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signal-processing - Scilab - 查找巴特沃斯系数并过滤模拟数据

问题描述

对于带有加速度计的项目，我正在寻找一种过滤一些高频的方法。我不是信号专家，但我通常会根据需要阅读，使用巴特沃斯滤波器。

我为此目的使用 Scilab，我正在努力解释我的结果：我编写了以下代码（在底部）并比较了 Scilab 输出函数以在 Arduino中实现这个过滤方程：

我的问题是：

“系数：Num / Den：”
1。

  1. 0.063662 0.0020264 0.0000323

我期望结果为规范形式 ，期望值为

b1 0.331785003 ; b2 0.99535501 ; b3 0.99535501 ; b4 0.331785003
a1 -0.965826145 ; a2 -0.582614466 ; a3 -0.106171201

从这里的外部软件（链接）计算，N=3，低通，Fc=5，Fs=15。

你能看看我的代码并给我一些建议来纠正它并有正确的系数 ai 和 bi 吗？

/////////////////// cleanup
clear;
//clc;
close;


////////////////////// variable declaration
fcut = 5; //cut off frequency hz (delta 1)
fsampl = 15 ; //sampling frequency hz (delta 2)
delta1_in_dB = -3; // attenuation value at fcut
delta2_in_dB = -21; // final attenuation
delta1 = 10^(delta1_in_dB/20)
delta2 = 10^(delta2_in_dB/20)
epsilon = 0; //ripple value [0 1]
rp = [epsilon epsilon] // ripple vector for analpf 

// conversion of attenuation
delta1 = 10^(delta1_in_dB/20);
delta2 = 10^(delta2_in_dB/20);

// N computation
N = log10((1/(delta2^2))-1)/(2*log10(fspan/fcut));
N = ceil(N);
disp("Order",N);

/////////////////// compute different functions to compaire Butterworth
[poleZP,gainZP]=zpbutt(N,fcut*2*%pi);

[hsAna,poleAna,zeroAna,gainAna]=analpf(N,'butt',rp,fcut*2*%pi);

//disp("Pole : Zpbutt ",poleZP , "Analpf ",poleAna)
//disp("Gain : Zpbutt ",gainZP , "Analpf ",gainAna)
//disp("function :",hsAna)
//       conclusion : zpbutt et analpf donnent la même sortie

/////////////////// paramters in linear system
// Generate the equivalent linear system of the filter
num   = gainAna * real(poly(zeroAna,'s'));
den   = real(poly(poleAna,'s'));
elatf = syslin('c',num,den);

Cnum=coeff(num);
Cden=coeff(den)/Cnum;
Cnum=1;

disp('coefficients : Num / Den : ',Cnum,Cden)





/////////////////// plot an exemple to compare csim and filter
rand('normal');
Input = rand(1,1000); // Produce a random gaussian noise
t     = 1:1000;
t     = t*0.01; // Convert sample index into time steps

y_csim = csim(Input,t,elatf); // Filter the signal with csim
y_res = filter(Cnum, Cden, Input) // Filter the signal with filter


// plot curves
subplot(3,1,1);
plot(t,Input);
xtitle('The gaussian noise','t','y');
subplot(3,1,2);
plot(t,y_csim,'b');
xtitle('The ''csim'' filtered gaussian noise','t','y');
subplot(3,1,3);
plot(t,y_res,'r');
xtitle('The ''filter'' filtered gaussian noise','t','y');

提前感谢您的支持！！

标签： signal-processingscilabbutterworth

解决方案

这是我更新的代码以及@Mark H 提出的解决方案（再次感谢！）。我还有一些问号，主要是面向 Scilab，如果有人可以教我（但这不是我项目的障碍）。

flts和filterfunction有什么区别？我的输出结果与这些功能不同。

代码 ：

////////////////////// cleanup
clear;
//clc; clear console
close;

////////////////////// variable declaration
fcut = 10000; //cut off frequency hz (delta 1)
fsampl = 100000 ; //sampling frequency hz (delta 2)
delta1_in_dB = -3; // attenuation value at fcut
delta2_in_dB = -21; // final attenuation

// conversion of attenuation
delta1 = 10^(delta1_in_dB/20);
delta2 = 10^(delta2_in_dB/20);

// order N computation
N = log10((1/(delta2^2))-1)/(2*log10(fsampl/fcut));
N = ceil(N);
disp("Order",N);

///////////////////// computer Butterworth transfer function
hz=iir(N,'lp','butt',fcut/fsampl,[ ]);

///////////////////////////// extract coefficient from transfer function
num   = coeff(hz(2));
den   = -1*coeff(hz(3));
gain = 1/num(1)

// display value and graph
disp('gain',gain)
disp('''b'' coefficients : num xi',num)
disp('''a'' coefficients : den yi',den(N:-1:1))

[hzm,fr]=frmag(hz,256);
f = scf(0)
plot(fr,hzm)


/////////////////// plot an exemple
rand('normal');
Input = rand(1,1000); // Produce a random gaussian noise
t     = 1:1000;
t     = t*0.01; // Convert sample index into time steps

//Change from transfer function to linear system
    sl= tf2ss(hz)

//Filter the signal
    fs=flts(Input,sl);

// plot curves of raw and filtered data
f = scf(1)
subplot(2,1,1);
plot(t,Input,'b');
xtitle('The gaussian noise','t','y');
subplot(2,1,2);
plot(t,fs,'r');
xtitle('The filtered gaussian noise','t','y');




///////////////////// export on CSV
filename = fullfile(TMPDIR, "data_test_filter.csv");
separator = ";"
M = [t' Input' fs']; //data matrix
csvWrite(M, filename, separator);

filename = fullfile(TMPDIR, "coeff.csv");
C = [gain num den(N:-1:1)] ;//coeff matrix
csvWrite(C, filename, separator);


disp("DONE !");

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