Hello,

this is related to my previous question about numeric ways to reverse

a function.

I think if it were possible to find an approximation-function then

that would execute much faster than any least-square-based

optimization.

Candidates would be polynomes, possibly a 2-dimensional taylor-series

and a 2-dimensional fourier-series as my personal favourite.

For a function with one variable in a predefined range, for example

0..pi this is done like this:

y(x) = a0 + sum( a(i) * sin(x*i) + b(i) * cos(x*i) ) with i=1..N,

each i being a harmonic of the base-period.

The parameters a and b can then the found numerically.

My question here:

What would be the corresponding formula for a function with 2 variables?

y(x1,x2) = some sum of sin() and cos()

I have not found that anywhere.

I am aware of the octave-functions fft2() and ifft2().

So far it seems to me that I cannot apply these for 2 reasons:

1) I would first need a regular grid of dependent variables, which is

exactly what I do not have, due to the fact that I want to reverse an

existing function.

This I could solve with a slow optimization-based algorithm

2) So far I don't see how to get ifft2() to calculate a single value

for a single pair of indepentent variables that are _between_ the

points of the original grid.

Other functions like interp2() allow arbitrary input-values which

are then interpolated between the original data-points.

fft2()/ifft2() does not seem to do this.

Maybe I am missing something here

THX

Stefan

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