Forums

FFT and normalization

Started by Doug March 31, 2006
Hi Group,

I know my question may sound stupid. But I can not come up with a
solution. So I post it here with the hope that someone could shed me
some light. Thanks in advance!

I am working on some image processing with FFT. It requires that the
function to be FFTed into spatial frequency space. However, I found out
that the result of FFT depends on the number of segments I choose. For
example,

%--------------code--------%
N=200;
t=linspace(-5,5,N);
x=exp(-pi*t.^2);

y=fftshift(fft(fftshift(x)));

plot(abs(y));

%------------end------------%

Here I wanted to do a Fourier transform of function exp(-t^2). When the
parameter N is changed, for instance, from 100 to 200, the plot
differs. It is understandable considering that the total DFT items
increases by a factor of 2. However, isn't it true that the FFT of the
function should be one single function exp(-pi*chi^2)? How can I
normalize the resulted DFT function with N so that every set of result
is consistent with each other? I have googled but still have not got a
clue.

Thank you!

Regards,
Doug