Apologies if my notation and/or terminology is way off - I'm not well versed in mathematics. I'm looking for the name of the field of mathematics that might help me solve my problem. Here's my problem:
I have a series containing samples of time data with values associated with them. If I was expressing this on a graph in terms of X & Y, let's say X=time(t) and Y=the value recorded at that time, like this:
- X=0.0, Y=0.0
- X=3.5, Y=4.0
- X=5.7, Y=3.0
- X=8.1, Y=2.1
- X=11.5, Y=5.6
What I want to do, is extrapolate based on the the time deltas between these values, what the values would be at 1-second intervals, that is, rebuild the series as:
- X=0,Y=0
- X=1,Y=?
- X=2,Y=?
- ... and so forth
I understand that the rebuilt series would only be an estimation based on the sample points and that the more sample points I have, the closer the estimation will be to the actual curve, but I care less about precision and more about being able to offer a reasonable estimate of what the value was at a given second interval based on the randomly gathered time data.
Currently I'm brute-force "solving" this by computing the delta between two points and then dividing by the time difference between those points to obtain an average for 1s intervals between those two points (cur.Y-prev.Y) / (cur.X-prev.X), but I believe this can be done more elegantly, I just don't know the field of mathematics that can help me do so.
Thanks in advance!