DFT functions in AForge.Math.FourierTransform and Accord.Math.Transforms

[conaonda]

for simple complex array [ 3+1i 9+14i 11+7i 40+31i]..

Accord.Math.Transforms.FourierTransform2.DFT(Forward) changes the array to
[ 63+53i -25+25i -35-37i 9-37i ]

AForge.Math.FourierTransform.DFT(Forward) changes the array to
[ 0.75+0.25i 2.25+3.5i 2.75+1.75i 10+7.75i ]

In Matlab answers same value with Accord.Math.Transforms.FourierTransform2.DFT.

Their function bodies(Accord and AForge) are almost same but direction is reversed.

And backward return operation of AForge may be incorrect.

In Accord..

        for (int i = 0; i < c.Length; i++)
        {
            ...
            c[i] = new Complex(sumRe, sumIm);
        }

        if (direction == FourierTransform.Direction.Backward)
        {
            for (int i = 0; i < c.Length; i++)
                data[i] = c[i] / n;
        }
        else
        {
            ...
        }

but AForge..

        for (int i = 0; i < dst.Length; i++)
        {
            for (int j = 0; j < data.Length; j++)
            {
                ...
                dst[i] += new Complex(re, im);
            }
        }

        // copy elements
        if (direction == Direction.Forward) //<< reversed direction
        {
            // devide also for forward transform
            for (int i = 0; i < data.Length; i++)
                data[i] /= n; //<< not using "dst" array
        }
        else
        {
            ...
        }

I think it needs to be validate.

(why same functions are exist?)

[DiegoCatalano]

Hello @conaonda,

The new version of dft/fft (Accord.NET) was coded for the compatibility with the Matlab. The old version (AForge.NET) exists only for the compatibility with the rest of the AForge.NET. I recommend to use the version of the Accord.NET because the fft can handle with size different of the power of 2.

There is differents scales for the directions. The matlab uses Asymmetric scale.

[cesarsouza]

Exactly, thanks @DiegoCatalano for the explanation! I will keep this issue open until I mark the AForge.NET implementation as obsolete and add more information about it in the documentation.

[cesarsouza]

The documentation for Accord.Math.FourierTransform has been updated. It now contains a pointer to FourierTransform2 explaining the limitations of the FourierTransform class and that FourierTransform2 should be preferred when trying to achieve compatibility with Octave and MATLAB implementations.