Re: Positive image interpolation


dudesinmexico@xxxxxxxxx wrote:
aruzinsky wrote:

Please, refresh my memory. What is wrong with the calculation of the
Fourier coeffcients for negative f(x)? How would this differ for f(x) +
c, where c is some small positive constant such that f(x) + c is positive
for all x?

My point is not that it is not possible to computer the Fourier
coefficients for negative f(x).

F { -f(x) } == - F{f(x)}

Is an identity. You are horribly confused.

There are no restrictions on computing Fourier coefficients or FFT of
any real number sequence of finite positive or negative (or complex)
data values. You may not get the anwer you expect if you use the wrong
algorithm to interpolate or grid your data for the FFT in the practical
case, but that is a separate issue.

I would like to understand exactly what makes f(x) negative, and use
this knowledge to improve the interpolation process.

If the interpolation process is intended only to make it easier to
compute the Fourier coefficients you really are going about it the
wrong way. Take a look at indirect imaging and signal processing
methods that use measurements in the Fourier domain to construct real
space images.

Regards,
Martin Brown

.

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