I understand that with a standard filter, higher order will yield sharper frequency selection at the cost of increased phase delay. However, with so-called zero-phase-distortion filters like that provided by scipy.signal.filtfilt, will a higher order get you sharper frequency selection "for free"? (I know higher order filters take more computation time, but let's ignore that)
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The sharper the filter is in the frequency domain, the longer the impulse response will be. This typically leads to "time blur" or "ringing" in the time domain. In addition, a zero phase filter is non-causal, so you get "pre-ringing" and any sharp onsets or transients in the time domain get degraded.
The long impulse response also leads to a long "transition" region at the beginning and the end of the signal. As a very rough rule: if you have a filter that does something drastic over 1Hz of bandwidth, it will need about 1 second of time domain signal until the effect of the filter is fully established.
The optimal choice is very dependent on the specific requirements of your application.
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The Python function scipy.signal.filtfilt increases the order of the filter by a factor of 2 because you are doing forward-backward filtering. Traditional filtering techniques employ forward filtering, which generates a phase. To negate the phase, backward filtering is applied to the output of the forward filter.
For example, if your original filter (forward filter) has $M$ zeros at $z = -1$, then the filter response obtained using scipy.signal.filtfilt will have $2M$ zeros at $z = -1$. As the number of filter coefficients has doubled, you observe a sharper filter response. In addition, the $3 \rm{dB}$ cutoff frequency also changes for a zero-phase filter.
