Re: Fourier vs. other methods?

On Aug 28, 6:52 am, Martin Brown <|||newspam...@xxxxxxxxxxxxxxxxxx>
wrote:
On Aug 28, 5:02 am, base...@xxxxxxxxx wrote:

I'm looking to fit f(a) to a Fourier series, and it
seems clear (Nyquist theorem as a particular case) that the more
points I sample at, the more terms I can fit meaningfully.

And that is always the case.

Big question here: is your problem truly periodic ?

It is.

If you have additional prior knowledge about the function - like the
location of any poles, zerores, positivity or smooth featureless zones
then you may be able to do better than the obvious linear FT by
choosing where to sample. But in general you cannot.

Thanks for the reference. I should have noted in the original post --
I'm particularly interested in how (whether) the situation changes in
two or three dimensions, still with periodic boundary conditions, or
(and I think this is exactly what you hinted at) if I'm looking to fit
spherical harmonics to a smooth function over the surface of a sphere.

Any pointers on the latter case?

.