Help with convolution algorithm

Hi guys,

I've been banging my head against the wall trying to convolve two data sets. They are of equal length. One is a gaussian, and the other is a Lorentzian. I haven't been able to get it to work using a regular convolution

i.e.

Code:

---

for (j = 0; j < 64; j += 1)
{   
      y[j]= 0.0;
      for (i = 0; i <= j; i++)
      {
        y[j] += x[i] * h[j - i];
      }
}

---

and I haven't been able to get it to work using a Fourier Transform (see below). My convolution is orders of magnitude larger than the input functions and a completely wrong shape.

Now, I have been getting all of my information about this from Google, so I must be missing something pretty obvious. Especially since both ways of doing it are failing for me. If anyone could give me a hand with either the FT or regular convolution, I would really appreciate it. You can download the project from here

Convolution project

I know I'm using the FFTW correctly, as I can FT and inverse FT a function without a problem. Thanks for any help.

Code:

---


#include "stdafx.h"
#include <fstream>
#include <iostream>
#include <conio.h>
#include "fftw3.h"

using namespace std;

int _tmain(int argc, _TCHAR* argv[])
{
        double *x = (double*)fftw_malloc(1000*sizeof(double));
        double *y = (double*)fftw_malloc(1000*sizeof(double));
        double *conv3 = (double*)fftw_malloc(1000*sizeof(double));
        int NumberofPoints = 0;
       
    fftw_plan p;
    fftw_complex* out1 = (fftw_complex*) fftw_malloc(sizeof(fftw_complex) * 1000);
        fftw_complex* out2 = (fftw_complex*) fftw_malloc(sizeof(fftw_complex) * 1000);
        fftw_complex* final = (fftw_complex*) fftw_malloc(sizeof(fftw_complex)* 1000);

        for(int i = 0; i < NumberofPoints; i++)
        {
                out1[i][0] = 0;
                out1[i][1] = 0;
                out2[i][0] = 0;
                out2[i][1] = 0;
                final[i][0] = 0;
                final[i][1] = 0;
        }

        //Read in our files
        ifstream stream("individgraphs.dat");

        if(stream.is_open() == false)
                cout << "Error" << endl;

        while(stream >> x[NumberofPoints]>>y[NumberofPoints])
        {
                NumberofPoints++;
        }
        stream.close();

        //FFTW

        //FT data file 1
        p = fftw_plan_dft_r2c_1d(NumberofPoints, x, out1, FFTW_ESTIMATE);
    fftw_execute(p);
        fftw_destroy_plan(p);
        //FT data file 2
        p =  fftw_plan_dft_r2c_1d(NumberofPoints, y, out2, FFTW_ESTIMATE);
        fftw_execute(p);
        fftw_destroy_plan(p);

        //Convolution - Complex multiplication and scaling
        for(int i = 0; i < NumberofPoints; i++)
        {
                        final[i][0] = (out1[i][0]*out2[i][0]-out1[i][1]*out2[i][1])*(1.0/(double)NumberofPoints);
                        final[i][1] = (out1[i][0]*out2[i][1]+out1[i][1]*out2[i][0])*(1.0/(double)NumberofPoints);
        }

        //Invert the product
        p = fftw_plan_dft_c2r_1d(NumberofPoints, final, conv3,FFTW_ESTIMATE);
        fftw_execute(p);
        fftw_destroy_plan(p);

        //Write output file
        ofstream test("outfile.txt");
        for (int i = 0; i < NumberofPoints; i++)
        {
                test << conv3[i]/NumberofPoints <<  endl;
        }
        test.close();

        //Free memory
        fftw_free(x);
        fftw_free(y);
        fftw_free(out1);
        fftw_free(out2);
        fftw_free(conv3);

        getch();
        return 0;
}

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First of all, when convolving 2 sequences of length M and L the output sequence has length M+L-1. Here is an example of convolving two sequences in C:

Code:

---

for (n = 0; n < L+M; n++)
{
    y[n] = 0;
    for (m = max(0, n-L+1); m <= min(n, M); m++)
        y[n] += h[m] * x[n-m];
}

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Anyway, why you think that your result is not correct? Give an example if possible.

Regards,
Theodore