Having a little trouble understanding this math. Hopefully someone here can help.
In the Fourier Series Expansion as shown below:
I noticed the Ao term is divided by two, where in other texts I see it like more this:
where the Ao term is not divided by two. What is the reason for this? Is there also a difference in the way Ao is defined between texts? I have plotted a Fourier Series expansion of a function, over the function itself, without dividing Ao by two, and the fourier series expansion fits nicely over top of it. If I divide Ao by two, the fourier expansion sits way too low on the plot. Is Ao supposed to be divided by two or not?
Also, on finding the Fourier Series Expansion Coefficients, is taking the integral from zero to T (one period) just the same as taking the integral from -T/2 to +T/2?
Finally, to someone experienced in such things, ignoring the slight roughness (didn't plot with a small enough time interval), does this look mostly correct, for n=8 terms?
Thanks.