MathNet.Numerics vs Matlab Forward Fourier answers mismatch?

Question

I'm little stuck here. The results of Forward Fourier by MathNet Numerics seem to be little less by half of those by MATLAB.

MathNet.Numerics on WindowsPhone 8

Complex[] samples = { new Complex(5, 0), new Complex(6, 0), new Complex(1, 0), new Complex(2, 0), new Complex(5, 0) };
MathNet.Numerics.IntegralTransforms.Transform.FourierForward(samples);
MathNet.Numerics.IntegralTransforms.Transform.FourierInverse(samples);

Original Signal

(5, 0) (6, 0) (1, 0) (2, 0) (5, 0)

Forward Fourier

(8.4970583144992, 4.96506830649455E-16) (2.67082039324994, -0.162459848116454) (-1.32917960675006, -0.688190960235587) (-1.32917960675006, 0.688190960235586) (2.67082039324994, 0.162459848116454)

Inverse Fourier

(5, -1.24126707662364E-15) (6, 0) (1, 1.78742459033804E-15) (2, 9.93013661298909E-16) (5, 7.94410929039127E-16)

Matlab FFT and IFFT

Original Signal

x=[5,6,1,2,5]

Forward Fourier fft(x)

ans = 19.0000 5.9721 - 0.3633i -2.9721 - 1.5388i -2.9721 + 1.5388i 5.9721 + 0.3633i

Inverse Fourier ifft(ans)

5.0000 6.0000 1.0000 2.0000 5.0000

Any ideas what I'm doing wrong here?

Answer 1

There are multiple FFT conventions around scaling and exponents. The default convention used by Math.NET Numerics is what is generally used in science and education (and also e.g. in Maple) with symmetric scaling. However, MATLAB uses asymmetric scaling. In order to get MATLAB's behavior and numeric results, add FourierOptions.Matlab as second parameter, i.e.

Transform.FourierForward(samples, FourierOptions.Matlab);
Transform.FourierInverse(samples, FourierOptions.Matlab);