{"id":2137,"date":"2023-10-09T18:53:08","date_gmt":"2023-10-09T10:53:08","guid":{"rendered":"https:\/\/www.huangrongzhen.ink\/?p=2137"},"modified":"2023-10-09T19:49:39","modified_gmt":"2023-10-09T11:49:39","slug":"c-%e8%af%ad%e8%a8%80-fir-%e6%bb%a4%e6%b3%a2%e5%99%a8%e8%ae%be%e8%ae%a1%e4%b8%8e%e5%ba%94%e7%94%a8","status":"publish","type":"post","link":"https:\/\/www.huangrongzhen.ink\/?p=2137","title":{"rendered":"C \u8bed\u8a00-FIR \u6ee4\u6ce2\u5668\u8bbe\u8ba1\u4e0e\u5e94\u7528"},"content":{"rendered":"

\u672c\u6587\u4e2d\u5c06\u4ecb\u7ecd\u5728 C \u8bed\u8a00\u5982\u4f55\u90e8\u7f72 FIR \u6ee4\u6ce2\u5668\uff0c\u5e76\u5c55\u793a\u5982\u4f55\u8bbe\u8ba1 FIR \u6ee4\u6ce2\u5668\u6765\u6ee4\u9664\u5fc3\u7535\u4fe1\u53f7 50Hz \u5de5\u9891… <\/p><\/div>\n\n\n

<\/span>\u9700\u8981\u5305\u542b\u7684\u5934\u6587\u4ef6<\/span><\/h2>\n\n\n\n

\u9700\u8981\u5305\u542b\u7684\u5934\u6587\u4ef6\u5982\u4e0b\u6240\u793a\u3002<\/p>\n\n\n\n

#include <stdio.h>\n#include <math.h>\n#include <malloc.h>\n#include <stdlib.h><\/code><\/pre>\n\n\n\n
<\/span>\u5b9e\u73b0 FIR \u6ee4\u6ce2\u5668<\/span><\/h2>\n\n\n\n
FIR \u6ee4\u6ce2\u5668\u7684\u5dee\u5206\u65b9\u7a0b\u5982\u4e0b\u6240\u793a\u3002<\/p>\n\n\n\n
\\(y(n)=\\sum_{m=0}^{M}h(m)x(n-m)\\)<\/p>\n\n\n\n
\u5176\u4e2d M \u88ab\u79f0\u4e3a FIR \u6ee4\u6ce2\u5668\u7684\u9636\u6570\uff0c\\(h(m)\\) \u4e3a FIR \u6ee4\u6ce2\u5668\u7cfb\u6570\u3002<\/p>\n\n\n\n
\u901a\u8fc7\u4e0a\u8ff0\u5dee\u5206\u65b9\u7a0b\uff0c\u53ef\u4ee5\u5f88\u5bb9\u6613\u5b9e\u73b0 FIR \u6ee4\u6ce2\u5668\uff0c\u5982\u4e0b\u6240\u793a\u3002<\/p>\n\n\n\n
\/*********************************************************************************************************\n* \u51fd\u6570\u540d\u79f0\uff1a FirFilter\n* \u51fd\u6570\u529f\u80fd\uff1a FIR \u6ee4\u6ce2\u5668\n* \u8f93\u5165\u53c2\u6570\uff1a h \uff1a\u53cc\u7cbe\u5ea6\u5b9e\u578b\u4e00\u7ef4\u6570\u7ec4\uff0c\u957f\u5ea6\u4e3a\uff08m+1\uff09\u3002\u5b58\u653e\u6ee4\u6ce2\u5668\u7684\u7cfb\u6570\u3002\n*            px\uff1a\u53cc\u7cbe\u5ea6\u5b9e\u578b\u4e00\u7ef4\u6570\u7ec4\uff0c\u957f\u5ea6\u4e3a\uff08m+1\uff09\u3002\u5b58\u653e\u5386\u53f2\u8f93\u5165\u6570\u636e\uff0c\u521d\u59cb\u72b6\u6001\u5fc5\u987b\u4e3a\u96f6\u3002\n*            m \uff1a\u6ee4\u6ce2\u5668\u7684\u9636\u6570\u3002\n*            x \uff1a\u65b0\u7684\u91c7\u6837\u503c\u3002\n* \u8f93\u51fa\u53c2\u6570\uff1a void\n* \u8fd4 \u56de \u503c\uff1a \u6ee4\u6ce2\u540e\u7684\u91c7\u6837\u503c\u3002\n* \u521b\u5efa\u65e5\u671f\uff1a 2023\u5e7410\u670809\u65e5\n* \u6ce8    \u610f\uff1a\n*********************************************************************************************************\/\ndouble FirFilter(double* h, double* px, int m, double x)\n{\n  int i;\n  double sum;\n\n  \/\/\u5c06\u65b0\u7684\u91c7\u6837\u6570\u636e\u5b58\u653e\u5230\u72b6\u6001\u6570\u7ec4\n  for (i = m; i >= 1; i--)\n  {\n    px[i] = px[i - 1];\n  }\n  px[0] = x;\n\n  \/\/\u6839\u636e FIR \u6ee4\u6ce2\u5668\u7684\u5b9a\u4e49\u6c42\u89e3\u6ee4\u6ce2\u540e\u7684\u7ed3\u679c\n  sum = 0;\n  for (i = 0; i <= m; i++)\n  {\n    sum = sum + h[i] * px[i];\n  }\n\n  \/\/\u8fd4\u56de\u6ee4\u6ce2\u540e\u7684\u91c7\u6837\u503c\n  return sum;\n}<\/code><\/pre>\n\n\n\n
<\/span>\u4f7f\u7528\u7a97\u51fd\u6570\u8bbe\u8ba1 FIR \u6570\u5b57\u6ee4\u6ce2\u5668<\/span><\/h2>\n\n\n\n
\u8bbe N-1 \u9636 FIR \u6570\u5b57\u6ee4\u6ce2\u5668\u7684\u5355\u4f4d\u51b2\u6fc0\u54cd\u5e94\u4e3a h(n)\uff0c\u5219\u4f20\u9012\u51fd\u6570 H(z) \u4e3a<\/p>\n\n\n\n
\\(H(z)=\\sum_{n=0}^{N-1}h(n)z^{-n}\\)<\/p>\n\n\n\n
\u7a97\u51fd\u6570\u6cd5\u7684\u8bbe\u8ba1\u6b65\u9aa4\u5982\u4e0b\uff1a<\/p>\n\n\n\n
1\u3001\u6839\u636e\u7ed9\u5b9a\u7684\u7406\u60f3\u9891\u7387\u54cd\u5e94 \\(H_{d}(e^{jw})\\)\uff0c\u5229\u7528\u5085\u91cc\u53f6\u53cd\u53d8\u6362\uff0c\u6c42\u51fa\u5355\u4f4d\u51b2\u6fc0\u54cd\u5e94 \\(h_{d}(n)\\)<\/p>\n\n\n\n
\\(h_{d}(n)=\\frac{1}{2\\pi }\\int_{-\\pi }^{\\pi }H_{d}(e^{jw})e^{jwn}dw\\)<\/p>\n\n\n\n
2\u3001\u5c06 \\(h_{d}(n)\\) \u4e58\u4ee5\u7a97\u51fd\u6570 \\(w(n)\\)\uff0c\u5f97\u5230\u6240\u8981\u6c42\u7684 FIR \u6ee4\u6ce2\u5668\u7684\u7cfb\u6570 \\(h(n)\\)<\/p>\n\n\n\n
\\(h(n)=w(n)h_{d}(n)\\)<\/p>\n\n\n\n
\u5e38\u7528\u7684\u7a97\u51fd\u6570\u6709\uff1a<\/p>\n\n\n\n
\u77e9\u5f62\u7a97<\/p>\n\n\n\n
\\(w(n)=1,0\\leqslant n\\leqslant (N-2)\/10\\)<\/p>\n\n\n\n
\u56fe\u57fa\uff08Tukey\uff09\u7a97<\/p>\n\n\n\n
\\(w(n)=0.5(1-cos\\left ( \\frac{10\\pi n}{N+8}) \\right ),0\\leqslant n\\leqslant (N-2)\/10\\)<\/p>\n\n\n\n
\\(w(n)=1,(N-2)\/10\\leqslant n\\leqslant 9(N-2)\/10\\)<\/p>\n\n\n\n
\\(w(n)=0.5\\left ( 1-cos\\left ( \\frac{10\\pi (N-n-1)}{N+8} \\right ) \\right ),9(N-2)\/10\\leqslant n\\leqslant N-1\\)<\/p>\n\n\n\n
\u4e09\u89d2\u7a97<\/p>\n\n\n\n
\\(w(n)=1-\\left | 1-\\frac{2n}{N-1} \\right |,0\\leq n\\leq N-1\\)<\/p>\n\n\n\n
\u6c49\u5b81\uff08Hanning\uff09\u7a97<\/p>\n\n\n\n
\\(w(n)=0.5-0.5cos\\frac{2\\pi n}{N-1},0\\leq n\\leq N-1\\)<\/p>\n\n\n\n
\u6d77\u660e\uff08Hamming\uff09\u7a97<\/p>\n\n\n\n
\\(w(n)=0.54-0.46cos\\frac{2\\pi n}{N-1},0\\leq n\\leq N-1\\)<\/p>\n\n\n\n
\u5e03\u62c9\u514b\u66fc\uff08Blackman\uff09\u7a97<\/p>\n\n\n\n
\\(w(n)=0.42-0.5cos\\frac{2\\pi n}{N-1}+0.08cos\\frac{4\\pi n}{N-1},0\\leq n\\leq N-1\\)<\/p>\n\n\n\n
\u51ef\u585e\uff08Kaiser\uff09\u7a97<\/p>\n\n\n\n
\\(w(n)=\\frac{I_{0}(\\beta \\sqrt{1-(1-2n\/(N-1))^{2}})}{I_{0}(\\beta )},0\\leq n\\leq N-1\\)<\/p>\n\n\n\n
\u5176\u4e2d \\(I_{0}(\\beta )\\) \u662f\u7b2c\u4e00\u7c7b\u96f6\u9636\u4fee\u6b63\u8d1d\u585e\u8033\u51fd\u6570\u3002\\(\\beta\\) \u662f\u63a7\u5236\u7a97\u51fd\u6570\u5f62\u72b6\u7684\u53c2\u6570\uff0c\\(\\beta\\) \u8d8a\u5927\uff0c\\(w(n)\\) \u7a97\u8d8a\u7a84\uff0c\u9891\u8c31\u7684\u65c1\u74e3\u8d8a\u5c0f\uff0c\u4f46\u4e3b\u74e3\u4e5f\u76f8\u5e94\u52a0\u5bbd\u3002\\(\\beta\\) \u7684\u5178\u578b\u503c\u4e3a \\(4\\leqslant \\beta \\leqslant 9\\)\u3002\\(\\beta =0\\) \u65f6\uff0c\u51ef\u585e\u7a97\u53d8\u4e3a\u77e9\u5f62\u7a97\uff1b\\(\\beta =5.44\\) \u65f6\uff0c\u51ef\u585e\u7a97\u4e0e\u6d77\u660e\u7a97\u63a5\u8fd1\uff1b\\(\\beta =8.5\\) \u65f6\uff0c\u51ef\u585e\u7a97\u4e0e\u5e03\u62c9\u514b\u66fc\u7a97\u63a5\u8fd1\u3002<\/p>\n\n\n\n
\u5b9e\u73b0\u4ee3\u7801\u5982\u4e0b\u3002<\/p>\n\n\n\n
\/*********************************************************************************************************\n* \u51fd\u6570\u540d\u79f0\uff1a Firwin\n* \u51fd\u6570\u529f\u80fd\uff1a FIR \u6570\u5b57\u6ee4\u6ce2\u5668\u7684\u8bbe\u8ba1\uff0c\u7a97\u51fd\u6570\u65b9\u6cd5\n* \u8f93\u5165\u53c2\u6570\uff1a n   \uff1a\u6574\u5f62\u53d8\u91cf\u3002\u6ee4\u6ce2\u5668\u7684\u9636\u6570\u3002\n*            band\uff1a\u6574\u5f62\u53d8\u91cf\u3002\u6ee4\u6ce2\u5668\u7684\u7c7b\u578b\u3002\u53d6\u503c\u4e3a 1\u30012\u30013 \u548c 4\uff0c\u5206\u522b\u5bf9\u5e94\u4f4e\u901a\u3001\u9ad8\u901a\u3001\u5e26\u901a\u548c\u5e26\u963b\u6ee4\u6ce2\u5668\u3002\n*            fln \uff1a\u53cc\u7cbe\u5ea6\u5b9e\u578b\u53d8\u91cf\u3002\n*            fhn \uff1a\u53cc\u7cbe\u5ea6\u5b9e\u578b\u53d8\u91cf\u3002\n*                  \u5bf9\u4e8e\u4f4e\u901a\u548c\u9ad8\u901a\u6ee4\u6ce2\u5668\uff0cfln\uff1a\u901a\u5e26\u8fb9\u754c\u9891\u7387\uff1b\n*                  \u5bf9\u4e8e\u5e26\u901a\u548c\u5e26\u963b\u6ee4\u6ce2\u5668\uff0cfln\uff1a\u5e26\u901a\u4e0b\u8fb9\u754c\u9891\u7387\uff0cfhn\uff1a\u5e26\u901a\u4e0a\u8fb9\u754c\u9891\u7387\u3002\n*            wn  \uff1a\u6574\u5f62\u53d8\u91cf\u3002\u7a97\u51fd\u6570\u7c7b\u578b\u3002\u53d6\u503c\u4e3a 1 \u5230 7\uff0c\u5206\u522b\u5bf9\u5e94\u77e9\u5f62\u7a97\u3001\u56fe\u57fa\u7a97\u3001\u4e09\u89d2\u7a97\u3001\u6c49\u5b81\u7a97\u3001\u6d77\u660e\u7a97\u3001\n*                  \u5e03\u62c9\u514b\u66fc\u7a97\u548c\u51ef\u585e\u7a97\n*            h   \uff1a\u53cc\u7cbe\u5ea6\u5b9e\u578b\u4e00\u7ef4\u6570\u7ec4\uff0c\u957f\u5ea6\u4e3a\uff08n+1\uff09\uff0c\u5b58\u653e FIR \u6ee4\u6ce2\u5668\u7684\u7cfb\u6570\u3002\n* \u8f93\u51fa\u53c2\u6570\uff1a void\n* \u8fd4 \u56de \u503c\uff1a void\n* \u521b\u5efa\u65e5\u671f\uff1a 2023\u5e7410\u670803\u65e5\n* \u6ce8    \u610f\uff1a\n*********************************************************************************************************\/\nvoid Firwin(int n, int band, double fln, double fhn, int wn, double* h)\n{\n  int i, n2, mid;\n  double s, pi, wc1, wc2, beta, delay;\n  double window(int type, int n, int i, double beta);\n  beta = 0.0;\n  if (wn == 7)\n  {\n    printf(\"input beta parameter of Kaiser window (3 < beta < 10)\\n\");\n    scanf(\"%lf\", &beta);\n  }\n  pi = 4.0 * atan(1.0);\n  if ((n % 2) == 0)\n  {\n    n2 = n \/ 2 - 1;\n    mid = 1;\n  }\n  else\n  {\n    n2 = n \/ 2;\n    mid = 0;\n  }\n  delay = n \/ 2.0;\n  wc1 = 2.0 * pi * fln;\n  if (band >= 3)\n  {\n    wc2 = 2.0 * pi * fhn;\n  }\n  switch (band)\n  {\n    case 1:\n    {\n      for (i = 0; i <= n2; i++)\n      {\n        s = i - delay;\n        h[i] = (sin(wc1 * s) \/ (pi * s)) * window(wn, n + 1, i, beta);\n        h[n - i] = h[i];\n      }\n      if (mid == 1)\n      {\n        h[n \/ 2] = wc1 \/ pi;\n      }\n      break;\n    }\n    case 2:\n    {\n      for (i = 0; i <= n2; i++)\n      {\n        s = i - delay;\n        h[i] = (sin(pi * s) - sin(wc1 * s)) \/ (pi * s);\n        h[i] = h[i] * window(wn, n + 1, i, beta);\n        h[n - i] = h[i];\n      }\n      if (mid == 1)\n      {\n        h[n \/ 2] = 1.0 - wc1 \/ pi;\n      }\n      break;\n    }\n    case 3:\n    {\n      for (i = 0; i <= n2; i++)\n      {\n        s = i - delay;\n        h[i] = (sin(wc2 * s) - sin(wc1 * s)) \/ (pi * s);\n        h[i] = h[i] * window(wn, n + 1, i, beta);\n        h[n - i] = h[i];\n      }\n      if (mid == 1)\n      {\n        h[n \/ 2] = (wc2 - wc1) \/ pi;\n      }\n      break;\n    }\n    case 4:\n    {\n      for (i = 0; i <= n2; i++)\n      {\n        s = i - delay;\n        h[i] = (sin(wc1 * s) + sin(pi * s) - sin(wc2 * s)) \/ (pi * s);\n        h[i] = h[i] * window(wn, n + 1, i, beta);\n        h[n - i] = h[i];\n      }\n      if (mid == 1)\n      {\n        h[n \/ 2] = (wc1 + pi - wc2) \/ pi;\n      }\n      break;\n    }\n  }\n}\nstatic double window(int type, int n, int i, double beta)\n{\n  int k;\n  double pi, w;\n  double keiser(int i, int n, double beta);\n  pi = 4.0 * atan(1.0);\n  w = 1.0;\n  switch (type)\n  {\n    case 1: \n    {\n      w = 1.0; \n      break;\n    }\n    case 2: \n    {\n      k = (n - 2) \/ 10;\n      if (i <= k)\n      {\n        w = 0.5 * (1.0 - cos(i * pi \/ (k + 1)));\n      }\n      if (i > n - k - 2)\n      {\n        w = 0.5 * (1.0 - cos((n - i - 1) * pi \/ (k + 1)));\n      }\n      break;\n    }\n    case 3:\n    {\n      w = 1.0 - fabs(1.0 - 2 * i \/ (n - 1.0));\n      break;\n    }\n    case 4:\n    {\n      w = 0.5 * (1.0 - cos(2 * i * pi \/ (n - 1)));\n      break;\n    }\n    case 5:\n    {\n      w = 0.54 - 0.46 * cos(2 * i * pi \/ (n - 1));\n      break;\n    }\n    case 6:\n    {\n      w = 0.42 - 0.5 * cos(2 * pi \/ (n - 1)) + 0.08 * cos(4 * i * pi \/ (n - 1));\n      break;\n    }\n    case 7:\n    {\n      w = keiser(i, n, beta);\n      break;\n    }\n  }\n  return (w);\n}\nstatic double keiser(int i, int n, double beta)\n{\n  double a, w, a2, b1, b2, beta1;\n  double bessel0(double x);\n  b1 = bessel0(beta);\n  a = 2.0 * i \/ (double)(n - 1) - 1.0;\n  a2 = a * a;\n  beta1 = beta * sqrt(1.0 - a2);\n  b2 = bessel0(beta1);\n  w = b2 \/ b1;\n  return (w);\n}\nstatic double bessel0(double x)\n{\n  int i;\n  double d, y, d2, sum;\n  y = x \/ 2.0;\n  d = 1.0;\n  sum = 1.0;\n  for (i = 1; i <= 25; i++)\n  {\n    d = d * y \/ i;\n    d2 = d * d;\n    sum = sum + d2;\n    if (d2 < sum * (1.0e-8))\n    {\n      break;\n    }\n  }\n  return (sum);\n}<\/code><\/pre>\n\n\n\n
\u4e0b\u9762\u7ed9\u51fa\u4e3b\u51fd\u6570\u7a0b\u5e8f\u3002\u5b83\u8c03\u7528 Firwin \u51fd\u6570\u3002\u901a\u8fc7\u4eba\u673a\u5bf9\u8bdd\uff0c\u5b83\u53ef\u4ee5\u8bbe\u8ba1\u4f4e\u901a\u3001\u9ad8\u901a\u3001\u5e26\u901a\u548c\u5e26\u963b\u8fd9\u56db\u79cd\u5f62\u5f0f\u7684\u6ee4\u6ce2\u5668\u3002\u4e0b\u9762\u5bf9\u8f93\u5165\u53c2\u6570\u8fdb\u884c\u8bf4\u660e\u3002<\/p>\n\n\n\n
band\uff1a\u6ee4\u6ce2\u5668\u7684\u7c7b\u578b\uff1b<\/p>\n\n\n\n
n \uff1a\u6ee4\u6ce2\u5668\u7684\u9636\u6570\uff1b<\/p>\n\n\n\n
fs \uff1a\u91c7\u6837\u9891\u7387\uff1b<\/p>\n\n\n\n
\u5bf9\u4e8e\u4f4e\u901a\u548c\u9ad8\u901a\u6ee4\u6ce2\u5668\uff0cfl\uff1a\u901a\u5e26\u8fb9\u754c\u9891\u7387\uff1b<\/p>\n\n\n\n
\u5bf9\u4e8e\u5e26\u901a\u548c\u5e26\u963b\u6ee4\u6ce2\u5668\uff0cf1\uff1a\u901a\u5e26\u4e0b\u8fb9\u754c\u9891\u7387\uff0cfh\uff1a\u901a\u5e26\u4e0a\u8fb9\u754c\u9891\u7387\uff1b<\/p>\n\n\n\n
wn\uff1a\u7a97\u51fd\u6570\u7684\u7c7b\u578b\uff1b<\/p>\n\n\n\n
fname\uff1a\u5e45\u9891\u54cd\u5e94\u6587\u4ef6\u540d\u3002<\/p>\n\n\n\n
\/*********************************************************************************************************\n* \u51fd\u6570\u540d\u79f0\uff1a Gain\n* \u51fd\u6570\u529f\u80fd\uff1a \u6570\u5b57\u6ee4\u6ce2\u5668\u7684\u9891\u7387\u54cd\u5e94\n* \u8f93\u5165\u53c2\u6570\uff1a b   \uff1a\u53cc\u7cbe\u5ea6\u5b9e\u578b\u4e00\u7ef4\u6570\u7ec4\uff0c\u957f\u5ea6\u4e3a\uff08m+1\uff09\u3002\u5b58\u653e\u6ee4\u6ce2\u5668\u5206\u5b50\u591a\u9879\u5f0f\u7684\u7cfb\u6570 b(i)\u3002\n*            a   \uff1a\u53cc\u7cbe\u5ea6\u5b9e\u578b\u4e00\u7ef4\u6570\u7ec4\uff0c\u957f\u5ea6\u4e3a\uff08n+1\uff09\u3002\u5b58\u653e\u6ee4\u6ce2\u5668\u5206\u6bcd\u591a\u9879\u5f0f\u7684\u7cfb\u6570 a(i)\u3002\n*            m   \uff1a\u6574\u578b\u53d8\u91cf\u3002\u6ee4\u6ce2\u5668\u5206\u5b50\u591a\u9879\u5f0f\u7684\u9636\u6570\u3002\n*            n   \uff1a\u6574\u5f62\u53d8\u91cf\u3002\u6ee4\u6ce2\u5668\u5206\u6bcd\u591a\u9879\u5f0f\u7684\u9636\u6570\u3002\n*            x   \uff1a\u53cc\u7cbe\u5ea6\u5b9e\u578b\u4e00\u7ef4\u6570\u7ec4\uff0c\u957f\u5ea6\u4e3a len\u3002\n*                  \u5f53 sign = 0 \u65f6\uff0c\u5b58\u653e\u6ee4\u6ce2\u5668\u9891\u7387\u54cd\u5e94\u7684\u5b9e\u90e8 Rc[H(w)]\uff1b\n*                  \u5f53 sign = 1 \u65f6\uff0c\u5b58\u653e\u6ee4\u6ce2\u5668\u5e45\u9891\u54cd\u5e94 |H(w)|\uff1b\n*                  \u5f53 sign = 2 \u65f6\uff0c\u5b58\u653e\u5206\u8d1d\u8868\u793a\u7684\u6ee4\u6ce2\u5668\u5e45\u9891\u54cd\u5e94 |H(w)|\u3002\n*            y   \uff1a\u53cc\u7cbe\u5ea6\u5b9e\u578b\u4e00\u7ef4\u6570\u7ec4\uff0c\u957f\u5ea6\u4e3a len\u3002\n*                  \u5f53 sign = 0 \u65f6\uff0c\u5b58\u653e\u6ee4\u6ce2\u5668\u9891\u7387\u54cd\u5e94\u7684\u865a\u90e8 Im[H(w)]\uff1b\n*                  \u5f53 sign = 1 \u6216 2 \u65f6\uff0c\u5b58\u653e\u6ee4\u6ce2\u5668\u7684\u76f8\u9891\u54cd\u5e94 \u03c6(w)\u3002\n*            sign\uff1a\u6574\u5f62\u53d8\u91cf\u3002\n*                  \u5f53 sign = 0 \u65f6\uff0c\u8ba1\u7b97\u6ee4\u6ce2\u5668\u9891\u7387\u54cd\u5e94\u7684\u5b9e\u90e8 Rc[H(w)] \u548c \u865a\u90e8 Im[H(w)]\uff1b\n*                  \u5f53 sign = 1 \u65f6\uff0c\u8ba1\u7b97\u6ee4\u6ce2\u5668\u7684\u5e45\u9891\u54cd\u5e94 |H(w)| \u548c\u76f8\u9891\u54cd\u5e94 \u03c6(w)\uff1b\n*                  \u5f53 sign = 2 \u65f6\uff0c\u8ba1\u7b97\u6ee4\u6ce2\u5668\u7684\u5e45\u9891\u54cd\u5e94 |H(w)| \uff08\u7528 dB \u8868\u793a\uff09\u548c\u76f8\u9891\u54cd\u5e94 \u03c6(w)\u3002\n* \u8f93\u51fa\u53c2\u6570\uff1a void\n* \u8fd4 \u56de \u503c\uff1a void\n* \u521b\u5efa\u65e5\u671f\uff1a 2023\u5e7409\u670829\u65e5\n* \u6ce8    \u610f\uff1a\n*********************************************************************************************************\/\nvoid Gain(double* b, double* a, int m, int n, double* x, double* y, int len, int sign)\n{\n  int i, k;\n  double ar, ai, br, bi, zr, zi, im, re, den, numr, numi, freq, temp;\n  for (k = 0; k < len; k++)\n  {\n    freq = k * 0.5 \/ (len - 1);\n    zr = cos(-8.0 * atan(1.0) * freq);\n    zi = sin(-8.0 * atan(1.0) * freq);\n    br = 0.0;\n    bi = 0.0;\n    for (i = m; i > 0; i--)\n    {\n      re = br;\n      im = bi;\n      br = (re + b[i]) * zr - im * zi;\n      bi = (re + b[i]) * zi + im * zr;\n    }\n    ar = 0.0;\n    ai = 0.0;\n    for (i = n; i > 0; i--)\n    {\n      re = ar;\n      im = ai;\n      ar = (re + a[i]) * zr - im * zi;\n      ai = (re + a[i]) * zi + im * zr;\n    }\n    br = br + b[0];\n    ar = ar + 1.0;\n    numr = ar * br + ai * bi;\n    numi = ar * bi - ai * br;\n    den = ar * ar + ai * ai;\n    x[k] = numr \/ den;\n    y[k] = numi \/ den;\n    switch (sign)\n    {\n      case 1:\n      {\n        temp = sqrt(x[k] * x[k] + y[k] * y[k]);\n        y[k] = atan2(y[k], x[k]);\n        x[k] = temp;\n        break;\n      }\n      case 2:\n      {\n        temp = x[k] * x[k] + y[k] * y[k];\n        y[k] = atan2(y[k], x[k]);\n        x[k] = 10.0 * log10(temp);\n      }\n    }\n  }\n}\n\n\/*********************************************************************************************************\n* \u51fd\u6570\u540d\u79f0\uff1a main\n* \u51fd\u6570\u529f\u80fd\uff1a \u4e3b\u51fd\u6570\n* \u8f93\u5165\u53c2\u6570\uff1a void\n* \u8f93\u51fa\u53c2\u6570\uff1a void\n* \u8fd4 \u56de \u503c\uff1a int\n* \u521b\u5efa\u65e5\u671f\uff1a 2023\u5e7410\u670803\u65e5\n* \u6ce8    \u610f\uff1a\n*********************************************************************************************************\/\nint main(void)\n{\n  int i, j, n, n2, band, wn;\n  double fl, fh, fs, freq;\n  static double h[10240], c[10240], x[300], y[300];\n  char fname[40];\n  FILE* fp;\n  c[1] = 0.0;\n  printf(\"Select one of the four types for FIR digital filter\\n\");\n  printf(\"1 -- lowpass; 2 -- highpass\\n\");\n  printf(\"3 -- bandpass; 4 -- bandstop\\n\");\n  scanf(\"%d\", &band);\n  printf(\"Input the filter order\\n\");\n  scanf(\"%d\", &n);\n  printf(\"Input low cutoff frequrncy fl\\n\");\n  scanf(\"%lf\", &fl);\n  fh = 0.0;\n  if (band >= 3)\n  {\n    printf(\"Input high cutoff frequrncy fh\\n\");\n    scanf(\"%lf\", &fh);\n  }\n  printf(\"Input sample frequence fs\\n\");\n  scanf(\"%lf\", &fs);\n  printf(\"Select window\\n\");\n  printf(\"1 -- rectangular; 2 -- tapered rectangular\\n\");\n  printf(\"3 -- triangular; 4 -- Hanning\\n\");\n  printf(\"5 -- Hamming; 6 -- Blackman\\n\");\n  printf(\"7 -- Kaiser\\n\");\n  scanf(\"%d\", &wn);\n  fl = fl \/ fs;\n  fh = fh \/ fs;\n  Firwin(n, band, fl, fh, wn, h);\n  printf(\"FIR digital filter\\n\");\n  printf(\" * * * * impulse respomse * * * * \\n\\n\");\n  n2 = n \/ 2;\n  for (i = 0; i <= n2; i++)\n  {\n    j = n - i;\n    printf(\"h(%2d) = %12.8lf = h(%2d)\\n\", i, h[i], j);\n  }\n  printf(\"\\n * * * * impulse respomse by C * * * * \\n\\n\");\n  printf(\"static const double s_arrFirH[%d] = {\\n\", n + 1);\n  for (i = 0; i <= n; i++)\n  {\n    printf(\"%12.8lf, \", h[i]);\n    if (0 == ((i + 1) % 10))\n    {\n      printf(\"\\n\");\n    }\n  }\n  printf(\"}\\n\");\n  \n  printf(\"\\nInput file name of frequency response\\n\");\n  scanf(\"%s\", fname);\n  fp = fopen(fname, \"w\");\n  if (fp == NULL)\n  {\n    printf(\"Cannot open this file\\n\");\n    exit(1);\n  }\n  Gain(h, c, n, 1, x, y, 300, 2);\n  for (i = 0; i < 300; i++)\n  {\n    freq = 0.5 * i \/ 299;\n    fprintf(fp, \"%lf,%lf\\n\", freq, x[i]);\n  }\n  fclose(fp);\n  return 0;\n}<\/code><\/pre>\n\n\n\n
\u4e0b\u9762\u8bbe\u8ba1\u4e00\u4e2a 128 \u9636\u7684 FIR \u4f4e\u901a\u6ee4\u6ce2\u5668\uff0c\u91c7\u6837\u7387 2kHz\uff0c\u901a\u5e26\u8fb9\u754c\u9891\u7387\u4e3a 25Hz\uff0c\u9009\u7528\u6c49\u5b81\u7a97\u3002\u9009\u62e9\u53c2\u6570 n = 128\uff0cband = 1\uff0cfl = 25\uff0c fs = 2000\uff0cwn = 4\u3002<\/p>\n\n\n\n
\u7ec8\u7aef\u7684\u8f93\u5165\u8f93\u51fa\u5982\u4e0b\u6240\u793a\u3002<\/p>\n\n\n\n
Select one of the four types for FIR digital filter\n1 -- lowpass; 2 -- highpass\n3 -- bandpass; 4 -- bandstop\n1\nInput the filter order\n128\nInput low cutoff frequrncy fl\n25\nInput sample frequence fs\n2000\nSelect window\n1 -- rectangular; 2 -- tapered rectangular\n3 -- triangular; 4 -- Hanning\n5 -- Hamming; 6 -- Blackman\n7 -- Kaiser\n4\nFIR digital filter\n * * * * impulse respomse * * * *\n\nh( 0) =  -0.00000000 = h(128)\nh( 1) =  -0.00000296 = h(127)\nh( 2) =  -0.00001221 = h(126)\nh( 3) =  -0.00002815 = h(125)\nh( 4) =  -0.00005097 = h(124)\nh( 5) =  -0.00008059 = h(123)\nh( 6) =  -0.00011670 = h(122)\nh( 7) =  -0.00015871 = h(121)\nh( 8) =  -0.00020575 = h(120)\nh( 9) =  -0.00025668 = h(119)\nh(10) =  -0.00031008 = h(118)\nh(11) =  -0.00036427 = h(117)\nh(12) =  -0.00041730 = h(116)\nh(13) =  -0.00046699 = h(115)\nh(14) =  -0.00051091 = h(114)\nh(15) =  -0.00054645 = h(113)\nh(16) =  -0.00057083 = h(112)\nh(17) =  -0.00058112 = h(111)\nh(18) =  -0.00057428 = h(110)\nh(19) =  -0.00054721 = h(109)\nh(20) =  -0.00049677 = h(108)\nh(21) =  -0.00041984 = h(107)\nh(22) =  -0.00031335 = h(106)\nh(23) =  -0.00017435 = h(105)\nh(24) =   0.00000000 = h(104)\nh(25) =   0.00021232 = h(103)\nh(26) =   0.00046500 = h(102)\nh(27) =   0.00076017 = h(101)\nh(28) =   0.00109963 = h(100)\nh(29) =   0.00148483 = h(99)\nh(30) =   0.00191684 = h(98)\nh(31) =   0.00239630 = h(97)\nh(32) =   0.00292340 = h(96)\nh(33) =   0.00349789 = h(95)\nh(34) =   0.00411901 = h(94)\nh(35) =   0.00478552 = h(93)\nh(36) =   0.00549567 = h(92)\nh(37) =   0.00624721 = h(91)\nh(38) =   0.00703742 = h(90)\nh(39) =   0.00786305 = h(89)\nh(40) =   0.00872043 = h(88)\nh(41) =   0.00960543 = h(87)\nh(42) =   0.01051350 = h(86)\nh(43) =   0.01143972 = h(85)\nh(44) =   0.01237883 = h(84)\nh(45) =   0.01332529 = h(83)\nh(46) =   0.01427329 = h(82)\nh(47) =   0.01521684 = h(81)\nh(48) =   0.01614980 = h(80)\nh(49) =   0.01706596 = h(79)\nh(50) =   0.01795909 = h(78)\nh(51) =   0.01882298 = h(77)\nh(52) =   0.01965152 = h(76)\nh(53) =   0.02043879 = h(75)\nh(54) =   0.02117906 = h(74)\nh(55) =   0.02186687 = h(73)\nh(56) =   0.02249711 = h(72)\nh(57) =   0.02306505 = h(71)\nh(58) =   0.02356640 = h(70)\nh(59) =   0.02399733 = h(69)\nh(60) =   0.02435454 = h(68)\nh(61) =   0.02463528 = h(67)\nh(62) =   0.02483737 = h(66)\nh(63) =   0.02495926 = h(65)\nh(64) =   0.02500000 = h(64)\n\n * * * * impulse respomse by C * * * *\n\nstatic const double s_arrFirH[129] = {\n -0.00000000,  -0.00000296,  -0.00001221,  -0.00002815,  -0.00005097,  -0.00008059,  -0.00011670,  -0.00015871,  -0.00020575,  -0.00025668,\n -0.00031008,  -0.00036427,  -0.00041730,  -0.00046699,  -0.00051091,  -0.00054645,  -0.00057083,  -0.00058112,  -0.00057428,  -0.00054721,\n -0.00049677,  -0.00041984,  -0.00031335,  -0.00017435,   0.00000000,   0.00021232,   0.00046500,   0.00076017,   0.00109963,   0.00148483,\n  0.00191684,   0.00239630,   0.00292340,   0.00349789,   0.00411901,   0.00478552,   0.00549567,   0.00624721,   0.00703742,   0.00786305,\n  0.00872043,   0.00960543,   0.01051350,   0.01143972,   0.01237883,   0.01332529,   0.01427329,   0.01521684,   0.01614980,   0.01706596,\n  0.01795909,   0.01882298,   0.01965152,   0.02043879,   0.02117906,   0.02186687,   0.02249711,   0.02306505,   0.02356640,   0.02399733,\n  0.02435454,   0.02463528,   0.02483737,   0.02495926,   0.02500000,   0.02495926,   0.02483737,   0.02463528,   0.02435454,   0.02399733,\n  0.02356640,   0.02306505,   0.02249711,   0.02186687,   0.02117906,   0.02043879,   0.01965152,   0.01882298,   0.01795909,   0.01706596,\n  0.01614980,   0.01521684,   0.01427329,   0.01332529,   0.01237883,   0.01143972,   0.01051350,   0.00960543,   0.00872043,   0.00786305,\n  0.00703742,   0.00624721,   0.00549567,   0.00478552,   0.00411901,   0.00349789,   0.00292340,   0.00239630,   0.00191684,   0.00148483,\n  0.00109963,   0.00076017,   0.00046500,   0.00021232,   0.00000000,  -0.00017435,  -0.00031335,  -0.00041984,  -0.00049677,  -0.00054721,\n -0.00057428,  -0.00058112,  -0.00057083,  -0.00054645,  -0.00051091,  -0.00046699,  -0.00041730,  -0.00036427,  -0.00031008,  -0.00025668,\n -0.00020575,  -0.00015871,  -0.00011670,  -0.00008059,  -0.00005097,  -0.00002815,  -0.00001221,  -0.00000296,  -0.00000000, }\n\nInput file name of frequency response\nresult.csv<\/code><\/pre>\n\n\n\n
\u8f93\u51fa\u7684\u5e45\u9891\u7279\u6027\u66f2\u7ebf\u5982\u4e0b\u6240\u793a\u3002<\/p>\n\n\n
\n
\"\"<\/figure><\/div>\n\n\n
\u672c\u6587\u63d0\u4f9b\u7684\u5fc3\u7535\u4fe1\u53f7\u662f\u7eaf\u51c0\u7684\uff0c\u4e0d\u5e26 50Hz \u5de5\u9891\u5e72\u6270\u7684\u3002\u6211\u4eec\u9700\u8981\u5148\u624b\u52a8\u6dfb\u52a0 50Hz \u5de5\u9891\u5e72\u6270\uff0c\u7136\u540e\u518d\u5bf9\u5fc3\u7535\u4fe1\u53f7\u8fdb\u884c\u6ee4\u6ce2\u3002\u5177\u4f53\u5982\u4e0b\u6240\u793a\u3002FIR \u6ee4\u6ce2\u5668\u7684\u53c2\u6570\u53ef\u4ee5\u76f4\u63a5\u4ece\u7ec8\u7aef\u91cc\u590d\u5236\uff0c\u4e0d\u7528\u624b\u52a8\u8f93\u5165\u3002<\/p>\n\n\n\n
int main(void)\n{\n  extern const double g_arrEcgWave[4000];\n  static double s_arrInput[4000] = {0};\n  static double s_arrOutput[4000] = {0};\n  static const double s_arrFirH[129] = {\n   -0.00000000,  -0.00000296,  -0.00001221,  -0.00002815,  -0.00005097,  -0.00008059,  -0.00011670,  -0.00015871,  -0.00020575,  -0.00025668,\n   -0.00031008,  -0.00036427,  -0.00041730,  -0.00046699,  -0.00051091,  -0.00054645,  -0.00057083,  -0.00058112,  -0.00057428,  -0.00054721,\n   -0.00049677,  -0.00041984,  -0.00031335,  -0.00017435,   0.00000000,   0.00021232,   0.00046500,   0.00076017,   0.00109963,   0.00148483,\n    0.00191684,   0.00239630,   0.00292340,   0.00349789,   0.00411901,   0.00478552,   0.00549567,   0.00624721,   0.00703742,   0.00786305,\n    0.00872043,   0.00960543,   0.01051350,   0.01143972,   0.01237883,   0.01332529,   0.01427329,   0.01521684,   0.01614980,   0.01706596,\n    0.01795909,   0.01882298,   0.01965152,   0.02043879,   0.02117906,   0.02186687,   0.02249711,   0.02306505,   0.02356640,   0.02399733,\n    0.02435454,   0.02463528,   0.02483737,   0.02495926,   0.02500000,   0.02495926,   0.02483737,   0.02463528,   0.02435454,   0.02399733,\n    0.02356640,   0.02306505,   0.02249711,   0.02186687,   0.02117906,   0.02043879,   0.01965152,   0.01882298,   0.01795909,   0.01706596,\n    0.01614980,   0.01521684,   0.01427329,   0.01332529,   0.01237883,   0.01143972,   0.01051350,   0.00960543,   0.00872043,   0.00786305,\n    0.00703742,   0.00624721,   0.00549567,   0.00478552,   0.00411901,   0.00349789,   0.00292340,   0.00239630,   0.00191684,   0.00148483,\n    0.00109963,   0.00076017,   0.00046500,   0.00021232,   0.00000000,  -0.00017435,  -0.00031335,  -0.00041984,  -0.00049677,  -0.00054721,\n   -0.00057428,  -0.00058112,  -0.00057083,  -0.00054645,  -0.00051091,  -0.00046699,  -0.00041730,  -0.00036427,  -0.00031008,  -0.00025668,\n   -0.00020575,  -0.00015871,  -0.00011670,  -0.00008059,  -0.00005097,  -0.00002815,  -0.00001221,  -0.00000296,  -0.00000000, };\n  static double s_arrPx[sizeof(s_arrFirH) \/ sizeof(double)] = {0};\n  int i, len;\n  long seed;\n  double pi, time;\n  FILE* fp;\n\n  \/\/\u5b9a\u4e49\u6570\u636e\u91cf\n  len = 4000;\n\n  \/\/\u83b7\u53d6\u8f93\u5165\u6570\u636e\uff0c\u52a0 50Hz \u5de5\u9891\u5e72\u6270\n  seed = 13579l;\n  pi = 3.1415926535;\n  time = 0;\n  for (i = 0; i < len; i++)\n  {\n    s_arrInput[i] = g_arrEcgWave[i] + 0.1 * sin(time * 2 * pi \/ (1.0 \/ 50.0));\n    time = time + 0.0005;\n  }\n\n  \/\/FIR \u6ee4\u6ce2\n  for (i = 0; i < len; i++)\n  {\n    s_arrOutput[i] = FirFilter(s_arrFirH, s_arrPx, (sizeof(s_arrFirH) \/ sizeof(double)) - 1, s_arrInput[i]);\n  }\n\n  \/\/\u8f93\u51fa\u6ce2\u5f62\u6570\u636e\uff0c\u6309\u7167\u539f\u59cb\u4fe1\u53f7\u3001\u53c2\u8003\u4fe1\u53f7\u3001\u6ee4\u6ce2\u540e\u4fe1\u53f7\u987a\u5e8f\n  fp = fopen(\"FirFilter.csv\", \"w\");\n  for (i = 0; i < len; i++)\n  {\n    fprintf(fp, \"%d,%10.7lf,%10.7lf,%10.7lf\\n\", i, s_arrInput[i], g_arrEcgWave[i], s_arrOutput[i]);\n  }\n  return 0;\n}<\/code><\/pre>\n\n\n\n
\u6700\u7ec8\u5b9e\u9a8c\u7ed3\u679c\u5982\u4e0b\u6240\u793a\u3002\u84dd\u8272\u4e3a\u53c2\u8003\u4fe1\u53f7\uff0c\u7eff\u8272\u4e3a\u8f93\u5165\u4fe1\u53f7\uff0c\u9ec4\u8272\u4e3a\u8f93\u51fa\u4fe1\u53f7\u3002<\/p>\n\n\n
\n
\"\"<\/figure><\/div>\n\n\n
<\/span>\u4f7f\u7528\u9891\u57df\u6700\u5c0f\u8bef\u5dee\u5e73\u65b9\u8bbe\u8ba1 FIR \u6570\u5b57\u6ee4\u6ce2\u5668<\/span><\/h2>\n\n\n\n
\u8bbe N-1 \u9636 FIR \u6570\u5b57\u6ee4\u6ce2\u5668\u7684\u5355\u4f4d\u51b2\u6fc0\u54cd\u5e94\u4e3a h(n)\uff0c\u5219\u4f20\u9012\u51fd\u6570 H(z) \u4e3a<\/p>\n\n\n\n
\\(H(z)=\\sum_{n=0}^{N-1}h(n)z^{-n}\\)<\/p>\n\n\n\n
FIR \u6ee4\u6ce2\u5668\u7684\u5b9e\u9645\u5e45\u5ea6\u76f8\u5e94 \\(H(w)\\) \u4e0e\u7406\u60f3\u5e45\u5ea6\u54cd\u5e94 \\(H_{d}(w)\\) \u7684\u8bef\u5dee\u51fd\u6570\u5b9a\u4e49\u4e3a<\/p>\n\n\n\n
\\(E=\\frac{1}{2\\pi }\\int_{-\\pi }^{\\pi }\\left | H(w)-H_{d}(w) \\right |^{2}dw\\)<\/p>\n\n\n\n
\u6839\u636e\u5e15\u585e\u74e6\u5b9a\u7406\uff0c\u8bef\u5dee\u51fd\u6570\u53ef\u4ee5\u8868\u793a\u4e3a<\/p>\n\n\n\n
\\(E=\\sum_{n=-\\infty }^{+\\infty }\\left | h(n)-h_{d}(n) \\right |^{2}=\\sum_{n=-M}^{M}\\left | h(n)-h_{d}(n) \\right |^{2}+\\sum_{n=M+1}^{\\infty }2h_{d}^{2}(n)\\)<\/p>\n\n\n\n
\u5176\u4e2d \\(M=(N-1)\/2\\)\u3002\u8be5\u5f0f\u8868\u660e\uff0c\u82e5\u8981\u4f7f \\(E\\) \u6700\u5c0f\uff0c\u5fc5\u987b\u9009\u62e9 \\(h(n)\\)\uff0c\u4f7f\u5b83\u4e0e \\(h_{d}(n)\\) \u5bf9\u5e94\u7684 N \u4e2a\u503c\u76f8\u7b49\uff0c\u5373 \\(h(n)=h_{d}(n),-M\\leqslant n\\leq M\\)\u3002<\/p>\n\n\n\n
\u4e3a\u4e86\u51cf\u5c11\u5409\u4f2f\u65af\uff08Gibbs\uff09\u6548\u5e94\uff0c\u901a\u5e38\u5728\u901a\u5e26\u548c\u963b\u5e26\u4e4b\u95f4\u52a0\u4e00\u4e2a\u8fc7\u6e21\u5e26\uff0c\\(f_{c}\\leqslant f\\leqslant f_{s}\\)\u3002\u8fc7\u6e21\u5e26\u51fd\u6570\u5e38\u91c7\u7528 \\(P\\) \u9636\u6837\u6761\u51fd\u6570\uff0c\u6b64\u65f6\u6ee4\u6ce2\u5668\u7684\u7cfb\u6570\u4e3a<\/p>\n\n\n\n
\\(h(n)=\\left ( \\frac{sin[\\pi (f_{s}-f_{c})(n-M)\/P]}{\\pi (f_{s}-f_{c})(n-M)\/P} \\right )^{p}\\frac{sin[\\pi (f_{s}+f_{c})(n-M)]}{\\pi (n-M)},0\\leqslant n\\leqslant N-1\\)<\/p>\n\n\n\n
\u8fc7\u6e21\u5e26\u51fd\u6570\u4e5f\u53ef\u91c7\u7528\u5347\u4f59\u5f26\u51fd\u6570\uff0c\u6b64\u65f6\u6ee4\u6ce2\u5668\u7684\u7cfb\u6570\u4e3a<\/p>\n\n\n\n
\\(h(n)=\\frac{cos[\\pi (f_{s}-f_{c})(n-M)]}{1-4(f_{s}-f_{c})^{2}(n-M)^{2}}\\frac{sin[\\pi (f_{s}+f_{c})(n-M)]}{\\pi (n-M)},0\\leqslant n\\leq N-1\\)<\/p>\n\n\n\n
\u5b9e\u73b0\u4ee3\u7801\u5982\u4e0b\u6240\u793a\u3002<\/p>\n\n\n\n
\/*********************************************************************************************************\n* \u51fd\u6570\u540d\u79f0\uff1a Firls\n* \u51fd\u6570\u529f\u80fd\uff1a FIR \u6570\u5b57\u6ee4\u6ce2\u5668\u7684\u8bbe\u8ba1\u3002\u7528\u9891\u57df\u6700\u5c0f\u8bef\u5dee\u5e73\u65b9\u65b9\u6cd5\u8bbe\u8ba1\u7ebf\u6027\u76f8\u4f4d FIR \u4f4e\u901a\u6570\u5b57\u6ee4\u6ce2\u5668\n* \u8f93\u5165\u53c2\u6570\uff1a n \uff1a\u6574\u5f62\u53d8\u91cf\u3002\u6ee4\u6ce2\u5668\u7684\u9636\u6570\u3002\n*            fc\uff1a\u53cc\u7cbe\u5ea6\u5b9e\u578b\u53d8\u91cf\u3002\u901a\u5e26\u8fb9\u754c\u9891\u7387\u3002\n*            fs\uff1a\u53cc\u7cbe\u5ea6\u5b9e\u578b\u53d8\u91cf\u3002\u963b\u5e26\u8fb9\u754c\u9891\u7387\u3002\n*            tp\uff1a\u6574\u5f62\u53d8\u91cf\u3002\u8fc7\u6e21\u5e26\u51fd\u6570\u7684\u7c7b\u578b\u3002tp = 0\uff0c\u8868\u793a\u5347\u4f59\u5f26\u51fd\u6570\uff1btp >= 1\uff0c\u8868\u793a tp \u9636\u6837\u6761\u51fd\u6570\u3002\n*            h \uff1a\u53cc\u7cbe\u5ea6\u5b9e\u578b\u4e00\u7ef4\u6570\u7ec4\uff0c\u957f\u5ea6\u4e3a\uff08n+1\uff09\uff0c\u5b58\u653e FIR \u6ee4\u6ce2\u5668\u7684\u7cfb\u6570\u3002\n* \u8f93\u51fa\u53c2\u6570\uff1a void\n* \u8fd4 \u56de \u503c\uff1a void\n* \u521b\u5efa\u65e5\u671f\uff1a 2023\u5e7410\u670803\u65e5\n* \u6ce8    \u610f\uff1a\n*********************************************************************************************************\/\nvoid Firls(int n, double fc, double fs, int tp, double* h)\n{\n  double fq, fr;\n  void ls(double* h, int n, double fc);\n  void wgt(double* h, int n, int tp, double fq);\n  fq = fs - fc;\n  fr = fs + fc;\n  ls(h, n, fr);\n  wgt(h, n, tp, fq);\n}\nstatic void ls(double* h, int n, double fc)\n{\n  int i, m, n2;\n  double q, am, pi;\n  pi = 4.0 * atan(1.0);\n  m = n \/ 2;\n  am = n \/ 2.0;\n  n2 = (n - 1) \/ 2;\n  if (m == am)\n  {\n    h[m] = fc;\n  }\n  for (i = 0; i <= n2; i++)\n  {\n    q = pi * (i - am);\n    h[i] = sin(fc * q) \/ q;\n  }\n}\nstatic void wgt(double* h, int n, int tp, double fq)\n{\n  int i;\n  double q, am, pi, ql, wt;\n  pi = 4.0 * atan(1.0);\n  q = pi * fq;\n  am = n \/ 2.0;\n  if (fq == 0.0)\n  {\n    return;\n  }\n  if (tp != 0)\n  {\n    for (i = 0; i < am; i++)\n    {\n      ql = q * (i - am) \/ tp;\n      wt = pow(sin(ql) \/ ql, tp);\n      h[i] = wt * h[i];\n    }\n  }\n  else\n  {\n    for (i = 0; i < am; i++)\n    {\n      wt = cos(q * (i - am));\n      if (fabs(wt) > 1.0e-6)\n      {\n        wt = wt \/ (1 - pow((2 * fq * (i - am)), 2));\n      }\n      else\n      {\n        wt = pi \/ 4.0;\n      }\n      h[i] = wt * h[i];\n    }\n  }\n  for (i = 0; i < am; i++)\n  {\n    h[n - i] = h[i];\n  }\n}<\/code><\/pre>\n\n\n\n
\u4e0b\u9762\u7ed9\u51fa\u4e3b\u51fd\u6570\u7a0b\u5e8f\uff0c\u5b83\u8c03\u7528 Firls \u51fd\u6570\u3002\u901a\u8fc7\u4eba\u673a\u5bf9\u8bdd\uff0c\u5b83\u53ef\u4ee5\u8bbe\u8ba1\u7ebf\u6027\u76f8\u4f4d FIR \u4f4e\u901a\u6570\u5b57\u6ee4\u6ce2\u5668\u3002\u4e0b\u9762\u5bf9\u8f93\u5165\u53c2\u6570\u8fdb\u884c\u8bf4\u660e\u3002<\/p>\n\n\n\n
n\uff1a\u6ee4\u6ce2\u5668\u7684\u9636\u6570\uff1b<\/p>\n\n\n\n
f\uff1a\u91c7\u6837\u9891\u7387\uff1b<\/p>\n\n\n\n
fc\uff1a\u901a\u5e26\u8fb9\u754c\u9891\u7387\uff1b<\/p>\n\n\n\n
fs\uff1a\u963b\u5e26\u8fb9\u754c\u9891\u7387\uff1b<\/p>\n\n\n\n
tp\uff1a\u6837\u6761\u51fd\u6570\u7684\u9636\u6570\uff1b<\/p>\n\n\n\n
fname\uff1a\u5e45\u9891\u76f8\u5e94\u6587\u4ef6\u540d\u3002<\/p>\n\n\n\n
int main(void)\n{\n  int i, j, n, n2, tp;\n  double f, fc, fs, freq;\n  static double h[10240], c[10240], x[300], y[300];\n  char fname[40];\n  FILE* fp;\n  c[1] = 0.0;\n  printf(\"Input this filter order\\n\");\n  scanf(\"%d\", &n);\n  printf(\"Input passband cutoff frequrncy fc\\n\");\n  scanf(\"%lf\", &fc);\n  printf(\"Input stopband edge frequrncy fs\\n\");\n  scanf(\"%lf\", &fs);\n  printf(\"Input sample frequrncy f\\n\");\n  scanf(\"%lf\", &f);\n  fc = fc \/ f;\n  fs = fs \/ f;\n  printf(\"Input the order of spline n\\n\");\n  scanf(\"%d\", &tp);\n  Firls(n, fc, fs, tp, h);\n  printf(\"FIR digital filter\\n\");\n  printf(\" * * * * impulse respomse * * * * \\n\\n\");\n  n2 = n \/ 2;\n  for (i = 0; i <= n2; i++)\n  {\n    j = n - i;\n    printf(\"h(%2d) = %12.8lf = h(%2d)\\n\", i, h[i], j);\n  }\n  printf(\"\\n * * * * impulse respomse by C * * * * \\n\\n\");\n  printf(\"static const double s_arrFirH[%d] = {\\n\", n + 1);\n  for (i = 0; i <= n; i++)\n  {\n    printf(\"%12.8lf, \", h[i]);\n    if (0 == ((i + 1) % 10))\n    {\n      printf(\"\\n\");\n    }\n  }\n  printf(\"}\\n\");\n  printf(\"\\nInput file name of frequency response\\n\");\n  scanf(\"%s\", fname);\n  fp = fopen(fname, \"w\");\n  if (fp == NULL)\n  {\n    printf(\"Cannot open this file\\n\");\n    exit(1);\n  }\n  Gain(h, c, n, 1, x, y, 300, 2);\n  for (i = 0; i < 300; i++)\n  {\n    freq = 0.5 * i \/ 299;\n    fprintf(fp, \"%lf,%lf\\n\", freq, x[i]);\n  }\n  fclose(fp);\n  return 0;\n}<\/code><\/pre>\n\n\n\n
\u8bbe\u8ba1\u4e00\u4e2a 128 \u9636\u7684 FIR \u4f4e\u901a\u6ee4\u6ce2\u5668\uff0c\u5176\u91c7\u6837\u7387\u4e3a 2kHz\uff0c\u901a\u5e26\u8fb9\u754c\u9891\u7387\u4e3a 20Hz\uff0c\u963b\u5e26\u8fb9\u754c\u9891\u7387\u4e3a 25Hz\uff0c\u91c7\u7528\u4e00\u9636\u6837\u6761\u51fd\u6570\u4f5c\u4e3a\u8fc7\u6e21\u5e26\u3002\u9009\u62e9\u53c2\u6570 n = 128\uff0cfc = 20\uff0cfs = 25\uff0cf = 2000\uff0ctp = 1\u3002<\/p>\n\n\n\n
\u7ec8\u7aef\u8f93\u5165\u8f93\u51fa\u5982\u4e0b\u6240\u793a\u3002<\/p>\n\n\n\n
Input this filter order\n128\nInput passband cutoff frequrncy fc\n20\nInput stopband edge frequrncy fs\n25\nInput sample frequrncy f\n2000\nInput the order of spline n\n1\nFIR digital filter\n * * * * impulse respomse * * * *\n\nh( 0) =  -0.00468235 = h(128)\nh( 1) =  -0.00468693 = h(127)\nh( 2) =  -0.00466754 = h(126)\nh( 3) =  -0.00462343 = h(125)\nh( 4) =  -0.00455392 = h(124)\nh( 5) =  -0.00445842 = h(123)\nh( 6) =  -0.00433640 = h(122)\nh( 7) =  -0.00418745 = h(121)\nh( 8) =  -0.00401123 = h(120)\nh( 9) =  -0.00380749 = h(119)\nh(10) =  -0.00357607 = h(118)\nh(11) =  -0.00331693 = h(117)\nh(12) =  -0.00303011 = h(116)\nh(13) =  -0.00271576 = h(115)\nh(14) =  -0.00237410 = h(114)\nh(15) =  -0.00200550 = h(113)\nh(16) =  -0.00161039 = h(112)\nh(17) =  -0.00118932 = h(111)\nh(18) =  -0.00074293 = h(110)\nh(19) =  -0.00027196 = h(109)\nh(20) =   0.00022274 = h(108)\nh(21) =   0.00074024 = h(107)\nh(22) =   0.00127951 = h(106)\nh(23) =   0.00183945 = h(105)\nh(24) =   0.00241883 = h(104)\nh(25) =   0.00301637 = h(103)\nh(26) =   0.00363072 = h(102)\nh(27) =   0.00426042 = h(101)\nh(28) =   0.00490395 = h(100)\nh(29) =   0.00555975 = h(99)\nh(30) =   0.00622616 = h(98)\nh(31) =   0.00690150 = h(97)\nh(32) =   0.00758400 = h(96)\nh(33) =   0.00827189 = h(95)\nh(34) =   0.00896332 = h(94)\nh(35) =   0.00965643 = h(93)\nh(36) =   0.01034934 = h(92)\nh(37) =   0.01104013 = h(91)\nh(38) =   0.01172688 = h(90)\nh(39) =   0.01240766 = h(89)\nh(40) =   0.01308055 = h(88)\nh(41) =   0.01374362 = h(87)\nh(42) =   0.01439497 = h(86)\nh(43) =   0.01503271 = h(85)\nh(44) =   0.01565498 = h(84)\nh(45) =   0.01625997 = h(83)\nh(46) =   0.01684589 = h(82)\nh(47) =   0.01741100 = h(81)\nh(48) =   0.01795362 = h(80)\nh(49) =   0.01847214 = h(79)\nh(50) =   0.01896500 = h(78)\nh(51) =   0.01943071 = h(77)\nh(52) =   0.01986787 = h(76)\nh(53) =   0.02027516 = h(75)\nh(54) =   0.02065133 = h(74)\nh(55) =   0.02099524 = h(73)\nh(56) =   0.02130585 = h(72)\nh(57) =   0.02158219 = h(71)\nh(58) =   0.02182344 = h(70)\nh(59) =   0.02202883 = h(69)\nh(60) =   0.02219775 = h(68)\nh(61) =   0.02232968 = h(67)\nh(62) =   0.02242421 = h(66)\nh(63) =   0.02248104 = h(65)\nh(64) =   0.02250000 = h(64)\n\n * * * * impulse respomse by C * * * *\n\nstatic const double s_arrFirH[129] = {\n -0.00468235,  -0.00468693,  -0.00466754,  -0.00462343,  -0.00455392,  -0.00445842,  -0.00433640,  -0.00418745,  -0.00401123,  -0.00380749,\n -0.00357607,  -0.00331693,  -0.00303011,  -0.00271576,  -0.00237410,  -0.00200550,  -0.00161039,  -0.00118932,  -0.00074293,  -0.00027196,\n  0.00022274,   0.00074024,   0.00127951,   0.00183945,   0.00241883,   0.00301637,   0.00363072,   0.00426042,   0.00490395,   0.00555975,\n  0.00622616,   0.00690150,   0.00758400,   0.00827189,   0.00896332,   0.00965643,   0.01034934,   0.01104013,   0.01172688,   0.01240766,\n  0.01308055,   0.01374362,   0.01439497,   0.01503271,   0.01565498,   0.01625997,   0.01684589,   0.01741100,   0.01795362,   0.01847214,\n  0.01896500,   0.01943071,   0.01986787,   0.02027516,   0.02065133,   0.02099524,   0.02130585,   0.02158219,   0.02182344,   0.02202883,\n  0.02219775,   0.02232968,   0.02242421,   0.02248104,   0.02250000,   0.02248104,   0.02242421,   0.02232968,   0.02219775,   0.02202883,\n  0.02182344,   0.02158219,   0.02130585,   0.02099524,   0.02065133,   0.02027516,   0.01986787,   0.01943071,   0.01896500,   0.01847214,\n  0.01795362,   0.01741100,   0.01684589,   0.01625997,   0.01565498,   0.01503271,   0.01439497,   0.01374362,   0.01308055,   0.01240766,\n  0.01172688,   0.01104013,   0.01034934,   0.00965643,   0.00896332,   0.00827189,   0.00758400,   0.00690150,   0.00622616,   0.00555975,\n  0.00490395,   0.00426042,   0.00363072,   0.00301637,   0.00241883,   0.00183945,   0.00127951,   0.00074024,   0.00022274,  -0.00027196,\n -0.00074293,  -0.00118932,  -0.00161039,  -0.00200550,  -0.00237410,  -0.00271576,  -0.00303011,  -0.00331693,  -0.00357607,  -0.00380749,\n -0.00401123,  -0.00418745,  -0.00433640,  -0.00445842,  -0.00455392,  -0.00462343,  -0.00466754,  -0.00468693,  -0.00468235, }\n\nInput file name of frequency response\nresult.csv<\/code><\/pre>\n\n\n\n
\u8f93\u51fa\u7684\u5e45\u9891\u7279\u6027\u66f2\u7ebf\u5982\u4e0b\u6240\u793a\u3002<\/p>\n\n\n
\n
\"\"<\/figure><\/div>\n\n\n
\u672c\u6587\u63d0\u4f9b\u7684\u5fc3\u7535\u4fe1\u53f7\u662f\u7eaf\u51c0\u7684\uff0c\u4e0d\u5e26 50Hz \u5de5\u9891\u5e72\u6270\u7684\u3002\u6211\u4eec\u9700\u8981\u5148\u624b\u52a8\u6dfb\u52a0 50Hz \u5de5\u9891\u5e72\u6270\uff0c\u7136\u540e\u518d\u5bf9\u5fc3\u7535\u4fe1\u53f7\u8fdb\u884c\u6ee4\u6ce2\u3002\u5177\u4f53\u5982\u4e0b\u6240\u793a\u3002FIR \u6ee4\u6ce2\u5668\u7684\u53c2\u6570\u53ef\u4ee5\u76f4\u63a5\u4ece\u7ec8\u7aef\u91cc\u590d\u5236\uff0c\u4e0d\u7528\u624b\u52a8\u8f93\u5165\u3002<\/p>\n\n\n\n
int main(void)\n{\n  extern const double g_arrEcgWave[4000];\n  static double s_arrInput[4000] = {0};\n  static double s_arrOutput[4000] = {0};\n  static const double s_arrFirH[129] = {\n   -0.00468235,  -0.00468693,  -0.00466754,  -0.00462343,  -0.00455392,  -0.00445842,  -0.00433640,  -0.00418745,  -0.00401123,  -0.00380749,\n   -0.00357607,  -0.00331693,  -0.00303011,  -0.00271576,  -0.00237410,  -0.00200550,  -0.00161039,  -0.00118932,  -0.00074293,  -0.00027196,\n    0.00022274,   0.00074024,   0.00127951,   0.00183945,   0.00241883,   0.00301637,   0.00363072,   0.00426042,   0.00490395,   0.00555975,\n    0.00622616,   0.00690150,   0.00758400,   0.00827189,   0.00896332,   0.00965643,   0.01034934,   0.01104013,   0.01172688,   0.01240766,\n    0.01308055,   0.01374362,   0.01439497,   0.01503271,   0.01565498,   0.01625997,   0.01684589,   0.01741100,   0.01795362,   0.01847214,\n    0.01896500,   0.01943071,   0.01986787,   0.02027516,   0.02065133,   0.02099524,   0.02130585,   0.02158219,   0.02182344,   0.02202883,\n    0.02219775,   0.02232968,   0.02242421,   0.02248104,   0.02250000,   0.02248104,   0.02242421,   0.02232968,   0.02219775,   0.02202883,\n    0.02182344,   0.02158219,   0.02130585,   0.02099524,   0.02065133,   0.02027516,   0.01986787,   0.01943071,   0.01896500,   0.01847214,\n    0.01795362,   0.01741100,   0.01684589,   0.01625997,   0.01565498,   0.01503271,   0.01439497,   0.01374362,   0.01308055,   0.01240766,\n    0.01172688,   0.01104013,   0.01034934,   0.00965643,   0.00896332,   0.00827189,   0.00758400,   0.00690150,   0.00622616,   0.00555975,\n    0.00490395,   0.00426042,   0.00363072,   0.00301637,   0.00241883,   0.00183945,   0.00127951,   0.00074024,   0.00022274,  -0.00027196,\n   -0.00074293,  -0.00118932,  -0.00161039,  -0.00200550,  -0.00237410,  -0.00271576,  -0.00303011,  -0.00331693,  -0.00357607,  -0.00380749,\n   -0.00401123,  -0.00418745,  -0.00433640,  -0.00445842,  -0.00455392,  -0.00462343,  -0.00466754,  -0.00468693,  -0.00468235, };\n  static double s_arrPx[sizeof(s_arrFirH) \/ sizeof(double)] = {0};\n  int i, len;\n  long seed;\n  double pi, time;\n  FILE* fp;\n\n  \/\/\u5b9a\u4e49\u6570\u636e\u91cf\n  len = 4000;\n\n  \/\/\u83b7\u53d6\u8f93\u5165\u6570\u636e\uff0c\u52a0 50Hz \u5de5\u9891\u5e72\u6270\n  seed = 13579l;\n  pi = 3.1415926535;\n  time = 0;\n  for (i = 0; i < len; i++)\n  {\n    s_arrInput[i] = g_arrEcgWave[i] + 0.1 * sin(time * 2 * pi \/ (1.0 \/ 50.0));\n    time = time + 0.0005;\n  }\n\n  \/\/FIR \u6ee4\u6ce2\n  for (i = 0; i < len; i++)\n  {\n    s_arrOutput[i] = FirFilter(s_arrFirH, s_arrPx, (sizeof(s_arrFirH) \/ sizeof(double)) - 1, s_arrInput[i]);\n  }\n\n  \/\/\u8f93\u51fa\u6ce2\u5f62\u6570\u636e\uff0c\u6309\u7167\u539f\u59cb\u4fe1\u53f7\u3001\u53c2\u8003\u4fe1\u53f7\u3001\u6ee4\u6ce2\u540e\u4fe1\u53f7\u987a\u5e8f\n  fp = fopen(\"FirFilter.csv\", \"w\");\n  for (i = 0; i < len; i++)\n  {\n    fprintf(fp, \"%d,%10.7lf,%10.7lf,%10.7lf\\n\", i, s_arrInput[i], g_arrEcgWave[i], s_arrOutput[i]);\n  }\n  return 0;\n}<\/code><\/pre>\n\n\n\n
\u6700\u7ec8\u5b9e\u9a8c\u7ed3\u679c\u5982\u4e0b\u6240\u793a\u3002\u84dd\u8272\u4e3a\u53c2\u8003\u4fe1\u53f7\uff0c\u7eff\u8272\u4e3a\u8f93\u5165\u4fe1\u53f7\uff0c\u9ec4\u8272\u4e3a\u8f93\u51fa\u4fe1\u53f7\u3002<\/p>\n\n\n
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\"\"<\/figure><\/div>\n\n\n
<\/span>\u5fc3\u7535\u6570\u636e<\/span><\/h2>\n\n\n\n
\u672c\u6587\u4e2d\u4f7f\u7528\u5230\u7684\u5fc3\u7535\u6570\u636e\u5982\u4e0b\u6240\u793a\u3002<\/p>\n\n\n\n
\/*\n * \u5fc3\u7535\u6ce2\u5f62\u6570\u636e\n * \u91c7\u6837\u7387 2kHz\n * \u8109\u7387\u503c 60BPM\n * \u5355\u4f4d mV\n *\/\nconst double g_arrEcgWave[4000] = 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