Matlab Filter函数学习及C语言2阶实现

1、Matlab Filter

Matlab脚本

• 在Matlab中使用butter函数设计n阶滤波器b、a系数
• 在Matlab中使用将b、a系数传入filter函数实现滤波

clc;
clear;
close all;

fc = 100;
fs = 1000;

[b,a] = butter(2,fc/(fs/2))

freqz(b,a,[],fs)

subplot(2,1,1)
ylim([-100 20])

dataIn = randn(1000,1);
dataOut = filter(b,a,dataIn);

figure()
plot(dataIn)
hold on
plot(dataOut)

运行结果

函数说明（来源Matlab）

butter

filter

2、C语言实现

公式

C代码（2阶）

void filter_2order(double *b, double *a, double* x, double* y, unsigned int len)
{
	unsigned int i = 0;
	y[0] = b[0] * x[0];
	y[1] = b[0] * x[1] + b[1] * x[0] - a[1] * y[0];
	for (i = 2; i < len; i++)
	{
		y[i] = b[0] * x[i] + b[1] * x[i - 1] + b[2] * x[i - 2] - a[1] * y[i - 1] - a[2] * y[i - 2];
	}
}

测试主函数

int main(void)
{
#define ORDER	2
#define LEN		1000

	double b[ORDER + 1] = { 0.067455274,0.134910548,0.067455274 };
	double a[ORDER + 1] = { 1,-1.142980503,0.412801598 };
	double x[LEN] = { -0.491328111,0.657745314,1.436083027,-1.535033015,1.752844532,1.283050852,0.093642419,1.580098828,0.244783676,-1.020254356,1.127840682,2.232468702,-0.774247093,-1.001457286,1.138326349,-0.023951589,-1.363832296,1.236316183,-0.154075344,-0.795206586,-0.581572584,-0.497663996,0.937428006,-1.155727401,0.469223861,1.004411364,-0.859842623,0.334386523,-1.653469212,0.696878623,-1.122209427,0.806363297,0.433565065,-0.411399971,-1.479868178,1.331586826,0.152702847,1.677299219,0.008565093,-1.778385222,1.690066583,-0.291388735,0.924400207,-0.722240284,0.611834579,0.834988463,1.013086105,0.499048921,-0.040810929,0.144477744,0.302344993,-0.738461735,0.550423231,-1.064474418,-1.905377815,0.166565726,0.197731836,0.220736301,1.772843881,1.232882475,1.863792959,0.220350637,0.908635455,-0.591170221,-0.230979854,-1.747769492,0.069832209,0.926980897,-1.058176043,-0.222484554,-0.72408143,-0.808408292,0.902393481,0.067267077,0.739593243,0.39677531,0.935791523,-2.257203967,-1.022122876,-0.171884806,0.347912133,1.148432523,-0.639623721,-0.604947425,-0.285155015,0.695220483,0.106434776,1.125701654,-0.771931903,0.411133643,0.387188439,-1.644007767,0.296388813,1.739693661,-1.197785212,-0.637081262,-1.016757906,1.129067957,-0.556514075,0.751357989,-1.644759821,-1.822552249,0.997355788,0.593306266,0.280074227,0.967067587,0.067591032,0.139905171,-0.874892317,0.009505575,-1.100317252,-0.890699813,-0.477231952,0.13873541,1.602834872,0.377530026,0.406144873,0.543279428,1.203667788,0.580418912,0.063672442,-0.433042715,0.597220105,-1.68351719,0.041732906,0.943244353,-0.227951816,0.576819232,0.172430276,0.585028268,-0.49346731,1.67126214,0.396610858,0.141009748,-1.190598616,-0.193148666,-1.445605833,-0.288587492,-1.229140422,-0.063965837,0.152206915,-0.484546103,1.632897838,1.368895506,1.413900768,0.590728575,0.780002129,-0.657244217,0.131814263,-1.122417171,0.239846434,1.142156113,-1.100866604,-0.208882455,-1.46608136,0.606281003,1.230829436,1.14345173,-1.02566565,-0.709034818,-0.102158521,-0.395123393,-0.527554291,-2.524534946,0.636676728,-0.234422175,0.693361433,0.264528592,-2.978544004,-0.301313132,0.786084975,1.045165478,-0.317219122,0.520515639,0.237981084,0.921874425,1.963604137,-0.911435262,2.09993653,0.214464095,-0.799034553,-0.810339567,0.117768314,0.138022894,0.410911288,0.827006697,0.361593114,-1.024509991,-0.690159113,-0.758888632,-0.590452742,0.355152945,0.340715749,-0.227538168,-0.998835959,-0.325849588,0.597047559,-0.129605967,1.440339764,-0.818393473,0.294179209,1.15137207,-0.860265311,-0.05609512,-1.214747045,-0.931103506,-1.447286497,-0.93474905,0.367631235,-0.240151113,0.58303962,1.027739958,0.362556895,0.77548101,0.754981737,2.357318467,0.757204413,-1.49199876,0.295768561,0.667410122,0.942656022,0.817138566,-0.491906131,0.027691451,0.345195484,0.215736984,2.028995444,-1.604517315,0.855678863,1.186423616,-0.590599071,0.495655924,-0.089001675,-1.033427345,0.100672297,1.668133275,-0.399147114,0.627519816,-1.121339544,-0.921659114,-1.239045479,-1.434684338,-0.942524572,-0.899643027,-0.442063537,-1.643538186,-0.506853297,-0.774918685,-0.793732023,-0.316836213,1.171767508,-0.004797876,0.421027773,1.585497243,0.684602385,0.12938685,1.086017158,2.229872638,-0.516964715,0.848372855,-0.813994061,-1.248465244,-0.677408992,-0.073731963,-1.961731227,-1.598594703,-0.057066145,0.600563607,0.785452724,0.437340298,-0.179804694,0.530015843,2.492850202,1.976814728,-0.059381352,1.414432228,-0.62058383,0.350801627,0.14442274,0.763297178,-1.214938461,0.624257038,0.168626236,0.328758593,-1.02861151,-0.393576332,-1.544140356,-0.733862581,-0.969899942,-0.3496269,0.169241311,0.847958684,-1.06906282,0.293622184,1.086485561,0.961315233,-1.594446358,0.732017984,-0.168767033,1.381407728,0.929302073,-0.348845746,0.269422539,0.510851504,-2.461178451,-0.613988223,-0.39544689,-1.144753672,-2.23236833,0.840037507,-0.613785968,1.17215934,-0.958240409,0.953125795,0.703446627,0.559895045,-1.037997901,-0.178315643,-0.469938546,-0.959886736,-0.445025298,-1.621173741,-0.157394384,-0.197458254,-0.831367451,0.637333937,-1.048598681,-0.248183185,0.524913159,0.213223909,-2.397377049,-0.772418839,-0.406103307,-0.553319721,-1.352965973,-0.043116229,-0.167630791,1.279593129,0.112219107,0.705481392,-0.130396955,-1.825464429,-1.473279377,-0.751403919,-0.433729916,0.576351041,-0.834456151,-0.628795362,0.255851793,-0.562049583,-1.228419863,-0.554040938,-0.680275588,0.691164599,0.221938054,0.545931143,-0.459746999,2.116712668,0.109101493,-0.919826045,-1.323605998,0.098650184,-0.406640029,-1.351891832,-0.469815207,-1.628010774,0.682417154,1.94370839,0.740237955,-0.323177184,1.359645942,0.291030256,-2.218994711,-0.144627255,0.078700061,0.562218061,-0.164275808,1.173703169,-1.328395111,2.459213462,1.352204826,-0.246773287,0.288016672,-0.872674102,-0.930755707,0.076155378,0.985664468,0.925841557,2.13149973,-0.325832926,-0.223013464,-2.734301273,-0.308548313,0.146108342,0.037732668,-0.647646618,-1.287407016,-0.4110156,2.200545337,-0.929047088,0.002664404,-1.157621762,1.16453125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};
	double y[LEN] = { 0 };

	filter_2order(b, a, x, y, LEN);

	FILE* fd = fopen("filter_demo.csv", "w");
	for (int i = 0; i < LEN; i++)
	{
		fprintf(fd, "%f,%f\n", x[i], y[i]);
	}
	fclose(fd);
}

运行结果

结果与Matlab计算的一样