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????



Fourier transform in Mathematica
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.


