How to normalise a FFT of a 3 variable function.

I have this function:

input = exp(-((W-w_o).^2)/deltaW.^2).*exp(-(Kx.^2+Ky.^2)/(deltaK.^2)).*exp(1i.*sqrt((W/c).^2-(Kx.^2+Ky.^2)).*z(j));

this is then fourier transformed:

fourier = fftn(input)

I need to normalise it. Dividing it by length() is not giving good results. Could someone please help!

[Rena Berman]

(Answers Dev) Restored edit

Answer 1

[Matt J]

To normalize so that the continuous Fourier transform is approximated, multiply by the sampling intervals, dT1*dT2*dT3

[J K]

The thing is that I was told to "best thing is to calculate the complete norm \int dw d)k_x dk_y ". I do not understand what is meant here. I think my normalisation has to involve triple integration.

[Matt J]

If you don't know what the goal is then no one does...

[J K]

Professor knows but i don't dare to ask again.

[Matt J]

Well, maybe this:

F = fftn(input);

F=F/norm(F(:));

[J K]

Thank you. I am going to try a few things and post the answer that worked.

[Matt J]

Maybe also

F=F*sqrt(T1*T2*T3)/norm(F)

where T1,2,3 are the sampling distances.

[J K]

Thank you so much!

Answer 2

[Matt J]

To normalize so that Parseval's equation holds, divide by sqrt(numel(input)).

Answer 3

[Matt J]

To normalize so as to obtain Discrete Fourier Series coefficients, divide by N=numel(input).