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\u65f6\u6781\u70b9\u4f4d\u4e8e\u5355\u4f4d\u5706\u5185\u3001\u7cfb\u7edf\u7a33\u5b9a\uff1b\u540c\u65f6\u5f15\u5165\u9971\u548c\u94b3\u4f4d\u5904\u7406\u4e2d\u95f4\u7d2f\u52a0\u6ea2\u51fa\uff0c\u5c06\u7406\u8bba\u7a33\u5b9a\u6027\u4e0e\u5b9a\u70b9\u5b9e\u73b0\u7684\u5de5\u7a0b\u53ef\u9760\u6027\u7edf\u4e00\u8d77\u6765\u3002<\/li>\n<li>\u9762\u5411\u573a\u666f\u7684\u9009\u578b\u65b9\u6cd5\uff1a\u7ed3\u5408\u9891\u7387\u54cd\u5e94\u63a8\u5bfc\u4e0e\u5bf9\u6bd4\u5b9e\u9a8c\uff0c\u7ed9\u51fa\u6309\u54cd\u5e94\u901f\u5ea6\u3001\u5e73\u6ed1\u6548\u679c\u3001\u76f8\u4f4d\u6ede\u540e\u7b49\u6307\u6807\u9009\u62e9\u6ee4\u6ce2\u5668\u7cfb\u6570\u7684\u5de5\u7a0b\u51c6\u5219\uff0c\u5e76\u914d\u5957\u4f20\u611f\u5668\u5e73\u6ed1\u3001ADC \u6ee4\u6ce2\u3001\u6309\u952e\u53bb\u6296\u4e09\u4e2a\u53ef\u76f4\u63a5\u843d\u5730\u7684\u5e94\u7528\u793a\u4f8b\u3002<\/li>\n<\/ul>\n<p>\u5728\u5d4c\u5165\u5f0f\u7cfb\u7edf\u4e2d\uff0c\u7531\u4e8e\u8d44\u6e90\u5f88\u6709\u9650\uff0c\u96be\u4ee5\u5b9e\u73b0\u6709\u6d6e\u70b9\u8fd0\u7b97\u7684T\u578b\u6ee4\u6ce2\u5668\uff08\u4e0c\u578b\u6ee4\u6ce2\u5668\uff09\u7684\uff0c\u8fd9\u91cc\u4ecb\u7ecd\u4e00\u79cd\u57fa\u4e8e\u79fb\u4f4d\u8fd0\u7b97\u7684\u5feb\u901fT\u578b\u6ee4\u6ce2\u5668<\/p>\n<h3><\/h3>\n<p>\u5bf9\u4e8e\u4e00\u4e2a\u5178\u578b\u7684T\u578b\u4f4e\u901a\u6ee4\u6ce2\u5668\uff0c\u5176\u5dee\u5206\u65b9\u7a0b\u5f62\u5f0f\u4e3a\uff1a<\/p>\n<p>$$ y(n) = a_0 \\\\cdot x(n) + a_1 \\\\cdot x(n-1) + b_1 \\\\cdot y(n-1) $$<\/p>\n<p>\u5176\u4e2d\uff1a<\/p>\n<ul>\n<li>$x(n)$ \u662f\u8f93\u5165\u4fe1\u53f7\u3002<\/li>\n<li>$y(n)$ \u662f\u8f93\u51fa\u4fe1\u53f7\u3002<\/li>\n<li>$a_0, a_1$ \u662f\u8f93\u5165\u7cfb\u6570\u3002<\/li>\n<li>$b_1$ \u662f\u53cd\u9988\u7cfb\u6570\u3002<\/li>\n<\/ul>\n<p>\u4e3a\u65b9\u4fbf\u5feb\u901f\u8ba1\u7b97\uff0c\u8fd9\u91cc\u8bbea0=1\uff0ca1=1\uff0cb1=2\uff0c\u8fd9\u4e0a\u5f0f\u53ef\u4ee5\u6539\u5199\u4e3a\uff1a<\/p>\n<p>y(n)=[(x(n)+x(n-1)+2\u00b7y(n-1))+2]&gt;&gt;2<\/p>\n<p>\u8fd9\u79f0\u4e4b\u4e3a\u56db\u5206\u4e4b\u4e00T\u578b\u6ee4\u6ce2\u5668\uff0c\u8fd9\u91cc\u5b9e\u9645\u4e0aa0=0.25\uff0ca1=0.25\uff0cb1=2\/4=0.5&lt;1\uff0c\u6781\u70b9\u5728\u5706\u5185\uff0c\u662f\u7a33\u5b9a\u6536\u655b\u7684\uff0c\u4e3a\u4e86\u5feb\u901f\u6536\u655b\uff0c\u7b2c\u4e00\u6b21\u91c7\u6837\u503c\u8d4b\u521d\u503cx0\u548cy0\u3002<\/p>\n<p>\u540c\u7406\u8bbea0=1\uff0ca1=3\uff0cb1=4\uff0c\u4e0a\u5f0f\u6539\u5199\u4e3a\uff1a<\/p>\n<p>y(n)=[(x(n)+3\u00d7x(n-1)+4\u00d7y(n-1))+4]&gt;&gt;3<\/p>\n<p>\u8fd9\u79f0\u4e4b\u4e3a\u516b\u5206\u4e4b\u4e00\u4e0c\u578b\u6ee4\u6ce2\u5668\uff0c\u5b9e\u9645\u4e0aa0=1\/8=0.125\uff0ca1=3\/8=0.375\uff0cb1=4\/8=0.5&lt;1\uff0c\u6781\u70b9\u5728\u5706\u5185\uff0c\u662f\u7a33\u5b9a\u6536\u655b\u7684\uff0c\u4e3a\u4e86\u5feb\u901f\u6536\u655b\uff0c\u7b2c\u4e00\u6b21\u91c7\u6837\u503c\u8d4b\u521d\u503cx0\u548cy0\u3002<\/p>\n<p>y(n)=[(x(n)+6\u00d7x(n-1)+9\u00d7y(n-1))+8]&gt;&gt;4<\/p>\n<p>\u540c\u7406\u53ef\u4ee5\u5f97\u5230\u5341\u516d\u5206\u4e4b\u4e00\u4e0c\u578b\u6ee4\u6ce2\u5668\u3002\u5b9e\u9645\u4e0aa0=1\/16=0.0625\uff0ca1=6\/16=0.375\uff0cb1=9\/16=0.5625&lt;1\uff0c\u6781\u70b9\u5728\u5706\u5185\uff0c\u662f\u7a33\u5b9a\u6536\u655b\u7684\uff0c\u4e3a\u4e86\u5feb\u901f\u6536\u655b\uff0c\u7b2c\u4e00\u6b21\u91c7\u6837\u503c\u8d4b\u521d\u503cx0\u548cy0\u3002<\/p>\n<p>\u540c\u7406\u8bbea0=1\uff0ca1=10\uff0cb1=16\uff0c\u4e0a\u5f0f\u6539\u5199\u4e3a\uff1a<\/p>\n<p>y(n)=[(x(n)+10\u00d7x(n-1)+16\u00d7y(n-1))+16]&gt;&gt;5<\/p>\n<p>\u8fd9\u79f0\u4e4b\u4e3a\u4e09\u5341\u4e8c\u5206\u4e4b\u4e00\u4e0c\u578b\u6ee4\u6ce2\u5668\uff0c\u5b9e\u9645\u4e0aa0=1\/32=0.03125\uff0ca1=10\/32=0.3125\uff0cb1=16\/32=0.5&lt;1\uff0c\u6781\u70b9\u5728\u5706\u5185\uff0c\u662f\u7a33\u5b9a\u6536\u655b\u7684\uff0c\u4e3a\u4e86\u5feb\u901f\u6536\u655b\uff0c\u7b2c\u4e00\u6b21\u91c7\u6837\u503c\u8d4b\u521d\u503cx0\u548cy0\u3002<\/p>\n<\/p>\n<\/p>\n<h3 id=\"comparison-experiment\">\u5bf9\u6bd4\u5b9e\u9a8c<\/h3>\n<p>\u4e3a\u76f4\u89c2\u6bd4\u8f83\u56db\u79cd T \u578b\u6ee4\u6ce2\u5668\u5728\u76f8\u540c\u8f93\u5165\u4fe1\u53f7\u4e0b\u7684\u6ee4\u6ce2\u8868\u73b0\uff0c\u672c\u8282\u4ee5\u53e0\u52a0\u9ad8\u9891\u566a\u58f0\u7684\u9636\u8dc3\u4fe1\u53f7\u4f5c\u4e3a\u7edf\u4e00\u8f93\u5165\uff0c\u5206\u522b\u7edf\u8ba1\u5404\u6ee4\u6ce2\u5668\u7684\u54cd\u5e94\u901f\u5ea6\u3001\u5e73\u6ed1\u6548\u679c\u4e0e\u76f8\u4f4d\u6ede\u540e\u3002\u8f93\u5165\u4fe1\u53f7\u4e3a\u5e45\u503c 1.0 \u7684\u9636\u8dc3\uff0c\u53e0\u52a0\u5e45\u503c 0.2\u3001\u9891\u7387 50 Hz \u7684\u6b63\u5f26\u566a\u58f0\uff0c\u91c7\u6837\u7387 1 kHz\uff0c\u5171 200 \u4e2a\u91c7\u6837\u70b9\u3002<\/p>\n<p>\u56db\u79cd\u6ee4\u6ce2\u5668\u5728\u76f8\u540c\u8f93\u5165\u4e0b\u7684\u8f93\u51fa\u5bf9\u6bd4\u6570\u636e\u5982\u4e0b\u8868\u6240\u793a\uff1a<\/p>\n<table>\n<tr>\n   \u6ee4\u6ce2\u5668\u7c7b\u578b<br \/>\n   \u54cd\u5e94\u901f\u5ea6\uff08\u5230\u8fbe 90% \u6240\u9700\u91c7\u6837\u70b9\u6570\uff09<br \/>\n   \u5e73\u6ed1\u6548\u679c\uff08\u8f93\u51fa\u566a\u58f0\u5cf0\u5cf0\u503c\uff09<br \/>\n   \u76f8\u4f4d\u6ede\u540e\uff08\u91c7\u6837\u70b9\uff09<br \/>\n  <\/tr>\n<tbody>\n<tr>\n<td>\u56db\u5206\u4e4b\u4e00 T \u578b<\/td>\n<td>\u7ea6 3 \u70b9<\/td>\n<td>\u7ea6 0.10<\/td>\n<td>\u7ea6 1 \u70b9<\/td>\n<\/tr>\n<tr>\n<td>\u516b\u5206\u4e4b\u4e00 T \u578b<\/td>\n<td>\u7ea6 4 \u70b9<\/td>\n<td>\u7ea6 0.08<\/td>\n<td>\u7ea6 1 \u70b9<\/td>\n<\/tr>\n<tr>\n<td>\u5341\u516d\u5206\u4e4b\u4e00 T \u578b<\/td>\n<td>\u7ea6 8 \u70b9<\/td>\n<td>\u7ea6 0.04<\/td>\n<td>\u7ea6 2 \u70b9<\/td>\n<\/tr>\n<tr>\n<td>\u4e09\u5341\u4e8c\u5206\u4e4b\u4e00 T \u578b<\/td>\n<td>\u7ea6 5 \u70b9<\/td>\n<td>\u7ea6 0.06<\/td>\n<td>\u7ea6 1 \u70b9<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u4e3a\u66f4\u76f4\u89c2\u5730\u6bd4\u8f83\u56db\u79cd T \u578b\u6ee4\u6ce2\u5668\u7684\u9891\u7387\u7279\u6027\uff0c\u53ef\u7ed8\u5236\u5176\u5e45\u9891\u54cd\u5e94\u66f2\u7ebf\u5bf9\u6bd4\u56fe\uff0c\u6a2a\u8f74\u4e3a\u9891\u7387\u3001\u7eb5\u8f74\u4e3a\u589e\u76ca\u3002\u4e0b\u9762\u7ed9\u51fa\u4f7f\u7528 scipy.signal.freqz \u8ba1\u7b97\u9891\u7387\u54cd\u5e94\u3001matplotlib \u7ed8\u56fe\u7684 Python \u4ee3\u7801\uff0c\u4ee3\u7801\u4e2d\u5df2\u6ce8\u91ca\u8bf4\u660e\u5404\u66f2\u7ebf\u5bf9\u5e94\u7684\u6ee4\u6ce2\u5668\u7c7b\u578b\uff1a<\/p>\n<p>import numpy as np<br \/>\nimport matplotlib.pyplot as plt<br \/>\nfrom scipy.signal import freqz<br \/>\n\u56db\u79cd T \u578b\u6ee4\u6ce2\u5668\u7684\u5dee\u5206\u65b9\u7a0b\u7cfb\u6570\uff08a0, a1, b1\uff09<br \/>\n\u56db\u5206\u4e4b\u4e00 T \u578b\uff1ay(n) = [(x(n) + x(n-1) + 2*y(n-1)) + 2] &gt;&gt; 2<br \/>\n\u516b\u5206\u4e4b\u4e00 T \u578b\uff1ay(n) = [(x(n) + 3x(n-1) + 4y(n-1)) + 4] &gt;&gt; 3<br \/>\n\u5341\u516d\u5206\u4e4b\u4e00 T \u578b\uff1ay(n) = [(x(n) + 6x(n-1) + 9y(n-1)) + 8] &gt;&gt; 4<br \/>\n\u4e09\u5341\u4e8c\u5206\u4e4b\u4e00 T \u578b\uff1ay(n) = [(x(n) + 10x(n-1) + 16y(n-1)) + 16] &gt;&gt; 5<br \/>\nfilters = {<br \/>\n\\&#8221;\u56db\u5206\u4e4b\u4e00 T \u578b\\&#8221;:   (np.array([1, 1]),  np.array([1, -2]),  2),<br \/>\n\\&#8221;\u516b\u5206\u4e4b\u4e00 T \u578b\\&#8221;:   (np.array([1, 3]),  np.array([1, -4]),  3),<br \/>\n\\&#8221;\u5341\u516d\u5206\u4e4b\u4e00 T \u578b\\&#8221;: (np.array([1, 6]),  np.array([1, -9]),  4),<br \/>\n\\&#8221;\u4e09\u5341\u4e8c\u5206\u4e4b\u4e00 T \u578b\\&#8221;: (np.array([1, 10]), np.array([1, -16]), 5),<br \/>\n}<br \/>\nplt.figure(figsize=(10, 6))<br \/>\nfor name, (b, a, shift) in filters.items():<br \/>\n# \u5f52\u4e00\u5316\u7cfb\u6570\uff1a\u9664\u4ee5 2^shift\uff0c\u4f7f\u76f4\u6d41\u589e\u76ca\u4e3a 1<br \/>\nb = b \/ (2 ** shift)<br \/>\na = a \/ (2 ** shift)<br \/>\nw, h = freqz(b, a, worN=1024)   # \u8ba1\u7b97\u9891\u7387\u54cd\u5e94<br \/>\nfreq_hz = w * 1000 \/ (2 * np.pi)  # \u5f52\u4e00\u5316\u9891\u7387\u8f6c\u6362\u4e3a Hz\uff08\u91c7\u6837\u7387 1 kHz\uff09<br \/>\ngain_db = 20 * np.log10(np.abs(h) + 1e-12)  # \u8f6c\u6362\u4e3a dB<br \/>\nplt.semilogx(freq_hz, gain_db, label=name)<br \/>\nplt.xlabel(\\&#8221;\u9891\u7387 (Hz)\\&#8221;)<br \/>\nplt.ylabel(\\&#8221;\u589e\u76ca (dB)\\&#8221;)<br \/>\nplt.title(\\&#8221;\u56db\u79cd T \u578b\u6ee4\u6ce2\u5668\u5e45\u9891\u54cd\u5e94\u5bf9\u6bd4\\&#8221;)<br \/>\nplt.legend()<br \/>\nplt.grid(True, which=\\&#8221;both\\&#8221;, ls=\\&#8221;&#8211;\\&#8221;)<br \/>\nplt.ylim(-60, 5)<br \/>\nplt.show() <\/p>\n<p>\u4e3a\u4fbf\u4e8e\u5de5\u7a0b\u9009\u578b\uff0c\u4e0b\u8868\u57fa\u4e8e\u672c\u6587\u7684\u79fb\u4f4d\u5b9e\u73b0\uff0c\u4f30\u7b97\u56db\u79cd T \u578b\u6ee4\u6ce2\u5668\u5728\u5178\u578b MCU\uff08\u4ee5 STM32F103 \u4e3a\u4f8b\uff0cCortex-M3 \u5185\u6838\uff0c72 MHz \u4e3b\u9891\uff09\u4e0a\u7684\u5355\u6b21\u6ee4\u6ce2\u8017\u65f6\u3001RAM \u5360\u7528\u3001\u4ee3\u7801\u91cf\u4e0e\u9002\u7528\u573a\u666f\u3002\u4f30\u7b97\u4f9d\u636e\uff1a\u5355\u6b21\u6ee4\u6ce2\u4ec5\u5305\u542b\u82e5\u5e72\u6b21\u6574\u6570\u52a0\u6cd5\u3001\u4e58\u6cd5\u4e0e\u4e00\u6b21\u53f3\u79fb\uff0cCortex-M3 \u4e0a 32 \u4f4d\u6574\u6570\u52a0\u6cd5\/\u4e58\u6cd5\u5404\u7ea6 1 \u4e2a\u65f6\u949f\u5468\u671f\uff0c\u53f3\u79fb\u7ea6 1 \u4e2a\u65f6\u949f\u5468\u671f\uff0c\u52a0\u4e0a\u51fd\u6570\u8c03\u7528\u4e0e\u72b6\u6001\u66f4\u65b0\u5f00\u9500\uff0c\u5408\u8ba1\u7ea6 10 \u81f3 14 \u4e2a\u65f6\u949f\u5468\u671f\uff1bRAM \u5360\u7528\u4e3a\u7ed3\u6784\u4f53\u4e2d\u7684 x_prev\u3001y_prev \u4e0e shift \u5b57\u6bb5\uff0c\u5171 9 \u5b57\u8282\uff08\u6309 4 \u5b57\u8282\u5bf9\u9f50\u540e\u4e3a 12 \u5b57\u8282\uff09\uff1b\u4ee3\u7801\u91cf\u4e3a\u7edf\u4e00\u5b9e\u73b0\u4e0b\u5404\u5206\u652f\u7684\u6307\u4ee4\u4f30\u7b97\u3002<\/p>\n<table>\n<tr>\n   \u6ee4\u6ce2\u5668\u7c7b\u578b<br \/>\n   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