a quick question: Is it a legit way to use a fraction as the upper limit of a summation? Given is a frequency $f$ and a sample rate $f_s$. I want to use a sum like this:
$\sum_{k=1}^{\frac{f_s}{2f}} \sin(2 \cdot \pi \cdot k) $
Is this a legit way to write it?
If you mean to include all the k that are less than $\frac{f_s}{2f}$, you can hedge and use the floor function:
$\sum_{k=1}^{\left\lfloor\frac{f_s}{2f}\right\rfloor} \sin(2 \cdot \pi \cdot k) $
This guarantees your bounds are both integers, but contain all the k you want.