SignalUtils.DcFilter Method

SignalUtils

Overload List

#SignatureDescription
1function DcFilter(NewValue: Double; var State: TCplx; alpha: Double): Double;State parameter holds the filter state.
2procedure DcFilter(alpha: Double; Num: TVec; Den: TVec);Design a DC-blocking (high-pass) IIR filter from alpha.
3procedure DcFilter(TransitionBandwidth: Double; FS: Double; Num: TVec; Den: TVec);Design a DC filter.

Overload 1: function DcFilter(NewValue: Double; var State: TCplx; alpha: Double): Double;

State parameter holds the filter state.

#NameTypeDescription
1NewValueDoublescalar
2StateTCplx
3alphaDoublescalar

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
uses MtxExpr, Math387, MtxVec, SignalUtils, MtxVecTee, MtxVecEdit;

procedure TForm1.Button1Click(Sender: TObject);
var b,c,Response,num,den,X: Vector;
n,i: integer;
IirState: TIirState;
DCState: TCplx;
begin
    Tone(b,300,5/300,0,1); //generate sine with 5 periods in 300 samples

    //   Alternative:
    //          b.RandGauss;

    b := b + 2;
    c.Copy(b);
    n := 10;
    DcFilter(0.95,num,den);
    IirInit(num,den,IirState);
    for i := 0 to b.Length div n-1 do   //only to test the streaming
begin
    b.SetSubRange(i*n,n);
    c.SetSubRange(i*n,n);
    IirFilter(b,c,IirState);
end;
b.SetFullRange;
c.SetFullRange;
DrawIt([b,c],['Unfiltered','Filtered'],'DC filter');

FrequencyResponse(num,den,Response,64);
DrawIt(Response,'Frequency response');

DcFilter(0.05,2,num,den);
IirInit(num,den,IirState);
for i := 0 to b.Length div n-1 do  // the loop is only to test the streaming
begin
    b.SetSubRange(i*n,n);
    c.SetSubRange(i*n,n);
    IirFilter(b,c,IirState);
end;
b.SetFullRange;
c.SetFullRange;
DrawIt([b,c],['Unfiltered','Filtered']);

FrequencyResponse(num,den,Response,64);
DrawIt(Response,'Frequency response');

DCState := C_ZERO;
for i := 0 to b.Length -1 do
c.Values[i] := DcFilter(b.Values[i],DcState,0.95);

DrawIt([b,c],['Unfiltered','Filtered']);
end;
See Also: SignalUtils.RemoveDC, SignalUtils.IirFilter, IIRFilters.ButterFilter, IIRFilters.ChebyshevIFilter, IIRFilters.ChebyshevIIFilter, IIRFilters.EllipticFilter, OptimalFir.RemezImpulse

Overload 2: procedure DcFilter(alpha: Double; Num: TVec; Den: TVec);

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

#NameTypeDescription
1alphaDoublescalar
2NumTVecsource TVec
3DenTVecsource 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: procedure DcFilter(TransitionBandwidth: Double; FS: Double; Num: TVec; Den: TVec);

Design a DC filter.

#NameTypeDescription
1TransitionBandwidthDoublescalar
2FSDoublescalar
3NumTVecsource TVec
4DenTVecsource 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.
Examples
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.