How can I write the Matlab “filter”-function myself?

Question

I would like to use a Butterworth filter on a 1D-Signal. In Matlab the script would look like this:

 f=100;
 f_cutoff = 20; 
 fnorm =f_cutoff/(f/2);
 [b,a] = but         


        

Answer 1

I implemented filter function used by Matlab in Java :

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.

public void filter(double [] b,double [] a, ArrayList inputVector,ArrayList outputVector){
        double rOutputY = 0.0;    
        int j = 0;
        for (int i = 0; i < inputVector.size(); i++) {
            if(j < b.length){
                rOutputY += b[j]*inputVector.get(inputVector.size() - i - 1);
            }
            j++;
        }
        j = 1;
        for (int i = 0; i < outputVector.size(); i++) {
            if(j < a.length){
                rOutputY -= a[j]*outputVector.get(outputVector.size() - i - 1);
            }
            j++;   
        }
        outputVector.add(rOutputY);
    }

and Here is an example :

ArrayListinputVector = new ArrayList();
ArrayListoutputVector = new ArrayList();
double [] a = new double [] {1.0000,-3.518576748255174,4.687508888099475,-2.809828793526308,0.641351538057564};
double [] b = new double [] { 0.020083365564211,0,-0.040166731128422,0,0.020083365564211};
double  []input = new double[]{1,2,3,4,5,6,7,8,9};
for (int i = 0; i < input.length; i++) {
    inputVector.add(input[i]);
    filter(b, a, inputVector, outputVector);
}
System.out.println(outputVector);

and output was :

[0.020083365564211, 0.11083159422936348, 0.31591188140651166, 0.6484669362153569, 1.099378239134486, 1.6451284697769086, 2.254636012320566, 2.894724888960297, 3.534126758562545]

as in Matlab output

That's it