SignalUtils.DcFilter Method

Overload List

#	Signature	Description
1	Double DcFilter(Double NewValue, ref TCplx State, Double alpha)	State parameter holds the filter state.
2	void DcFilter(Double alpha, TVec Num, TVec Den)	Design a DC-blocking (high-pass) IIR filter from alpha.
3	void DcFilter(Double TransitionBandwidth, Double FS, TVec Num, TVec Den)	Design a DC filter.

Overload 1: Double DcFilter(Double NewValue, ref TCplx State, Double alpha)

State parameter holds the filter state.

#	Name	Type	Description
1	NewValue	Double	scalar
2	State	TCplx (ref)	output
3	alpha	Double	scalar

Returns: Double

Remarks:

NewValue is the next sample and alpha is typically between 0.99 and 0.9999 and must be < 1. Big alpha will cause longer filter delay and more ringing. State should be initialized to zero before the routine is called for the first time.

Examples

using Dew.Math;
    using Dew.Math.Editors;
    using Dew.Math.Units;
    using Dew.Signal;
    using Dew.Signal.Units;
    using Dew.Math.Tee;
    using Dew.Signal.Tee;

    private void button1_Click(object sender, EventArgs e)
    {
        Vector b = new Vector(0);
        Vector c = new Vector(0);
        Vector num = new Vector(0);
        Vector x = new Vector(0);
        Vector den = new Vector(0);
        Vector Response = new Vector(0);

        int n;
        int i;

        TIirState IirState = new TIirState();
        TCplx DCState;

        SignalUtils.Tone(b,300,5.0/300,0,1,false); //generate sine with 5 periods in 300 samples

    //   Alternative:
    //          b.RandGauss;

        b = b + 2;
        c.Copy(b);
        n = 10;
        SignalUtils.DcFilter(0.95,num,den);
        SignalUtils.IirInit(num,den,ref IirState,false);
        int bLength = b.Length;
        for (i = 0; i < (bLength/n); i++)   //only to test the streaming
        {
            b.SetSubRange(i*n,n);
            c.SetSubRange(i*n,n);
            SignalUtils.IirFilter(b,c,ref IirState);
        }
        b.SetFullRange();
        c.SetFullRange();
        MtxVecTee.DrawIt(new TVec[2] { b, c }, new string[2] { "Unfiltered", "Filtered" }, "DC IirFilter", false);

        SignalUtils.FrequencyResponse(num,den,Response,64,false,TSignalWindowType.wtRectangular,0);
        MtxVecTee.DrawIt(Response,"Frequency response",false);

        SignalUtils.DcFilter(0.05,2,num,den);
        SignalUtils.IirInit(num,den,ref IirState,false);
        bLength = b.Length;
        for (i = 0; i < (bLength/n); i++)   //only to test the streaming
        {
            b.SetSubRange(i*n,n);
            c.SetSubRange(i*n,n);
            SignalUtils.IirFilter(b,c,ref IirState);
        }
        b.SetFullRange();
        c.SetFullRange();
        MtxVecTee.DrawIt(new TVec[2] { b, c }, new string[2] { "Unfiltered", "Filtered" }, "DC IirFilter", false);

        SignalUtils.FrequencyResponse(num,den,Response,64,false,TSignalWindowType.wtRectangular,0);
        MtxVecTee.DrawIt(Response,"Frequency response",false);

        DCState = Math387.C_ZERO;
        for (i = 0; i < (b.Length); i++)   //only to test the streaming
        {
            c.Values[i] = SignalUtils.DcFilter(b.Values[i],ref DCState,0.95);
        }

        MtxVecTee.DrawIt(new TVec[2] { b, c }, new string[2] { "Unfiltered", "Filtered" }, "DC IirFilter", false);
}

Overload 2: void DcFilter(Double alpha, TVec Num, TVec Den)

Design a DC-blocking (high-pass) IIR filter from alpha.

#	Name	Type	Description
1	alpha	Double	scalar
2	Num	TVec	source TVec
3	Den	TVec	source TVec

Result: stored in self (calling object)

Remarks:

Builds the transfer function of a first-order DC blocker and stores it in num / den for use with IirInit / IirFilter; the filtered signal is centred around zero (its mean is removed). With unity-DC-gain correction g = alpha/big(alpha + 1/2(1-alpha)big) the filter is

H(z) = g (1 - z^(-1))/(1 - alpha z^(-1))

i.e. a differentiator/integrator pair with a zero at z=1 (DC) and a pole at z=alpha. Domain: 0 < alpha < 1 (typically 0.99-0.9999); alpha nearer 1 pushes the cut-off lower and lengthens the transient. A finite alpha in range yields finite coefficients.

Overload 3: void DcFilter(Double TransitionBandwidth, Double FS, TVec Num, TVec Den)

Design a DC filter.

#	Name	Type	Description
1	TransitionBandwidth	Double	scalar
2	FS	Double	scalar
3	Num	TVec	source TVec
4	Den	TVec	source TVec

Result: stored in self (calling object)

Remarks:

Design a DC filter with TransitionBandwidth and place the transfer function in Num (numerator) and Den (denominator). You can then use this transfer function to initialize an IIR filter with a call to IirInit.

A DC filtered signal will be centered around zero. This DC filter is a simple differentiator/integrator pair. Transition bandwidth is the width of the frequency band where the amplitude is not yet completely attenuated. With DC filters, the transition band starts at 0 Hz. Narrow transition band (TransitionBandwidth/FS ratio is small) will result in filters with longer delays. FS is the sampling frequency. The filter implements the following difference equation:

y[i] = x[i] - x[i-1] + alpha y[i-1]

x.. input signal
y.. output signal
alpha.. parameter

Alpha paremeter can control the 3dB frequency of the transition bandwidth:

alpha := 1-(TransitionBandwidth/FS)*Pi;

FS.. sampling frequency
TransitionBandwidth.. frequency up to which will the filter have more
                      then 3dB attenuation. Must be less then FS/2.