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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3$\begingroup$ off topic, see the FAQ $\endgroup$– Gerald EdgarCommented Jul 30, 2011 at 18:44
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$\begingroup$ Obviously, they're using different definitions. The notation and conventions associated with the Fourier transform differ between different authors, although it's usually easy to figure out the differences and adjust your results accordingly. A look at the documentation for the R and Mathematica functions should help you figure this out. $\endgroup$– Brian BorchersCommented Jul 30, 2011 at 18:51
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1 Answer
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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.
