Hey, one first subject where I disagree, although only partially, with Sophiecentaur!
As EEG signals are at low frequency, I prefer to pass the full DC up to the digital signal.
Digital processing can remove the DC component and still react quickly, while analogue circuits that cut at 5Hz or 10Hz take very long to stabilize, which is irritating for real - you don't even know for sure if equilibrium has been reached, when converging from 1V unbalance to 1µV.
This needs the whole circuit to accept all offsets without saturation, so limit the gain (remember Seebeck effect), have a wide ADC dynamics and consider commercial
autozero op amps. These improve LF noise anyway.
About Bessel low-pass: more poles would increase only the slope at frequencies much higher than the corner, that's what Bessel do. And far from the corner, all two-pole low-pass are identical. I wouldn't worry too much about it. If out-of-band noise hampers the conversion to digital, add some poles, but if not, filter by software.
50Hz and 60Hz is not interesting for EEG signals, is it? So instead of adding poles to the low-pass, you could put
notches there. At both frequencies, so your design works everywhere - as voltmeters do. If one notch at each frequency needs a too tight tuning, put more notches.
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In the cases where time response is important and selectivity is necessary (EEG?) a Bessel is a bad answer. The best among the well-known functions is the inverse Chebychev, or type-II Chebychev, while an hourglass is good and an elliptic not bad.
Before telling me something else, please kindly consider that
(1) I've spent several months on that exact topic, and invented better filters for that, while book authors only copy on previous books.
(2) Response functions should be compared at identical selectivity, not at identical number of poles. Needing fewer poles, an elliptic has a far better step response than a type-I Chebychev which is less bad than a Butterworth with its many poles and resulting high Q factors.
Thank you.
To design filters, the old free
FilterCAD saves much time and has built-in knowledge. It computes step responses as well. Usable without the circuits sold by LT. Download it.