I feel like this is a lot easier than I'm making it, but for some reason I just can't wrap my head around it.
Let's say I'm sampling a voltage, for argument's sake. I want to know the average voltage over a period of time. If I know the number of samples - it's simply:
$$\frac{\sum_0^n s_n}{n}$$
But, what if I'm trying to do it live? It becomes:
$$\frac{1}{T}\int_0^T s(x) dx$$
But in that case, since $T$ is changing, the first sample will be weighted most heavily, with weight decreasing over time.
Is there an easy way to get the average when I don't know how many samples I have ($n$ or $T$ in this case)? What if the number of samples is significantly large?