filter - 我如何自己编写 Matlab "filter"函数？

Question

我想在一维信号上使用巴特沃斯滤波器。在 Matlab 中，脚本如下所示:

 f=100;
 f_cutoff = 20; 
 fnorm =f_cutoff/(f/2);
 [b,a] = butter(8,fnorm,'low');
 filteredData = filter(b,a,rawData); % I want to write this myself

现在不想直接用Matlab给的filter函数而是自己写。在Matlab文档中是这样描述的:

The filter function is implemented as a direct form II transposed structure,

y(n) = b(1)*x(n) + b(2)*x(n-1) + ... + b(nb+1)*x(n-nb) - a(2)*y(n-1) - ... - a(na+1)*y(n-na)

where n-1 is the filter order, which handles both FIR and IIR filters [1], na is the feedback filter order, and nb is the feedforward filter order.

所以我已经尝试编写这样的函数:

f=100;
f_cutoff = 20; 
fnorm =f_cutoff/(f/2);
[b,a] = butter(8,fnorm,'low');
for n = 9:size(rawData,1)
    filteredData(n,1) = b(1)*n + b(2)*(n-1) + b(3)*(n-2) + b(4)*(n-3) + b(5)*(n-4) ...
                      - a(2)*rawData(n-1,1) - a(3)*rawData(n-2,1) - a(4)*rawData(n-3,1) - a(5)*accel(n-4,1);
end

但这行不通。你能帮我么？我做错了什么？

真诚的，切尔多

PS:过滤器文档可以在这里找到:http://www.mathworks.de/de/help/matlab/ref/filter.html#f83-1015962当扩展更多关于 -> 算法

Answer 1

检查我的答案

过滤器

    public static double[] filter(double[] b, double[] a, double[] x) {
      double[] filter = null;
      double[] a1 = getRealArrayScalarDiv(a,a[0]);
      double[] b1 = getRealArrayScalarDiv(b,a[0]);
      int sx = x.length;
      filter = new double[sx];
      filter[0] = b1[0]*x[0];
      for (int i = 1; i < sx; i++) {
        filter[i] = 0.0;
        for (int j = 0; j <= i; j++) {
          int k = i-j;
          if (j > 0) {
            if ((k < b1.length) && (j < x.length)) {
              filter[i] += b1[k]*x[j];
            }
            if ((k < filter.length) && (j < a1.length)) {
              filter[i] -= a1[j]*filter[k];
            }
          } else {
            if ((k < b1.length) && (j < x.length)) {
              filter[i] += (b1[k]*x[j]);
            }
          }
        }
      }
      return filter;
    }

转化

    public static double[] conv(double[] a, double[] b) {
      double[] c = null;
      int na = a.length;
      int nb = b.length;
      if (na > nb) {
        if (nb > 1) {
          c = new double[na+nb-1];
          for (int i = 0; i < c.length; i++) {
            if (i < a.length) {
              c[i] = a[i];
            } else {
              c[i] = 0.0;
            }
          }
          a = c;
        }
        c = filter(b, new double [] {1.0} , a);
      } else {
        if (na > 1) {
          c = new double[na+nb-1];
          for (int i = 0; i < c.length; i++) {
            if (i < b.length) {
              c[i] = b[i];
            } else {
              c[i] = 0.0;
            }
          }
          b = c;
        }
        c = filter(a, new double [] {1.0}, b);
      }
      return c;
    }

反卷积

    public static double[] deconv(double[] b, double[] a) {
      double[] q = null;
      int sb = b.length;
      int sa = a.length;
      if (sa > sb) {
        return q;
      }
      double[] zeros = new double[sb - sa +1];
      for (int i =1; i < zeros.length; i++){
        zeros[i] = 0.0;
      }
      zeros[0] = 1.0;
      q = filter(b,a,zeros);
      return q;
    }

反卷积结果

    public static double[] deconvRes(double[] b, double[] a) {
      double[] r = null;
      r = getRealArraySub(b,conv(a,deconv(b,a)));
      return r;
    }

getRealArraySub

    public static double[] getRealArraySub(double[] dSub0, double[] dSub1) {
      double[] dSub = null;
      if ((dSub0 == null) || (dSub1 == null)) { 
        throw new IllegalArgumentException("The array must be defined or diferent to null"); 
      }
      if (dSub0.length != dSub1.length) { 
        throw new IllegalArgumentException("Arrays must be the same size"); 
      }
      dSub = new double[dSub1.length];
      for (int i = 0; i < dSub.length; i++) {
        dSub[i] = dSub0[i] - dSub1[i];
      }
      return dSub;
    }

getRealArrayScalarDiv

    public static double[] getRealArrayScalarDiv(double[] dDividend, double dDivisor) {
      if (dDividend == null) {
        throw new IllegalArgumentException("The array must be defined or diferent to null");
      }
      if (dDividend.length == 0) {
        throw new IllegalArgumentException("The size array must be greater than Zero");
      }
      double[] dQuotient = new double[dDividend.length];

      for (int i = 0; i < dDividend.length; i++) {
        if (!(dDivisor == 0.0)) {
          dQuotient[i] = dDividend[i]/dDivisor;
        } else {
          if (dDividend[i] > 0.0) {
            dQuotient[i] = Double.POSITIVE_INFINITY;
          }
          if (dDividend[i] == 0.0) {
            dQuotient[i] = Double.NaN;
          }
          if (dDividend[i] < 0.0) {
            dQuotient[i] = Double.NEGATIVE_INFINITY;
          }
        }
      }
      return dQuotient;
    }

示例使用

使用示例

  double[] a, b, q, u, v, w, r, z, input, outputVector;


  u = new double [] {1,1,1};
  v = new double [] {1, 1, 0, 0, 0, 1, 1};
  w = conv(u,v);
  System.out.println("w=\n"+Arrays.toString(w));

  a = new double [] {1, 2, 3, 4};
  b = new double [] {10, 40, 100, 160, 170, 120};
  q = deconv(b,a);
  System.out.println("q=\n"+Arrays.toString(q));

  r = deconvRes(b,a);
  System.out.println("r=\n"+Arrays.toString(r));

  a = new double [] {2, -2.5, 1};
  b = new double [] {0.1, 0.1};
  u = new double[31];
  for (int i = 1; i < u.length; i++) {
    u[i] = 0.0;
  }
  u[0] = 1.0;
  z = filter(b, a, u);
  System.out.println("z=\n"+Arrays.toString(z));

  a = new double [] {1.0000,-3.518576748255174,4.687508888099475,-2.809828793526308,0.641351538057564};
  b = new double [] { 0.020083365564211,0,-0.040166731128422,0,0.020083365564211};
  input = new double[]{1,2,3,4,5,6,7,8,9};

  outputVector = filter(b, a, input);
  System.out.println("outputVector=\n"+Arrays.toString(outputVector));

输出

w=
[1.0, 2.0, 2.0, 1.0, 0.0, 1.0, 2.0, 2.0, 1.0]
q=
[10.0, 20.0, 30.0]
r=
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
z=
[0.05, 0.1125, 0.115625, 0.08828125, 0.0525390625, 0.021533203124999997, 6.469726562499979E-4, -0.009957885742187502, -0.012770843505859377, -0.010984611511230471, -0.007345342636108401, -0.003689372539520266, -9.390443563461318E-4, 6.708808243274683E-4, 0.0013081232085824014, 0.0012997135985642675, 9.705803939141337E-4, 5.633686931105333E-4, 2.189206694310998E-4, -8.033509766391922E-6, -1.195022219235398E-4, -1.453610225212288E-4, -1.219501671897661E-4, -7.975719772659323E-5, -3.8721413563358476E-5, -8.523168090901481E-6, 8.706746668052387E-6, 1.5145017380516224E-5, 1.4577898391619086E-5, 1.0649864299265747E-5, 6.023381178272641E-6]
outputVector=
[0.020083365564211, 0.11083159422936348, 0.31591188140651166, 0.648466936215357, 1.0993782391344866, 1.6451284697769106, 2.25463601232057, 2.8947248889603028, 3.534126758562552]

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