I am trying to make sense of the filter coefficients.
The author claims that they are running a 3rd order lowpass Butterworth filter and were willing to give their design. They are not the most communicative type and it is typically weeks until I am able to get any sort of answer from them.
The coefficients are as follows:
1.22293 1.394312 1.994313
-0.3339159 -0.6572268 -0.9943293
They also provided the transfer function:
$$ H_k(z) = \frac{b_{k0}+b_{k1}z^{-1}+b_{k2}z^{-2}}{1-a_{k1}z^{-1}-a_{k2}z^{-2}},\quad k = 1, 2, 3. $$
Whey I plug in these coefficients into the FDA toolbox in MATLAB, I get the following frequency response (sampling rate was set to $20833\textrm{ Hz}$):
What is the correct way to interpret these numbers? I am somewhat out of my element when it comes to the Digital Filtering and could use some help.