Goertz Routine

Summary

The Discrete Fourier transformation (DFT) for a given frequency.

Declaration

Function Goertz(Src: TVec; var State: TGoertzState): TCplx;

Description

Calculates the Discrete Fourier transformation (DFT) for a given frequency. Goertz returns the DFT at the Frequency defined with GoertzInit. Each value of the DFT computed by the Goertzel algorithm takes 2N+2 real multiplications and 4N real additions. FFT computes the DFT with N*log2(N) of real multiplications and additions. The algorithm is very efficient if the frequency at which the DFT is being estimated does not change between calls and the algorithm is reduced to a simple dot product.

See Also
GoertzInit

Example 1

DFT of a single frequency.


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

    procedure TForm1.Button1Click(Sender: TObject);
    var a: Vector;
        State: TGoertzState;
    begin
        Tone(a,256,5.5/256,0,12.53); //generate a tone
        GoertzInit(5.5/256,false,State);
        //And now detect the amplitude at non-integer frequency:
        ShowMessage('Amplitude = ' + SampleToStr(CAbs(Goertz(a,State))/128));
    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 a;
        TGoertzState State;

        Tone(a,256,5.5/256,0,12.53); //generate a tone with Amplt = 12.53
        GoertzInit(5.5/256,false,State);
        //And now detect the amplitude at non-integer frequency:
        ShowMessage("Amplitude = " + SampleToStr(CAbs(Goertz(a,State))/128));
    }


    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 a = new Vector(0);
       TGoertzState State = new TGoertzState();

       SignalUtils.Tone(a,256,5.5/256,0,12.53,false); //generate a tone
       SignalUtils.GoertzInit(5.5/256,false,ref State);
    //And now detect the amplitude at non-integer frequency:
       MessageBox.Show("Amplitude = " + Math387.SampleToStr(Math387.CAbs(SignalUtils.Goertz(a,ref State))/128,0,15));
    }