Okay you have, (shown below)Originally Posted by parallel
This is a strictly monotonic function whose discountinuity points are not replacable, therefore it can be represented as a fourier series.
The constant term,
Now these intervals the function behaves like,
The same idea of spliting the function on the interval is used to find the sine and cosine coefficients. I just do not want to do that because I know how long these fourier computations can take.