# Fourier Parameters

I need to use the built-in function Fourier, to get the Fourier transformation of a list of numbers. Unfortunately, I would need to set the second argument of the FourierParameter option to a non-integer number, and indeed the precision of the Fourier transformation I get is very low. Do you know how I could proceed to get some precise results?

Let us consider this example

\[Beta] = 10.;
l = 10^2;
\[Omega] = Table[(2 \[Pi])/\[Beta] (n + 1/2), {n, -l, l}];
Gfbegin = I/\[Omega];
Gt = Fourier[Gfbegin, FourierParameters -> {0, 2 (2 l + 1)/(2 l - 1)}];
Gf = InverseFourier[Gt,FourierParameters -> {0, 2 (2 l + 1)/(2 l - 1)}]


In principle, the list Gf should be equal to the list Gfbegin but actually the two lists are very different. On the contrary, if I use the standard FourierParameter as follows

 \[Beta] = 10.;
l = 10^2;
\[Omega] = Table[(2 \[Pi])/\[Beta] (n + 1/2), {n, -l, l}];
Gfbegin = I/\[Omega];
Gt = Fourier[Gfbegin, FourierParameters -> {0, 1}];
Gf = InverseFourier[Gt,FourierParameters -> {0,1}]


the result is correct: the two lists Gf and Gfbegin are equal to each other.

Thank you a lot!

• I suggest that you add a specific example, including a list of numbers to transform, the FourierParameters you use and an explanation of why you think the result is inaccurate. – mikado Jul 19 '18 at 7:08
• Thank you very much for your comment. I added the example as you asked! – Dario Rosa Jul 19 '18 at 7:52