Two cents from a signal processing guy :)

according to the classic book "Discrete-Time Signal Processing" by
Oppenheim & Schafer, if you are doing non-real time filtering (like in
your case), the best approach is the Parks–McClellan FIR with zero
phase (=two pass). As you wrote, having N "resting" time points at the
beginning and at the end of your experiment would be ideal to deal
with any FIR transient. In practice things are not as bad as the
theory tells us, sometimes you are able to detect statistically
significant activations even during those N "noisy" time points.

However DCT and other frequency based approaches are always worth
trying. In the end, it all goes down to what signals you are dealing
with (i.e. to the "speed" of your experimental paradigm), so the best
is to test various approaches and compare the final results at the end
of the pipeline. You can easily generate an optimal FIR filter with
the matlab functions firpmord and firpm.

When it comes to sources of noise and frequency spectrum of the BOLD
signal, I've spent some time trying to gather as many sources as
possible, so feel free to check the introduction part from my open
access paper "Functional magnetic resonance imaging phase
synchronization as a measure of dynamic functional connectivity"
http://www.ncbi.nlm.nih.gov/pubmed/22559794

best
Enrico

On 6 July 2013 18:10, Bruno L. Giordano <[log in to unmask]> wrote:
> Dear Pierre,
>
> thank you for your detailed response.
>
> The default cutoff makes perfect sense now, thank you. Additional
> information about this issue is also present in the thread referenced by
> Donald.
>
> Concerning the filtering approach, point (2) makes sense, although should be
> of no concern when inference is at the group level. Concerning point (1), I
> wonder whether a possible approach to minimizing edge effects with non-DCT
> filters could be to simply acquire an additional N baseline scans at the
> beginning and end of the fMRI time series of interest, with N = order of FIR
> filter, and then discard those 2*N scans after forward-reverse filtering.
>
> I am also curious about the comparisons of different filtering approaches
> reported in this page:
>
> http://nipy.sourceforge.net/nitime/examples/filtering_fmri.html
>
> Different approaches appear to lead to different levels of distortion of the
> spectral band of interest. It would be interesting to include the DCT
> approach in the comparison. If this has been done before, I would appreciate
> if someone could point me to the relevant literature.
>
> Best,
>
>         Bruno
>
>
>
>
> On 05/07/2013 7:22 PM, Pierre Bellec wrote:
>>
>> Dear Bruno,
>>
>> I am aware of at least two reasons. First edges effects. Standard FIR
>> filters (e.g. Butterworth) with off-the-shelf parameters are very poorly
>> adapted to fMRI time series. This is because the TR in fMRI (~1s) is
>> very long compared to typical applications in signal processing. If you
>> filter time series over the full brain, normalize the time series to
>> zero mean and unit variance and then compute standard deviation across
>> the brain, you'll find larger deviations at the edges (or at least
>> that's what I remember from a few experiments I ran years ago). The DCT
>> solves that problem, because it relies on a periodization of the signal
>> that does not introduce discontinuities at the edges. It may be possible
>> to tweak a FIR filter better for fMRI time series, but I don't have
>> experience with that. (2) the regression of discrete cosines fits in the
>> linear model framework and it thus properly handled in the statistical
>> inference.
>>
>> Otherwise, regarding the amount of noise in different frequency band, I
>> guess that at least part of the reasoning is the 1/f spectral power of
>> fMRI time series (http://www.citeulike.org/user/pbellec/article/956093).
>> There is lot of variance below 0.01 Hz , and that variance is mostly
>> noise. That can be seen by observing the spatial distribution of the
>> relative variance in ultra-low frequencies, which follows notably the
>> edges of the brain. We also showed a couple years ago that simulation of
>> motion generates slow time drifts (below 0.01 Hz) in an amount somewhat
>> similar to what is actually observed in real data
>> (http://www.ncbi.nlm.nih.gov/pubmed/19570641, Fig. 6a). The simulation
>> model was very crude, but it does suggest that this frequency band is
>> very noisy.
>>
>> If you find some good reference down the road about this issue, please
>> share, I'd be interested. I hope this helps, best regards,
>>
>> Pierre Bellec, PhD
>> Researcher / Chercheur, Research Centre of the Montreal Geriatric
>> Institute
>> Professeur adjoint sous octroi, Department of Computer Science and
>> Operations Research
>> University of Montreal, Québec, Canada
>> 1 514 340 3540 #3367
>> http://simexp-lab.org/brainwiki/doku.php?id=pierrebellec
>>
>>
>> 2013/7/4 Bruno L. Giordano <[log in to unmask] <mailto:[log in to unmask]>>
>>
>>
>>     Hello,
>>
>>     I am interested in the implementation of the temporal filtering of
>>     fMRI time series. In particular, I am trying to understand the
>>     advantages associated with the method based on the discrete cosine
>>     transform (DCT) basis set: are they simply computational, or there
>>     is something else that makes it preferable to a more classical
>>     forward-reverse filtering approach based on, e.g., FIR filters?
>>
>>     Additionally, could someone please point me towards studies of the
>>     amount of noise in different frequency bands of fMRI time series?
>>     What's the reasoning behind the default of a 128-s period high pass
>>     in SPM?
>>
>>     Thank you,
>>
>>              Bruno
>>
>>     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~__~~
>>
>>     Bruno L. Giordano, PhD
>>     Institute of Neuroscience and Psychology
>>     58 Hillhead Street, University of Glasgow
>>     Glasgow, G12 8QB, Scotland
>>     T +44 (0) 141 330 5484 <tel:%2B44%20%280%29%20141%20330%205484>
>>     Www: http://www.brunolgiordano.net
>>
>>
>
> --
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
> Bruno L. Giordano, PhD
> Institute of Neuroscience and Psychology
> 58 Hillhead Street, University of Glasgow
> Glasgow, G12 8QB, Scotland
> T +44 (0) 141 330 5484
> Www: http://www.brunolgiordano.net