I'm currently reading a paper and I can't seem to make sense of a certain part. A link to the paper: removed
The part I don't quite get is on page 286 (after the part where they explain their filters). It starts with the sentence "Two common methods can be used ...". They explain how they calculate the interbeat intervals of a signal.
The things I do not understand:
Cubic spline interpolation is applied to the data for ensuring the existence of continuous ﬁrst-order differential and second-order differential
1. Do they mean that the first & second order derivative of two sequential splines should be the same to ensure that they are smooth ?
$m$ is the number of feature points
2. Is this the $n$ in the formula ? ( really none of the symbols are explained of the formula. I doubt t is the value at a certain frame, since the values are really small, which would make it impossible to be in the defined interval.)
We consider the interval between [0.25, 2]
3. what is this interval ? With respect to which variable ?
And this sentence I can't figure out entirely.
We choose the ﬁrst-order differential point in each cycle of BVP as characteristic point to demarcate the interval. The number of ﬁrst-order differential points in a period of wave ﬂuctuates narrowly than the number of usual maximum points in the presence of measuring errors.
4. How do they know anything about any cycle at this point, this is what they are trying to determine at this point ...
5. What is a first-order differential point in a cycle ?
6. Is a feature point a first-order differential point ?
I am trying to implement this (in python), based on this explanation I can't seem to figure out the details to do this.