[Mne_analysis] Low pass filtering questions

[Martin Luessi]

Hari,

Please excuse the long silence. In the C code, method (1) is used, i.e., 
the filter is designed in the freq. domain with smooth transitions at 
the corner frequencies (using a cosine). In MNE-Python on the other hand 
method (2) is used. It can use both IIR or FIR filters, the FIR filters 
are designed using

http://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.firwin2.html

the actual implementation uses an overlap-add FFT applied in forward and 
backward direction to get zero phase (like filtfilt, as you mentioned).

I hope this helps,

Martin

On 03/14/13 14:08, Hari Bharadwaj wrote:
> Hi Don, Alex and Matti,
>      Not to introduce any more confusion but I have a clarification question:
> Which of the following is true about the C-code?
> (1) The filter is realized in the frequency domain fully (i.e) the FFT
> coefficients for blocks of 2048 time samples are tapered to have a
> transition band of 5 Hz around the cutoff and then going back to time. In
> this case, the filter is a non-causal IIR filter with zero-group delay.
>
> (2) An FIR filter is designed first and then then implemented in the
> frequency domain using the overlap-add method with FFT blocks of 2048
> points each. In this case, the filter is FIR and non-causal with
> zero-group delay but there are (small) sidebands extending upto the
> Nyquist rate. This would be like MATLAB's fftfilt().
>
> Thanks,
> Hari
>
>
> On Thu, March 14, 2013 8:45 am, Matti Hamalainen wrote:
>>
>> On Mar 14, 2013, at 8:30 AM, Alexandre Gramfort wrote:
>>
>>> hi Don,
>>>
>>>> Please bear with a further question:
>>>> If the low-pass is set at 40 Hz, then the cos^2 drop off is applied
>>>> beginning at the 40 hz components and falling to zero at 45 ?  Or is it
>>>> applied beginning at something like 38 hz so that the fourier
>>>> coefficients are attenuated by a fact of 2 at 40 ?
>>>
>>> I am not 100% about the C code but I bet for 40 to 45 with 0 at 45 Hz
>>>
>>>> And pardon this stupid question: Does this produce a gain of 0.0 for
>>>> all higher frequencies in the filtered signal above 45?  Or is there
>>>> some kind of ringing which occurs?
>>>
>>> it does remove all frequencies about 45Hz up to some numerical errors
>>> and if there is some ringing it will be in time. The less the stop
>>> band (here 5) the more ringing in time domain.
>>
>> Hi Don,
>>
>> In the C code the default width of the lowpass transition is 5 Hz. For 40
>> Hz lowpass this means that the falloff starts at 37.5 Hz and ends at 42.5
>> Hz. You can adjust this value in the mne_browse_raw or with the --lowpassw
>> option in mne_process_raw and mne_browse_raw.
>>
>> The manual tells this in sections 4.5.1 and 4.2.1.
>>
>> - Matti
>>
>>
>>
>>
>> ---------
>>
>> Matti Hamalainen, Ph.D.
>> Athinoula A. Martinos Center for Biomedical Imaging
>> Massachusetts General Hospital
>>
>> msh at nmr.mgh.harvard.edu
>> mhamalainen at partners.org
>>
>>
>>
>>
>>
>>
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>
>


-- 
Martin Luessi, Ph.D.

Research Fellow

Department of Radiology
Athinoula A. Martinos Center for Biomedical Imaging
Massachusetts General Hospital
Harvard Medical School
149 13th Street
Charlestown, MA 02129

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