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From: Kelly Jones on 29 Mar 2010 06:22
I measured the temperature of several points in a 3-dimensional space,
and want to curve-fit the results to a "simple" function.

Sine/cosine functions are the most obvious choice, but how do you
Fourier transform 3-dimensional data?

And what exactly is a 3-dimensional Fourier transform?

I'm guessing it's the sum of terms like:

Cos[r*x]*Cos[s*y]*Cos[t*z]

over all integer values of r,s,t, with the appropriate phase shifts,
amplitude shifts, etc, thrown in.

What Mathematica functions can help me + where can I learn more about them?

--
We're just a Bunch Of Regular Guys, a collective group that's trying
to understand and assimilate technology. We feel that resistance to
new ideas and technology is unwise and ultimately futile.

From: dh on 29 Mar 2010 07:56
Hi Kelly,
as long as your data points are on a rectangular grid, "Fourier" will
have no problems.
But do you have any reason to assume that your data is periodic?
Otherwise, I would first try with polynomials, using e.g. "Fit"
Daniel


On 29.03.2010 12:22, Kelly Jones wrote:
> I measured the temperature of several points in a 3-dimensional space,
> and want to curve-fit the results to a "simple" function.
>
> Sine/cosine functions are the most obvious choice, but how do you
> Fourier transform 3-dimensional data?
>
> And what exactly is a 3-dimensional Fourier transform?
>
> I'm guessing it's the sum of terms like:
>
> Cos[r*x]*Cos[s*y]*Cos[t*z]
>
> over all integer values of r,s,t, with the appropriate phase shifts,
> amplitude shifts, etc, thrown in.
>
> What Mathematica functions can help me + where can I learn more about them?
>


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Daniel Huber
Metrohm Ltd.
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CH-9100 Herisau
Tel. +41 71 353 8585, Fax +41 71 353 8907
E-Mail:<mailto:dh(a)metrohm.com>
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