Look into convolutions, not sure if that is what you want tho, but it is how i know to do it. The 3×3 matrix is basicly like a gaussian blur filter for pictures. Imagine you take your operator/kernel and you slide it over your signal.
Lets say [2, 5, 3, 4, 1].
Add padding on the edges = [0, 2, 5, 3, 4, 1, 0]
First value in new smoothed signal is calculated: 1/4•0 + 1/2•2 + 1/4•5 = [2.25, ?, ?, ?, ?]
Move the kernel one step so the middle value is over 5. Then repeat:
1/4•2 + 1/2•5 + 1/4•3 = [2.25, 3.75, ?, ?, ?]
.
This is how the algorithm works if you wanna program it. You can write it as a matrix multiplication, Notice each column is one shift to the right from your original signal, for each step.
| 0 2 5 3 4 |
[1/4, 1/2, 1/4] • | 2 5 3 4 1 |
| 5 3 4 1 0 |
I wrote it on my phone so it might look weird, and there is probably better ways to do it, but this works as a smooth filter as you asked.
