I have a signal $s$ that can take 2 values: $\{0, 1\}$ and is defined over $\mathbb{Z}$:
$s(\mathbb{Z}) \rightarrow \{0, 1\}$
$s$ is a train of rectangular pulses:
________ _______
| |______| |__
--------------------------------> n
<---A--->
<-------T------>
The average of the 1 length among all the cycles of all the signals is $\mu_A$ which I have (let's say 100) and $\sigma_A$ its scale (ex: 5).
The average length of 1 cycle among all the cycles of all the signals is $\mu_T$ which I have (let's say 500) and $\sigma_T$ its scale (ex: 20).
For a given signal $i$ ($s_i$), it also has a specific set of ${\mu_A}_i$ ${\sigma_A}_i$ and ${\mu_T}_i$ ${\sigma_T}_i$ and:
$ {\mu_A}_i \sim N (\mu_A,\,{\sigma_A}^{2})$
$ {\mu_T}_i \sim N (\mu_T,\,{\sigma_T}^{2})$
For a given cycle $j$ of the signal $s_i$ the length $A$ and $T$ are not constant over time:
$ A_{i,j} \sim N ({\mu_A}_i,\,{{\sigma_A}_i}^{2})$
$ T_{i,j} \sim N ({\mu_T}_i,\,{{\sigma_T}_i}^{2})$
I was wondering if I have a set of points ({n=1, y=0}, {n=10, y=0}, {n=15, y=1}...), how can I create a model to predict $s_i$ for a given $n$ (ex: $s_i(n = 20)= ?$)?
I'm trying to create a script which give the probability of the the signal being 0 or 1 for a given $n$ from the already known points.