Dana DeLouis shared this with us in microsoft.public.excel.misc:

Hi. If your data on the x-axes is evenly spaced out, Excel has a
Fourier Transform function under Data | Analysis. However, it's a
Radix-2 algorithm only. My opinion is that Solver can not do a LSQ
very well, especially with more than just a few data points. I've
never had much success with a LSQ fitting. The main problem is that
by definition, one is squaring the error, so the "error" never goes
negative. This confuses Solver. With multiple values, Solver gets
confused, and will quickly give up.

Dana,

Unfortunately my data is not exactly evenly spaced out. I could
extrapolate additional data points that are evenly spaced out, using a
linear or other trendline. However this would add more work, complexity
and error.
And Radix-2, that would imply that I need exactly 2^x data points,
right? That's not the case.
Also, I don't have "just a few" data points, but hundreds or even
thousands. These are measurements made approximately every 5 minutes
over several weeks. I can clearly see a dayly cycle, so the period will
be exactly 24 hours. Phase isn't very interesting but amplitude is.

But overall I get the impression that Excel isn't exactly the best
software to do this kind of analysis. Should I seek other software, and
if yes, what?

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Amedee Van Gasse