Bartlett Routines

Summary

Bartlett window.

Declaration

Function Bartlett(Src: TVec): TVec;

Declaration

Function Bartlett(Src: TVec; Index: integer; Len: integer): TVec;

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

See Also
[1] "Digital signal processing, Vinay K. Ingle and John G. Proakis, Brooks-Cole, 2000".
Hanning
Kaiser
SignalWindow

Example 1

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.Length := 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 "MtxVecCPP.h"  //MtxVecCPP.cpp must be included in the project
    #include "MtxVecEdit.hpp"
    #include "MtxVecTee.hpp"
    #include "SignalUtils.hpp"

    void __fastcall TForm1::BitBtn1Click(TObject *Sender)
    {
        Vector 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,0,200*0.5/Response->Length);
        DrawIt(FreqFr, Response,"",false);
    }


    using Dew.Math;
    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 h = new Vector(100);
        Vector Response = new Vector(0);
        Vector FreqFr = new Vector(0);

        SignalUtils.FirImpulse(h, new double[1] {40},0, TFilterType.ftLowPass, TSignalWindowType.wtRectangular,1,200);
        SignalUtils.Bartlett(h);  //window the sinc impulse response
        SignalUtils.FrequencyResponse(h,null,Response,8,false,
                                      TSignalWindowType.wtRectangular, 0);
        FreqFr.Size(Response.Length);
        FreqFr.Ramp(0,200*0.5/Response.Length);
        TeeChart.DrawIt(FreqFr, Response,"Frequency response",false);
    }