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SignalUtils.Bartlett Function
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Bartlett window.

Pascal
function Bartlett(const Src: TVec): TVec; overload;
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Description

Applies Bartlett window to Src vector. Window functions are applied to the signal prior to conversion to frequency domain with the FFT algorithm, to reduce the spectral leakage. Their side-effect is a lower frequency resolution. Bartlett window is a "triangular" window defined as [1] p. 248: 

           2*n              M - 1
w[n] =  -------, 0 <= n <= ------
         M - 1               2

             2*n     M - 1
w[n] = 2 - -------, ------ <= n <=  M - 1
            M - 1      2

w[n] = 0, for other n's

References:  

[1] Digital signal processing, Vinay K. Ingle and John G. Proakis, Brooks-Cole, 2000.

See Also
Example

Compute the frequency response of a lowpass filter with a cutoff at 40 Hz, if the sampling frequency is 200Hz and the filter is designed with the bartlett window. 

uses MtxExpr, Math387, MtxVec, SignalUtils, MtxVecTee;

procedure TForm1.Button1Click(Sender: TObject);
var h,Response,FreqFr: Vector;
begin
    h.Size(100);
    FirImpulse(h,[40],0,ftLowpass,wtRectangular,1,200);
    Bartlett(H);  //window the sinc impulse response
    FrequencyResponse(h,nil,Response,8);
    FreqFr.Size(Response.Length);
    FreqFr.Ramp(0,200*0.5/Response.Length);
    DrawIt(FreqFr, Response);
end;

 

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

void __fastcall TForm1::BitBtn1Click(TObject *Sender)
{
    sVector h,Response,FreqFr;

    h.Length = 100;
    FirImpulse(h,OPENARRAY(double,(40)),0,ftLowpass,wtRectangular,1,200);
    Bartlett(h);  //window the sinc impulse response
    FrequencyResponse(h,NULL,Response,8);

    FreqFr = Ramp(Response.Length, mvDouble, 0,200*0.5/Response.Length);
    DrawIt(FreqFr, Response,"",false);
}
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