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SignalUtils.KaiserImpulse Function
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Design a FIR filter with a Kaiser window.

Pascal
procedure KaiserImpulse(const H: TVec; W: array of double; Ripple: double; FilterType: TFilterType; Gain: double = 1; FS: double = 2; EnsuredOdd: boolean = false); overload;
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Description

Compute a FIR impulse response filter with kaiser window applied and place the result in H. The transition regions are defined with the W array. There must be at least one (lowpass, highpass) and at most two (bandpass, bandstop) transition regions (2 or 4 elements). Filter type is defined with TFilterType. 

FS is the sampling frequency. The length of the filter (H.Length) is based on the narrowest transition region in combination with the passband Ripple parameter. 20*Log10(Ripple) is also the required attenuation of the stopband in decibel. Gain defines the filter gain. The resulting H vector contains FIR type impulse response, which can be passed to the FirInit routine. 

If EnsuredOdd is True, the filter length is guaranteed to have odd length. H.FloatPrecision value on input defines the precision (single or double) of the result on output.

See Also
Example

Impulse responses of FIR filters windowed with the Kaiser window. 

 

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

procedure TForm1.Button1Click(Sender: TObject);
var FS, Ripple: double;
    H,Response, X: Vector;
begin
    FS := 2;  //sampling frequency
    Ripple := 0.001;  // 60 dB stopband and 0.001 ripple in the passband

// Lowpass design with transition band between 0.3 and 0.5 Hz.
    KaiserImpulse(H, [0.3,0.5], ripple, ftLowpass,1,FS);
    FrequencyResponse(H,nil,Response,8);
    X := Ramp(Response.Length, mvDouble, 0,1.0/Response.Length);
    DrawIt(X,Response,'Lowpass design with transition band between 0.3 and 0.5 Hz',false);

// Highpass design with transition band between 0.3 and 0.5 Hz.
    KaiserImpulse(H, [0.3,0.5], Ripple,ftHighpass,1,FS);
    FrequencyResponse(H,nil,Response,8);
    DrawIt(X,Response,'Highpass design with transition band between 0.3 and 0.5 Hz',false);

// Bandpass design with transition bands between 0.3..0.4 Hz and between 0.5...06 Hz.
    KaiserImpulse(H, [0.3,0.4,0.5,0.6], Ripple,ftBandpass,1,FS);
    FrequencyResponse(H,nil,Response,8);
    X := Ramp(Response.Length,  mvDouble,0,1.0/Response.Length);
    DrawIt(X,Response,'Bandpass with transition bands 0.3-0.4 Hz and 0.5-0.6 Hz.',false);

// Bandstop design with transition bands between 0.3..0.4 Hz and between 0.5...06 Hz.
    KaiserImpulse(H, [0.3,0.4,0.5,0.6], Ripple,ftBandstop,1,FS);
    FrequencyResponse(H,nil,Response,8);
    X := Ramp(Response.Length,  mvDouble,0,1.0/Response.Length);
    DrawIt(X,Response,'Bandstop with transition bands 0.3-0.4 Hz and 0.5-0.6 Hz.',false);

//Hilbert III with transition bands between 0.0-0.1 Hz and 0.9-1.0 Hz.
    KaiserImpulse(H, [0.9,1], Ripple,ftHilbertIII,1,FS);
    FrequencyResponse(H,nil,Response,8);
    X := Ramp(Response.Length, mvDouble,0,1.0/Response.Length);
    DrawIt(X,Response,'Hilbert III with transition bands between 0.0-0.1 Hz and 0.9-1.0 Hz.',false);

//Hilbert IV with transition band between 0.0-0.1 Hz.
    KaiserImpulse(H, [0.9,1], Ripple,ftHilbertIV,1,FS);
    FrequencyResponse(H,nil,Response,8);
    X := Ramp(Response.Length, mvDouble,0,1.0/Response.Length);
    DrawIt(X,Response,'Hilbert IV with transition band between 0.0-0.1 Hz',false);

//Differentiator III with transition band between 0.0-0.1 and 0.9-1.0 Hz.
    KaiserImpulse(H, [0.9,1], Ripple,ftDifferentiatorIII,1,FS);
    FrequencyResponse(H,nil,Response,8);
    X := Ramp(Response.Length, mvDouble,0,1.0/Response.Length);
    DrawIt(X,Response,'Differentiator III with transitions between 0.0-0.1 and 0.9-1.0 Hz',false);

//Differentiator IV with transition band between 0.0 and 0.1 Hz.
    KaiserImpulse(H, [0.9,1], Ripple,ftDifferentiatorIV,1,FS);
    FrequencyResponse(H,nil,Response,8);
    X := Ramp(Response.Length, mvDouble,0,1.0/Response.Length);
    DrawIt(X,Response,'Differentiator IV with transitions between 0.0-0.1 Hz',false);
end;

 

#include "MtxExpr.hpp"
#include "MtxVecEdit.hpp"
#include "MtxVecTee.hpp"
#include "SignalUtils.hpp"

void __fastcall TForm41::BitBtn1Click(TObject *Sender)
{
    sVector H,Response, X;

    double FS = 2;  //sampling frequency
    double Ripple = 0.001;  // 60 dB stopband and 0.001 ripple in the passband

  // Lowpass design with transition band between 0.3 and 0.5 Hz.
    KaiserImpulse(H, OPENARRAY(double,(0.3,0.5)), Ripple, ftLowpass,1,FS);
    FrequencyResponse(H,NULL,Response,8);
    X = Ramp(Response.Length, mvDouble, 0,1.0/Response.Length);
    DrawIt(X,Response,"Lowpass design with transition band between 0.3 and 0.5 Hz",false);

  // Highpass design with transition band between 0.3 and 0.5 Hz.
    KaiserImpulse(H, OPENARRAY(double,(0.3,0.5)), Ripple,ftHighpass,1,FS);
    FrequencyResponse(H,NULL,Response,8);
    DrawIt(X,Response,"Highpass design with transition band between 0.3 and 0.5 Hz",false);

  // Bandpass design with transition bands between 0.3..0.4 Hz and between 0.5...06 Hz.
    KaiserImpulse(H, OPENARRAY(double,(0.3,0.4,0.5,0.6)), Ripple,ftBandpass,1,FS);
    FrequencyResponse(H,NULL,Response,8);
    X = Ramp(Response.Length, mvDouble, 0,1.0/Response.Length);
    DrawIt(X,Response,"Bandpass with transition bands 0.3-0.4 Hz and 0.5-0.6 Hz.",false);

  // Bandstop design with transition bands between 0.3..0.4 Hz and between 0.5...06 Hz.
    KaiserImpulse(H, OPENARRAY(double,(0.3,0.4,0.5,0.6)), Ripple,ftBandstop,1,FS);
    FrequencyResponse(H,NULL,Response,8);
    X = Ramp(Response.Length, mvDouble, 0,1.0/Response.Length);
    DrawIt(X,Response,"Bandstop with transition bands 0.3-0.4 Hz and 0.5-0.6 Hz.",false);

  //Hilbert III with transition bands between 0.0-0.1 Hz and 0.9-1.0 Hz.
    KaiserImpulse(H, OPENARRAY(double,(0.9,1)), Ripple,ftHilbertIII,1,FS);
    FrequencyResponse(H,NULL,Response,8);
    X = Ramp(Response.Length, mvDouble, 0,1.0/Response.Length);
    DrawIt(X,Response,"Hilbert III with transition bands between 0.0-0.1 Hz and 0.9-1.0 Hz.",false);

  //Hilbert IV with transition band between 0.0-0.1 Hz.
    KaiserImpulse(H, OPENARRAY(double,(0.9,1)), Ripple,ftHilbertIV,1,FS);
    FrequencyResponse(H,NULL,Response,8);
    X = Ramp(Response.Length, mvDouble, 0,1.0/Response.Length);
    DrawIt(X,Response,"Hilbert IV with transition band between 0.0-0.1 Hz",false);

  //Differentiator III with transition band between 0.0-0.1 and 0.9-1.0 Hz.
    KaiserImpulse(H, OPENARRAY(double,(0.9,1)), Ripple,ftDifferentiatorIII,1,FS);
    FrequencyResponse(H,NULL,Response,8);
    X = Ramp(Response.Length, mvDouble, 0,1.0/Response.Length);
    DrawIt(X,Response,"Differentiator III with transitions between 0.0-0.1 and 0.9-1.0 Hz",false);

  //Differentiator IV with transition band between 0.0 and 0.1 Hz.
    KaiserImpulse(H, OPENARRAY(double,(0.9,1)), Ripple,ftDifferentiatorIV,1,FS);
    FrequencyResponse(H,NULL,Response,8);
    X = Ramp(Response.Length, mvDouble, 0,1.0/Response.Length);
    DrawIt(X,Response,"Differentiator IV with transitions between 0.0-0.1 Hz",false);
}
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