C- Peak detection via quadratic fit

问题

I have an application where I need to find the position of peaks in a given set of data. The resolution must be much higher than the spacing between the datapoints (i.e. it is not sufficient to find the highest datapoint, instead a "virtual" peak position has to be estimated given the shape of the peak). A peak is made of about 4 or 5 datapoints. A dataset is acquired every few ms and the peak detection has to be performed in real time.

I compared several methods in LabVIEW and I found the best result (in terms of resolution and speed) is given by the LabVIEW PeakDetector.vi, which scans the dataset with a moving window (>= 3 points width) and for each position performs a quadratic fit. The resulting quadratic function (a parabola) has a local maximum, which is in turn compared to nearby points.

Now I want to implement the same method in C. The polynomial fit is implemented as follows (using Gaussian matrix):

// Fits *y from x_start to (x_start + window) with a parabola and returns x_max and y_max
int polymax(uint16_t * y_data, int x_start, int window, double *x_max, double *y_max)
{
    float sum[10],mat[3][4],temp=0,temp1=0,a1,a2,a3;
    int i,j;

    float x[window];
    for(i = 0; i < window; i++)
        x[i] = (float)i;

    float y[window];
    for(i = 0; i < window; i++)
        y[i] = (float)(y_data[x_start + i] - y_data[x_start]);

    for(i = 0; i < window; i++)
    {
        temp=temp+x[i];
        temp1=temp1+y[i];
    }
    sum[0]=temp;
    sum[1]=temp1;
    sum[2]=sum[3]=sum[4]=sum[5]=sum[6]=0;

    for(i = 0;i < window;i++)
    {
        sum[2]=sum[2]+(x[i]*x[i]);
        sum[3]=sum[3]+(x[i]*x[i]*x[i]);
        sum[4]=sum[4]+(x[i]*x[i]*x[i]*x[i]);
        sum[5]=sum[5]+(x[i]*y[i]);
        sum[6]=sum[6]+(x[i]*x[i]*y[i]);
    }
    mat[0][0]=window;
    mat[0][1]=mat[1][0]=sum[0];
    mat[0][2]=mat[1][2]=mat[2][0]=sum[2];
    mat[1][2]=mat[2][3]=sum[3];
    mat[2][2]=sum[4];
    mat[0][3]=sum[1];
    mat[1][3]=sum[5];
    mat[2][3]=sum[6];

    temp=mat[1][0]/mat[0][0];
    temp1=mat[2][0]/mat[0][0];
    for(i = 0, j = 0; j < 3 + 1; j++)
    {
        mat[i+1][j]=mat[i+1][j]-(mat[i][j]*temp);
        mat[i+2][j]=mat[i+2][j]-(mat[i][j]*temp1);
    }

    temp=mat[2][4]/mat[1][5];
    temp1=mat[0][6]/mat[1][7];
    for(i = 1,j = 0; j < 3 + 1; j++)
    {
        mat[i+1][j]=mat[i+1][j]-(mat[i][j]*temp);
        mat[i-1][j]=mat[i-1][j]-(mat[i][j]*temp1);
    }

    temp=mat[0][2]/mat[2][2];
    temp1=mat[1][2]/mat[2][2];
    for(i = 0, j = 0; j < 3 + 1; j++)
    {
        mat[i][j]=mat[i][j]-(mat[i+2][j]*temp);
        mat[i+1][j]=mat[i+1][j]-(mat[i+2][j]*temp1);
    }

    a3 = mat[2][3]/mat[2][2];
    a2 = mat[1][3]/mat[1][8];
    a1 = mat[0][3]/mat[0][0];

    // zX^2 + yX + x

    if (a3 < 0)
    {
        temp = - a2 / (2*a3);
        *x_max = temp + x_start;
        *y_max = (a3*temp*temp + a2*temp + a1) + y_data[x_start];
        return 0;
    }
    else
       return -1;
}

The scan is performed in an outer function, which calls the above function repeatedly and chooses then the highest local y_max.

The above works and peaks are found. Only the noise is much worse than the LabVIEW counterpart (i.e. I get a very oscillating peak position, given the same input dataset and the same parameters). As the algorithm works the above code should be conceptually correct, so I think it might be a numerical problem as I simply use "floats" without further effort to improve numerical accuracy. Is this a possible answer? Does anyone have a tip, where I should be looking to?

Thanks.

PS: I have done my search and found this very good overview and also this question, similar to mine (unfortunately with not many answers). I will study these further.

EDIT: I have found my problems being elsewhere. Improving the algorithm by removing certain output values (a sort of post-validation in which a result is only accepted if the result is within the moving window) brought the solution to the issue. Now I am satisfied with the results, i.e. they are comparable to those from LabVIEW. Nevertheless, thanks a lot for your comments.

回答1:

Sorry to be late to the part, but if you have C/C++ it is really easy to port it to C# code using VS2013 Express (free version) and just port that into Labview using the .NET toolset.

来源：https://stackoverflow.com/questions/26485295/c-peak-detection-via-quadratic-fit

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