Re: filter raw EEG by frequency bands in time domain

[Sergei Steshenko]

On 03/05/2020 19:01, ingber via Help-octave wrote:
> Additional note (in reply to one person):
>
>
> I have readhttps://www.mathworks.com/help/signal/ref/bandpass.html  , but
> I'm not sure if this is the best way to proceed.
>
> bandpass() seems able to deliver results without an additional step, e.g.,
> not needing both fft and ifft.
>
>
>
> -----
> https://www.PhysicalStudiesInstitute.org
> --
> Sent from:https://octave.1599824.n4.nabble.com/Octave-General-f1599825.html

"bandpass() seems able to deliver results without an additional step, 
e.g., not needing both fft and ifft" - you have to decide what you 
really want.


If you are using a typical IIR filter, it's most likely a minimum phase 
system. This by itself is neither bad nor good, though quite often good 
- unless you want to compensate for linear distortions introduced by a 
non-minimum phase system.


With fft -> filter -> ifft approach you can have a filter with arbitrary 
magnitude response and arbitrary phase response. In a minimum phase 
system there is strict relation between magnitude and phase responses: 
https://en.wikipedia.org/wiki/Kramers%E2%80%93Kronig_relations -> 
https://en.wikipedia.org/wiki/Kramers%E2%80%93Kronig_relations#Magnitude_(gain)%E2%80%93phase_relation 
, 
https://en.wikipedia.org/wiki/Minimum_phase#Relationship_of_magnitude_response_to_phase_response 
.


So, with fft -> filter -> ifft approach you can easily test various 
filters - because you can arbitrarily assign both magnitude and phase 
responses. But you have to understand really well what you are doing, 
especially taking into account wrap around - read the 
https://dsp.stackexchange.com/questions/51427/how-to-get-around-the-circular-shift-property-of-discrete-fourier-transform 
thread. You can still use traditional filter - you simply measure its 
complex frequency response and multiply the signal spectrum by the 
measured frequency response, then perform ifft.


--Sergei.