Matlab – Low Pass filter on a digital signal in matlab

Here is a Butterworth Low Pass filter I wrote for a recent project.

It has some magic numbers as constants that was given to me. If you can figure out how to create the magic numbers with your poles, coefficients, etc, then this might be helpful.

using System;
using System.Collections.Generic;
using System.Text;

namespace Filter
{
public class ButterworthLowPassFilter
{

    //filter fc = 2hz, fs = 10hz

    private const int LowPassOrder = 4;

    private double[] inputValueModifier;
    private double[] outputValueModifier;
    private double[] inputValue;
    private double[] outputValue;
    private int valuePosition;

    public ButterworthLowPassFilter()
    {
        inputValueModifier = new double[LowPassOrder];
        inputValueModifier[0] = 0.098531160923927;
        inputValueModifier[1] = 0.295593482771781;
        inputValueModifier[2] = 0.295593482771781;
        inputValueModifier[3] = 0.098531160923927;

        outputValueModifier = new double[LowPassOrder];
        outputValueModifier[0] = 1.0;
        outputValueModifier[1] = -0.577240524806303;
        outputValueModifier[2] = 0.421787048689562;
        outputValueModifier[3] = -0.0562972364918427;
    }

    public double Filter(double inputValue)
    {
        if (this.inputValue == null && this.outputValue == null)
        {
            this.inputValue = new double[LowPassOrder];
            this.outputValue = new double[LowPassOrder];

            valuePosition = -1;

            for (int i=0; i < LowPassOrder; i++)
            {
                this.inputValue[i] = inputValue;
                this.outputValue[i] = inputValue;
            }

            return inputValue;
        }
        else if (this.inputValue != null && this.outputValue != null)
        {
            valuePosition = IncrementLowOrderPosition(valuePosition);

            this.inputValue[valuePosition] = inputValue;
            this.outputValue[valuePosition] = 0;

            int j = valuePosition;

            for (int i = 0; i < LowPassOrder; i++)
            {
                this.outputValue[valuePosition] += inputValueModifier[i] * this.inputValue[j] -
                    outputValueModifier[i] * this.outputValue[j];

                j = DecrementLowOrderPosition(j);
            }

            return this.outputValue[valuePosition];
        }
        else
        {
            throw new Exception("Both inputValue and outputValue should either be null or not null.  This should never be thrown.");
        }
    }

    private int DecrementLowOrderPosition(int j)
    {
        if (--j < 0)
        {
            j += LowPassOrder;
        }
        return j;
    }

    private int IncrementLowOrderPosition(int position)
    {
        return ((position + 1) % LowPassOrder);
    }

}
}

Keith

Look at the filter function.

If you just need a 1-pole low-pass filter, it's

xfilt = filter(a, [1 a-1], x);

where a = T/τ, T = the time between samples, and τ (tau) is the filter time constant.

Here's the corresponding high-pass filter:

xfilt = filter([1-a a-1],[1 a-1], x);

If you need to design a filter, and have a license for the Signal Processing Toolbox, there's a bunch of functions, look at fvtool and fdatool.