The logical implications are the following:
"non-recursive" $\Longrightarrow$ FIR
IIR $\Longrightarrow$ "recursive"
But the opposites are not necessarily true because a FIR system can be implemented recursively (transfer function poles can be cancelled by zeros).
Of course, when referring to "recursive" or "non-recursive" we always talk ...
is it correct to say that FIR system is always non-recursive?
You answer that yourself:
We could express an finite accumulator up to past N inputs (FIR system) in both non-recursive and recursive forms.
exactly. A common example of a recursive filter that's in fact an FIR is the CIC filter.
Also is it correct to say that a non-recursive system is always ...
I'm aware I can subtract the mean of the data
That's actually a high-pass filter!
You can see in the time domain output that the filter takes some time to settle.
That is true for any causal system, i.e. any system that can't look into the future; you'll want to read up on "group delay"
Can anyone help with me with what parameters to tweek to ...
The filter you desire is often called a “DC removal” or a “DC cancelation” filter. Unfortunately there’s no way to design a useful IIR DC removal filter that has no “settling time”. Your designed filter’s “transition region” is the lower passband frequency (50 Hz) minus the upper stopband frequency (10 Hz). So your designed filter’s transition region is 40 ...
Can you use deconvolution to convert these decaying impulses back into impulses?
Proof of concept:
import numpy as np
from scipy import signal
import matplotlib.pyplot as plt
impulses = np.zeros(150)
times = [3, 20, 30, 40, 45, 50, 55, 80, 90]
heights = [-8, -7, -1, -9, -1, -2, -1, -8, -1]
impulses[times] = heights
b, a = signal.butter(1, 0.04)
Your y-axis is in volts does the voltage increase overtime or does it fluctuate within a range? Without knowing more about the signals characteristics and what kind of frequency content you're dealing with it's hard to say..
You could possibly use a wavelet type approach to capture slope changes in your signal.
To get an idea of what I mean see this ...