Fourier Series are a little bit tricky to do right. There is the DFT that maps a list of N values to N complex values. But some questions what you are looking for here.
Q: Is the number of data points a power of 2, i.e. 512,1024 etc. If N is large and a prime this is very slow, to the point of being considered an input error.
Q: Are you interested in the magnitude of the values, often called the spectrum. The N values you get back from the raw DFT really only have N/2 complex values since you hand in real numbers. And as you get closer to the N/2 index the values are inaccurate if you assume that the inital N values were sampling a function that you want the FS for.
Q: What comes out is technically amplitudes of standing frequencies in the domain. And technically if you have a domain from [2,3] and 100 values that means you have values at 2,2.01,…2.99, i.e. the value at 3 is assumed to be the same as the value at 2 and not repeated in the list. If it was you really should have 513,1025 values etc so that the signal to the DFT has 512,1024 etc. It isn’t that slow to handle 100 values, but large Mersenne prime numbers will be very slow (such as 524287).
Where this would fit in is in a new mechanism similar to the Plot Action column. That column uses a x,y pair of columns and returns a single column. The Fourier Series would take in a single column and return another column. Let’s call this a Column Action for now. The function evaluation would fit naturally into this, and some smoothing options would too. The answer to the above questions would help in fleshing out this functionality.
david.
yderay
david