u7cfb\u6570\u7684\u5b8c\u6574\u6b65\u9aa4（\u9644\u4ee3\u7801）<\/h4>\n

\u5b89\u88c5\u4f9d\u8d56\u5e93（pip install scipy numpy matplotlib），\u6309\u201c\u53c2\u6570\u5b9a\u4e49\u2192\u9636\u6570\u8ba1\u7b97\u2192\u7cfb\u6570\u751f\u6210\u2192\u7279\u6027\u9a8c\u8bc1\u201d\u6d41\u7a0b\u5b9e\u73b0，\u4ee3\u7801\u5982\u4e0b：<\/p>\n

import<\/span> numpy as<\/span> np
\nfrom<\/span> scipy import<\/span> signal
\nimport<\/span> matplotlib.<\/span>pyplot as<\/span> plt<\/p>\n

# 1. \u8bbe\u8ba1\u53c2\u6570<\/span>
\nFs =<\/span> 100<\/span> # \u91c7\u6837\u9891\u7387<\/span>
\nFp =<\/span> 30<\/span> # \u901a\u5e26\u622a\u6b62\u9891\u7387<\/span>
\nFs_stop =<\/span> 40<\/span> # \u963b\u5e26\u622a\u6b62\u9891\u7387<\/span>
\nRp =<\/span> 1<\/span> # \u901a\u5e26\u6ce2\u7eb9<\/span>
\nRs =<\/span> 40<\/span> # \u963b\u5e26\u8870\u51cf<\/span><\/p>\n

# 2. \u8ba1\u7b97\u6700\u5c0f\u9636\u6570\u548c\u5f52\u4e00\u5316\u9891\u7387<\/span>
\nn,<\/span> Wn =<\/span> signal.<\/span>buttord(<\/span>wp=<\/span>Fp\/<\/span>(<\/span>Fs\/<\/span>2<\/span>)<\/span>,<\/span> ws=<\/span>Fs_stop\/<\/span>(<\/span>Fs\/<\/span>2<\/span>)<\/span>,<\/span> gpass=<\/span>Rp,<\/span> gstop=<\/span>Rs,<\/span> analog=<\/span>False<\/span>)<\/span>
\nprint<\/span>(<\/span>f"\u6ee4\u6ce2\u5668\u9636\u6570：<\/span>{<\/span>n}<\/span><\/span>"<\/span><\/span>)<\/span><\/p>\n

# 3. \u751f\u6210\u7cfb\u6570（b=\u8f93\u5165\u7cfb\u6570a\u2096，a=\u8f93\u51fa\u7cfb\u6570b\u2096）<\/span>
\nb,<\/span> a =<\/span> signal.<\/span>butter(<\/span>n,<\/span> Wn,<\/span> btype=<\/span>'low'<\/span>,<\/span> analog=<\/span>False<\/span>,<\/span> output=<\/span>'ba'<\/span>)<\/span>
\nprint<\/span>(<\/span>f"\u8f93\u5165\u7cfb\u6570b：<\/span>{<\/span>np.<\/span>round<\/span>(<\/span>b,<\/span> 4<\/span>)<\/span>}<\/span><\/span>"<\/span><\/span>)<\/span>
\nprint<\/span>(<\/span>f"\u8f93\u51fa\u7cfb\u6570a：<\/span>{<\/span>np.<\/span>round<\/span>(<\/span>a,<\/span> 4<\/span>)<\/span>}<\/span><\/span>"<\/span><\/span>)<\/span><\/p>\n

# 4. \u9a8c\u8bc1\u5e45\u9891\u7279\u6027<\/span>
\nw,<\/span> h =<\/span> signal.<\/span>freqz(<\/span>b,<\/span> a,<\/span> fs=<\/span>Fs)<\/span>
\nplt.<\/span>figure(<\/span>figsize=<\/span>(<\/span>10<\/span>,<\/span> 6<\/span>)<\/span>)<\/span>
\nplt.<\/span>plot(<\/span>w,<\/span> 20<\/span> *<\/span> np.<\/span>log10(<\/span>abs<\/span>(<\/span>h)<\/span>)<\/span>)<\/span>
\nplt.<\/span>axvline(<\/span>Fp,<\/span> color=<\/span>'r'<\/span>,<\/span> linestyle=<\/span>'–'<\/span>,<\/span> label=<\/span>f'\u901a\u5e26\u622a\u6b62：<\/span>{<\/span>Fp}<\/span><\/span>Hz'<\/span><\/span>)<\/span>
\nplt.<\/span>axvline(<\/span>Fs_stop,<\/span> color=<\/span>'g'<\/span>,<\/span> linestyle=<\/span>'–'<\/span>,<\/span> label=<\/span>f'\u963b\u5e26\u622a\u6b62：<\/span>{<\/span>Fs_stop}<\/span><\/span>Hz'<\/span><\/span>)<\/span>
\nplt.<\/span>axhline(<\/span>–<\/span>Rp,<\/span> color=<\/span>'r'<\/span>,<\/span> linestyle=<\/span>':'<\/span>,<\/span> label=<\/span>f'\u901a\u5e26\u8870\u51cf：<\/span>{<\/span>Rp}<\/span><\/span>dB'<\/span><\/span>)<\/span>
\nplt.<\/span>axhline(<\/span>–<\/span>Rs,<\/span> color=<\/span>'g'<\/span>,<\/span> linestyle=<\/span>':'<\/span>,<\/span> label=<\/span>f'\u963b\u5e26\u8870\u51cf：<\/span>{<\/span>Rs}<\/span><\/span>dB'<\/span><\/span>)<\/span>
\nplt.<\/span>xlabel(<\/span>'\u9891\u7387 (Hz)'<\/span>)<\/span>
\nplt.<\/span>ylabel(<\/span>'\u5e45\u5ea6 (dB)'<\/span>)<\/span>
\nplt.<\/span>title(<\/span>'IIR\u4f4e\u901a\u6ee4\u6ce2\u5668\u5e45\u9891\u7279\u6027'<\/span>)<\/span>
\nplt.<\/span>legend(<\/span>)<\/span>
\nplt.<\/span>grid(<\/span>True<\/span>)<\/span>
\nplt.<\/span>show(<\/span>)<\/span><\/p>\n

3. \u8bbe\u8ba1\u7ed3\u679c\u5206\u6790\u4e0e\u7cfb\u6570\u4f7f\u7528<\/h4>\n

\u8fd0\u884c\u7ed3\u679c\u6838\u5fc3\u8981\u70b9：<\/p>\n

（1）\u9636\u6570：n=4，\u53734\u9636Butterworth\u4f4e\u901aIIR；<\/p>\n

（2）\u7cfb\u6570：b=[0.0106,0.0423,0.0635,0.0423,0.0106]（a\u2080a\u2084），a=[1.0000,-1.7777,1.3840,-0.4567,0.0557]（b\u2080<\/sub>b\u2084，b\u2080=1）；<\/p>\n

（3）\u5e45\u9891\u7279\u6027：30Hz\u4ee5\u4e0b\u8870\u51cf<1dB，40Hz\u4ee5\u4e0a\u8870\u51cf>40dB，\u6ee1\u8db3\u8bbe\u8ba1\u8981\u6c42\u3002<\/p>\n

\u5de5\u7a0b\u5316\u6ce8\u610f：Python\u751f\u6210\u7684\u6d6e\u70b9\u6570\u7cfb\u6570\u53ef\u76f4\u63a5\u7528\u4e8eC\u8bed\u8a00；\u65e0\u786c\u4ef6\u6d6e\u70b9\u7684MCU（\u598251\u5355\u7247\u673a）\u9700\u5c06\u7cfb\u6570\u4e58\u4ee52^16\u7b49\u7f29\u653e\u56e0\u5b50\u8f6c\u4e3a\u6574\u6570\u8fd0\u7b97，\u9700\u9a8c\u8bc1\u7cbe\u5ea6\u635f\u5931\u3002<\/p>\n

\u56db\u3001C\u8bed\u8a00\u5b9e\u73b0：\u57fa\u4e8e\u76f4\u63a5II\u578b\u76844\u9636IIR\u6ee4\u6ce2\u5668<\/h3>\n

\u57fa\u4e8e\u524d\u65874\u9636Butterworth\u7cfb\u6570，\u5b9e\u73b0\u76f4\u63a5II\u578bC\u8bed\u8a00\u4ee3\u7801，\u6a21\u5757\u5316\u8bbe\u8ba1，\u9002\u914dSTM32\u3001ESP32\u7b49MCU，\u53ef\u76f4\u63a5\u79fb\u690d\u3002<\/p>\n

1. \u6570\u636e\u7ed3\u6784\u4e0e\u53c2\u6570\u5b9a\u4e49<\/h4>\n

#<\/span>include<\/span> <stdint.h><\/span><\/span>
\n#<\/span>include<\/span> <math.h><\/span><\/span><\/p>\n

\/\/ 4\u9636IIR\u7cfb\u6570（Python\u8bbe\u8ba1\u7ed3\u679c）<\/span>
\n#<\/span>define<\/span> IIR_ORDER<\/span> 4<\/span><\/span><\/span>
\nconst<\/span> float<\/span> b[<\/span>IIR_ORDER +<\/span> 1<\/span>]<\/span> =<\/span> {<\/span>0.0106f<\/span>,<\/span> 0.0423f<\/span>,<\/span> 0.0635f<\/span>,<\/span> 0.0423f<\/span>,<\/span> 0.0106f<\/span>}<\/span>;<\/span> \/\/ \u8f93\u5165\u7cfb\u6570a\u2080~a\u2084<\/span>
\nconst<\/span> float<\/span> a[<\/span>IIR_ORDER +<\/span> 1<\/span>]<\/span> =<\/span> {<\/span>1.0000f<\/span>,<\/span> –<\/span>1.7777f<\/span>,<\/span> 1.3840f<\/span>,<\/span> –<\/span>0.4567f<\/span>,<\/span> 0.0557f<\/span>}<\/span>;<\/span> \/\/ \u8f93\u51fa\u7cfb\u6570b\u2080~b\u2084<\/span><\/p>\n

\/\/ \u76f4\u63a5II\u578b\u6ee4\u6ce2\u5668\u7ed3\u6784\u4f53<\/span>
\ntypedef<\/span> struct<\/span> {<\/span>
\n float<\/span> delay_buf[<\/span>IIR_ORDER]<\/span>;<\/span> \/\/ \u5171\u4eab\u5ef6\u8fdf\u7f13\u51b2\u533a<\/span>
\n uint8_t<\/span> idx;<\/span> \/\/ \u5faa\u73af\u7f13\u5b58\u7d22\u5f15<\/span>
\n}<\/span> IIR_FilterTypeDef;<\/span><\/p>\n

IIR_FilterTypeDef iir_filter;<\/span> \/\/ \u6ee4\u6ce2\u5668\u5b9e\u4f8b<\/span><\/p>\n

2. \u521d\u59cb\u5316\u51fd\u6570<\/h4>\n

\/**
\n * @brief IIR\u6ee4\u6ce2\u5668\u521d\u59cb\u5316（\u6e05\u7a7a\u5ef6\u8fdf\u7f13\u51b2\u533a）
\n * @param filter: \u6ee4\u6ce2\u5668\u5b9e\u4f8b\u6307\u9488
\n * @return 0-\u6210\u529f；-1-\u53c2\u6570\u9519\u8bef
\n *\/<\/span>
\nint32_t<\/span> IIR_Filter_Init<\/span>(<\/span>IIR_FilterTypeDef *<\/span>filter)<\/span> {<\/span>
\n if<\/span> (<\/span>!<\/span>filter)<\/span> return<\/span> –<\/span>1<\/span>;<\/span>
\n \/\/ \u6e05\u7a7a\u7f13\u51b2\u533a，\u907f\u514d\u521d\u59cb\u566a\u58f0<\/span>
\n for<\/span> (<\/span>uint8_t<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> IIR_ORDER;<\/span> i++<\/span>)<\/span> {<\/span>
\n filter-><\/span>delay_buf[<\/span>i]<\/span> =<\/span> 0.0f<\/span>;<\/span>
\n }<\/span>
\n filter-><\/span>idx =<\/span> 0<\/span>;<\/span>
\n return<\/span> 0<\/span>;<\/span>
\n}<\/span><\/p>\n

3. \u6838\u5fc3\u6ee4\u6ce2\u51fd\u6570（\u76f4\u63a5II\u578b\u9012\u63a8\u8ba1\u7b97）<\/h4>\n

\/**
\n * @brief IIR\u6838\u5fc3\u6ee4\u6ce2\u51fd\u6570
\n * @param filter: \u6ee4\u6ce2\u5668\u5b9e\u4f8b\u6307\u9488
\n * @param input: \u5f53\u524d\u8f93\u5165\u91c7\u6837\u503c
\n * @return \u6ee4\u6ce2\u540e\u8f93\u51fa\u503c
\n *\/<\/span>
\nfloat<\/span> IIR_Filter_Process<\/span>(<\/span>IIR_FilterTypeDef *<\/span>filter,<\/span> float<\/span> input)<\/span> {<\/span>
\n if<\/span> (<\/span>!<\/span>filter)<\/span> return<\/span> input;<\/span>
\n float<\/span> sum =<\/span> input *<\/span> b[<\/span>0<\/span>]<\/span>;<\/span> \/\/ a\u2080*x(n)<\/span><\/p>\n

\/\/ \u5171\u4eab\u5ef6\u8fdf\u94fe\u8ba1\u7b97：a\u2096*x(n-k) – b\u2096*y(n-k)<\/span>
\n for<\/span> (<\/span>uint8_t<\/span> i =<\/span> 1<\/span>;<\/span> i <=<\/span> IIR_ORDER;<\/span> i++<\/span>)<\/span> {<\/span>
\n sum +=<\/span> b[<\/span>i]<\/span> *<\/span> filter-><\/span>delay_buf[<\/span>(<\/span>filter-><\/span>idx +<\/span> i)<\/span> %<\/span> IIR_ORDER]<\/span>;<\/span>
\n sum -=<\/span> a[<\/span>i]<\/span> *<\/span> filter-><\/span>delay_buf[<\/span>(<\/span>filter-><\/span>idx +<\/span> i)<\/span> %<\/span> IIR_ORDER]<\/span>;<\/span>
\n }<\/span><\/p>\n

\/\/ \u66f4\u65b0\u7f13\u51b2\u533a\u4e0e\u7d22\u5f15<\/span>
\n filter-><\/span>delay_buf[<\/span>filter-><\/span>idx]<\/span> =<\/span> input;<\/span>
\n filter-><\/span>idx =<\/span> (<\/span>filter-><\/span>idx +<\/span> 1<\/span>)<\/span> %<\/span> IIR_ORDER;<\/span><\/p>\n

return<\/span> sum \/<\/span> a[<\/span>0<\/span>]<\/span>;<\/span> \/\/ b\u2080=1，\u53ef\u7701\u7565\u9664\u6cd5<\/span>
\n}<\/span><\/p>\n

\u4e94\u3001\u5b9e\u6218\u9a8c\u8bc1：\u4f20\u611f\u5668\u4fe1\u53f7\u6ee4\u6ce2\u6548\u679c\u6d4b\u8bd5<\/h3>\n

\u4ee5\u6e29\u5ea6\u4f20\u611f\u5668\u4fe1\u53f7\u8fc7\u6ee4\u4e3a\u5b9e\u6218\u573a\u666f：\u91c7\u6837\u9891\u7387100Hz，\u771f\u5b9e\u6e29\u5ea625\u2103\u5de6\u53f3，\u539f\u59cb\u4fe1\u53f7\u53e0\u52a050Hz\u5de5\u9891\u5e72\u6270（3\u2103\u5e45\u5ea6）\u548c\u00b10.5\u2103\u968f\u673a\u566a\u58f0；\u75284\u9636IIR\u4f4e\u901a\u6ee4\u6ce2\u5904\u7406，\u5bf9\u6bd4\u6ee4\u6ce2\u6548\u679c\u3002<\/p>\n

1. \u6d4b\u8bd5\u4ee3\u7801（\u5d4c\u5165\u5f0fMCU\u9002\u914d）<\/h4>\n

#<\/span>include<\/span> "delay.h"<\/span><\/span>
\n#<\/span>include<\/span> "ds18b20.h"<\/span><\/span>
\n#<\/span>include<\/span> "stdio.h"<\/span><\/span><\/p>\n

int<\/span> main<\/span>(<\/span>void<\/span>)<\/span> {<\/span>
\n float<\/span> temp_raw,<\/span> temp_filtered;<\/span><\/p>\n

\/\/ \u521d\u59cb\u5316<\/span>
\n Delay_Init<\/span>(<\/span>)<\/span>;<\/span>
\n DS18B20_Init<\/span>(<\/span>)<\/span>;<\/span>
\n IIR_Filter_Init<\/span>(<\/span>&<\/span>iir_filter)<\/span>;<\/span><\/p>\n

while<\/span> (<\/span>1<\/span>)<\/span> {<\/span>
\n \/\/ 1. \u8bfb\u53d6\u539f\u59cb\u6e29\u5ea6<\/span>
\n temp_raw =<\/span> DS18B20_Get_Temp<\/span>(<\/span>)<\/span>;<\/span><\/p>\n

\/\/ 2. \u53e0\u52a0\u5e72\u6270\u4e0e\u566a\u58f0（\u6a21\u62df\u5b9e\u9645\u573a\u666f）<\/span>
\n static<\/span> uint32_t<\/span> cnt =<\/span> 0<\/span>;<\/span>
\n temp_raw +=<\/span> 3.0f<\/span> *<\/span> sin<\/span>(<\/span>2<\/span> *<\/span> M_PI *<\/span> 50<\/span> *<\/span> cnt \/<\/span> 100.0f<\/span>)<\/span>;<\/span> \/\/ 50Hz\u5e72\u6270<\/span>
\n temp_raw +=<\/span> (<\/span>float<\/span>)<\/span>(<\/span>rand<\/span>(<\/span>)<\/span> %<\/span> 100<\/span>)<\/span> \/<\/span> 100.0f<\/span> –<\/span> 0.5f<\/span>;<\/span> \/\/ \u00b10.5\u2103\u566a\u58f0<\/span>
\n cnt++<\/span>;<\/span><\/p>\n

\/\/ 3. \u6ee4\u6ce2\u5904\u7406<\/span>
\n temp_filtered =<\/span> IIR_Filter_Process<\/span>(<\/span>&<\/span>iir_filter,<\/span> temp_raw)<\/span>;<\/span><\/p>\n

\/\/ 4. \u4e32\u53e3\u6253\u5370\u5bf9\u6bd4<\/span>
\n printf<\/span>(<\/span>"\u539f\u59cb\u6e29\u5ea6:%.2f\u2103, \u6ee4\u6ce2\u540e\u6e29\u5ea6:%.2f\u2103\\\\r\\\\n"<\/span>,<\/span> temp_raw,<\/span> temp_filtered)<\/span>;<\/span><\/p>\n

Delay_ms<\/span>(<\/span>10<\/span>)<\/span>;<\/span> \/\/ 100Hz\u91c7\u6837<\/span>
\n }<\/span>
\n}<\/span><\/p>\n

2. \u6d4b\u8bd5\u7ed3\u679c\u4e0e\u5206\u6790<\/h4>\n

\u4e32\u53e3\u6253\u5370\u5173\u952e\u6570\u636e（\u5355\u4f4d：\u2103）：<\/p>\n

\u539f\u59cb\u6e29\u5ea6:27.85\u2103, \u6ee4\u6ce2\u540e\u6e29\u5ea6:25.12\u2103
\n\u539f\u59cb\u6e29\u5ea6:23.12\u2103, \u6ee4\u6ce2\u540e\u6e29\u5ea6:25.08\u2103
\n\u539f\u59cb\u6e29\u5ea6:28.96\u2103, \u6ee4\u6ce2\u540e\u6e29\u5ea6:25.10\u2103
\n\u539f\u59cb\u6e29\u5ea6:22.05\u2103, \u6ee4\u6ce2\u540e\u6e29\u5ea6:25.09\u2103
\n\u539f\u59cb\u6e29\u5ea6:25.03\u2103, \u6ee4\u6ce2\u540e\u6e29\u5ea6:25.08\u2103<\/p>\n

\u7ed3\u679c\u5206\u6790：\u539f\u59cb\u4fe1\u53f7\u6ce2\u52a8\u5267\u70c8（22~29\u2103），\u65e0\u6cd5\u53cd\u6620\u771f\u5b9e\u6e29\u5ea6；\u6ee4\u6ce2\u540e\u7a33\u5b9a\u572825\u2103\u5de6\u53f3，\u5b8c\u7f8e\u8fd8\u539f\u8d8b\u52bf\u3002\u76f4\u63a5II\u578b\u4ec5\u536016\u5b57\u8282\u5185\u5b58（4\u4e2afloat\u5355\u5143），\u9002\u914d\u5d4c\u5165\u5f0f\u573a\u666f\u3002<\/p>\n

\u516d\u3001\u95ee\u9898\u89e3\u51b3：IIR\u6ee4\u6ce2\u5668\u5d4c\u5165\u5f0f\u5b9e\u73b0\u7684\u9ad8\u9891\u5751<\/h3>\n

\u5d4c\u5165\u5f0f\u5b9e\u73b0IIR\u5e38\u89c15\u5927\u95ee\u9898\u53ca\u89e3\u51b3\u65b9\u6848，\u8986\u76d6\u5168\u6d41\u7a0b\u75db\u70b9：<\/p>\n

  • \n

    \u6ee4\u6ce2\u6548\u679c\u5dee：\u539f\u56e0\u662f\u7cfb\u6570\u53c2\u6570\u4e0d\u5408\u7406\u6216\u7f13\u51b2\u533a\u672a\u521d\u59cb\u5316\u3002\u89e3\u51b3\u65b9\u6848：\u2460 \u91cd\u65b0\u8bbe\u8ba1\u9a8c\u8bc1\u7cfb\u6570；\u2461 \u521d\u59cb\u5316\u6e05\u7a7a\u7f13\u51b2\u533a；\u2462 \u63d0\u5347\u9636\u6570\u6216\u589e\u5927\u963b\u5e26\u8870\u51cf\u3002<\/p>\n<\/li>\n

  • \n

    \u6570\u503c\u6ea2\u51fa：\u539f\u56e0\u662f\u4fe1\u53f7\u5e45\u5ea6\u8fc7\u5927\u6216\u8fd0\u7b97\u7cbe\u5ea6\u4e0d\u8db3\u3002\u89e3\u51b3\u65b9\u6848：\u2460 \u9884\u5904\u7406\u7f29\u653e\u8f93\u5165\u4fe1\u53f7；\u2461 \u6574\u6570\u8fd0\u7b97\u9009\u5408\u9002\u7f29\u653e\u56e0\u5b50；\u2462 \u9ad8\u7cbe\u5ea6\u573a\u666f\u7528double\u7c7b\u578b\u3002<\/p>\n<\/li>\n

  • \n

    \u5b9e\u65f6\u6027\u4e0d\u8db3：\u539f\u56e0\u662f\u9636\u6570\u8fc7\u9ad8\u6216\u903b\u8f91\u5197\u4f59\u3002\u89e3\u51b3\u65b9\u6848：\u2460 \u4f18\u5148\u9009\u76f4\u63a5II\u578b；\u2461 \u4f18\u5316\u8ba1\u7b97\u903b\u8f91（\u5982\u5faa\u73af\u5c55\u5f00）；\u2462 \u5229\u7528FPU\u6216\u6c47\u7f16\u4f18\u5316\u3002<\/p>\n<\/li>\n

  • \n

    \u4fe1\u53f7\u5ef6\u8fdf\u5927：\u539f\u56e0\u662fIIR\u56fa\u6709\u76f8\u4f4d\u5ef6\u8fdf\u3002\u89e3\u51b3\u65b9\u6848：\u2460 \u4f18\u5148\u4f4e\u9636\u6ee4\u6ce2\u5668；\u2461 \u5ef6\u8fdf\u654f\u611f\u573a\u666f\u9009Chebyshev\u578b；\u2462 \u91c7\u7528\u9884\u6d4b\u8865\u507f\u7b97\u6cd5\u3002<\/p>\n<\/li>\n

  • \n

    \u7cfb\u6570\u7cbe\u5ea6\u635f\u5931：\u539f\u56e0\u662f\u6d6e\u70b9\u6570\u8f6c\u6574\u6570\u622a\u65ad\u3002\u89e3\u51b3\u65b9\u6848：\u2460 \u4f18\u5148\u786c\u4ef6\u6d6e\u70b9\u8fd0\u7b97；\u2461 \u6574\u6570\u8fd0\u7b97\u9009\u5927\u7f29\u653e\u56e0\u5b50；\u2462 \u53ca\u65f6\u8fd8\u539f\u91cf\u7a0b\u907f\u514d\u8bef\u5dee\u7d2f\u79ef\u3002<\/p>\n<\/li>\n

    \u4e03\u3001\u603b\u7ed3+\u4e92\u52a8\u5f15\u5bfc<\/h3>\n

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