How to normalise a FFT of a 3 variable function.

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J K
J K 2019-7-11
评论： Rena Berman 2019-9-19
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!

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回答（3 个）

Matt J
Matt J 2019-7-11
编辑：Matt J 2019-7-11
To normalize so that the continuous Fourier transform is approximated, multiply by the sampling intervals, dT1*dT2*dT3
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Matt J
Matt J 2019-7-12
编辑：Matt J 2019-7-12
Maybe also
F=F*sqrt(T1*T2*T3)/norm(F)
where T1,2,3 are the sampling distances.

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Matt J
Matt J 2019-7-11
编辑：Matt J 2019-7-11
To normalize so that Parseval's equation holds, divide by sqrt(numel(input)).
Matt J
Matt J 2019-7-11
编辑：Matt J 2019-7-11
To normalize so as to obtain Discrete Fourier Series coefficients, divide by N=numel(input).

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