R and Mathematica software differ when computing fft(c(1,1)) and Fourier[{1,1}],
2+0i 0+0i
and
{1.41421+ 0i, 0} respectively. How can this be????
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closed as off topic by Gerald Edgar, Yemon Choi, Torsten Ekedahl, Felipe Voloch, Andres Caicedo Jul 30 2011 at 22:21 |
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Normalizing factor. It looks like R defines the Discrete Fourier Transform matrix as $F = [1$ $1; 1$ $-1]$ while Mathematica defines it as $F = \frac{1}{\sqrt{2}}[1$ $1; 1$ $-1]$. If you do inverse fft - R would define it to be $F^{-1} = \frac{1}{2}[1$ $1; 1$ $-1]$ while Mathematica would define it as $F^{-1} = F^{H} = \frac{1}{\sqrt{2}}[1$ $1; 1$ $-1]$ where $H$ is Hermitian transpose. |
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