Method comparison

[MakotoMiyakoshi]

Tom Donoghue pointed me to his preprint. Thank you Tom!
https://www.biorxiv.org/content/10.1101/2024.09.15.613114v1

[MarjanZamani1990]

Hi @MakotoMiyakoshi
I would like to propose a preliminary (and likely naive) idea for approximating the separation between periodic and aperiodic components in EEG signals, and I would greatly appreciate your feedback.
Instead of relying solely on parametric spectral models, I am exploring decomposition-based approaches such as Variational Mode Decomposition (VMD) and Empirical Wavelet Transform (EWT) in matlab.

The general idea is:

●Decompose the EEG signal into band-limited components using VMD or EWT
●Identify components (or bands) that are dominated by narrowband oscillatory peaks
●Treat these components as an approximation of the periodic activity
●Treat the remaining signal (or the signal after attenuating/removing these components) as an approximation of the aperiodic activity

I am aware that this does not provide a strict physiological separation, since broadband (aperiodic) activity is distributed across frequencies and may also be present within the extracted modes. Therefore, this should be considered as a coarse and approximate decomposition, or a form of spectral perturbation, rather than a true separation.
The motivation is to explore how removing or attenuating peak-dominated components affects the overall spectral structure, and whether this can provide insight into the interaction between oscillatory (periodic) and broadband (aperiodic) activity.
Additionally, the resulting “aperiodic-like” component could be further analyzed using methods described in the mentioned literature, including model-based spectral parameterization approaches and GLM-based separation strategies(as suggested by Cedric)
, to better characterize its structure.

This approach is intended as a simple and approximate framework that could potentially be combined with more established methods.

[MakotoMiyakoshi]

Hi @MarjanZamani1990,

So this is an idea to develop a variation of FOOOF. I can see your point, but I am more inclined to dig into generative mechanisms rather than signal processing starting from observations. I wish there are someone who are interested in this engineering aspect of this problem in this community. I suggest you post (or I can do it for you if you think it is better) brief summary of your idea to the EEGLAB mailing list and ask any engineer who are interested in this engineering task.

[MarjanZamani1990]

Hi @MakotoMiyakoshi

Thanks, I understand your perspective and agree that generative mechanisms is an important direction. My idea is mainly focused on the signal-processing side—whether oscillatory and aperiodic components can be consistently separated and used as independent feature spaces for analysis.
To some extent, this has also come up in discussions related to periodic vs aperiodic separation. I am still not sure whether it would be useful to share a brief summary of the idea on the EEGLAB mailing list, and I would appreciate your thoughts on that?

[MarjanZamani1990]

After thinking more carefully about the problem, I think I may have initially underestimated how intertwined the periodic and aperiodic components are.

At first, I was imagining them as relatively separable contributions to the signal, but now it seems more likely that their relationship is much more coupled and possibly even generative rather than simply additive.

This also makes me think that purely removing frequency bands or comparing residuals may be too simplistic to fully capture the underlying dynamics.

I’m starting to see why approaches based on spectral parameterization or generative modeling may be more appropriate for this problem.

[MakotoMiyakoshi]

Hi @MarjanZamani1990

After thinking more carefully about the problem, I think I may have initially underestimated how intertwined the periodic and aperiodic components are.

In fact, I have been against the use of the name periodic vs. aperiodic to refer to alpha peak vs. 'background slope' of PSD. Alpha = periodic is rather ok. The problem is the aperiodic: I can make a smooth 1/f slope from multiple sinusoids. Are they not periodic?

now it seems more likely that their relationship is much more coupled and possibly even generative rather than simply additive.

I'm curious to know what you realized.

[MarjanZamani1990]

Hi all,
This idea is presented as a proposed approach for discussion in signal analysis across both time and frequency domains, combining wavelet entropy and wavelet AR-based methods.

In the spectral domain, the signal is first transformed into the frequency domain using wavelet decomposition, after which entropy-based measures are used to extract features associated with periodic and aperiodic components. Signal reconstruction can also be considered within this framework if required.

In the temporal domain, Variational Mode Decomposition (VMD) is used to decompose the signal into multiple frequency-specific components. Subsequently, pole-zero analysis is applied to investigate periodic and aperiodic behavior.

From a theoretical perspective, wavelet entropy behavior suggests that:
In 1/f (aperiodic) signals, energy is distributed across multiple scales, resulting in higher entropy.
In oscillatory signals, energy is concentrated in one or a few scales, leading to lower entropy.
Accordingly, wavelet entropy may serve as a discriminative feature for different signal structures.

Based on Donoghue’s studies(2020,2024),frequency-domain methods are more strongly associated with aperiodic components, whereas time-domain methods are more influenced by oscillatory activity. Therefore, a combined use of both domains may lead to a more complete and accurate analysis.

[EugenMasherov]

I'm also interested in the problem of detecting short-duration sinusoidal activity. Quite a while ago, I heard a paper that demonstrated short bursts of alpha activity in EEG. I'm trying to contact the authors (Fingelkurts and Fingelkurts) to clarify the details of their method. пт, 1 мая 2026 г. в 02:04, Marjan Z ***@***.***>:

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Hi @MakotoMiyakoshi <https://github.com/MakotoMiyakoshi> Thanks, I understand your perspective and agree that generative modeling is an important direction. My idea is mainly focused on the signal-processing side—whether oscillatory and aperiodic components can be consistently separated and used as independent feature spaces for analysis. To some extent, this has also come up in discussions related to periodic vs aperiodic separation. I am still not sure whether it would be useful to share a brief summary of the idea on the EEGLAB mailing list, and I would appreciate your thoughts on that? — Reply to this email directly, view it on GitHub <#13 (reply in thread)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/B2DLTZEPYEQ54TFVCZVUQVT4YPLZRAVCNFSM6AAAAACSNKWJTWVHI2DSMVQWIX3LMV43URDJONRXK43TNFXW4Q3PNVWWK3TUHMYTMNZXGQ3TQMA> . Triage notifications on the go with GitHub Mobile for iOS <https://apps.apple.com/app/apple-store/id1477376905?ct=notification-email&mt=8&pt=524675> or Android <https://play.google.com/store/apps/details?id=com.github.android&referrer=utm_campaign%3Dnotification-email%26utm_medium%3Demail%26utm_source%3Dgithub>. You are receiving this because you are subscribed to this thread.Message ID: ***@***.***>

[amisepa]

Hi everyone,
Just seeing all this recent disscussion.
@MakotoMiyakoshi I saw that paper when it came out, a very good one!

@MarjanZamani1990 thanks for your work above.

I think these types of contributions can fit in the other discussion we've worked on (#12), where we compare various methods for trying to separate the periodic and aperiodic components. I think that can be a 1st paper soon. And see this new relevant point and suggestion from Eric Rawls today in eeglablist:
"SPRiNT (Spectral Parameterization Resolved in Time) as developed by Luc Wilson and the Brainstorm group (PI Sylvain Baillet). Article in eLife: https://doi.org/10.7554/eLife.77348. The main idea is to use specparam (formerly FOOOF) on slices of an STFT representation of the underlying data, to measure (in)stability and variability in 1/f and oscillatory parameters."

paper: https://elifesciences.org/articles/77348
code: https://github.com/erawls-neuro/NeuroFreq

But this will be, of course, an agnostic paper on how to separate them if one desires, but most of the work will remain for this community, to try to identify whether or not they should be separated in the first place, depending on what the generative mechanisms and nature of these 2 components are. I will be all in to try to help answer this deeper question when I have more time! :)

[amisepa]

Another note to remember to also include Julie Onton's and Scott Makeig's IMA method:
https://sccn.ucsd.edu/~julie/AlphaPosterMini.pdf
https://sccn.ucsd.edu/~julie/AlphaIMposter.pdf

Scott: "IMA takes an approach orthogonal to FOOOF. Wherease FOOOF considers the form of the log spectrum of a data source - in itself - IMA pays no attention to the mean log spectrum (removing it from consideration first of all). IMA then considers the following question: What maximally distinct modes of log spectral variability does the data source exhibit across time? IMA, for example, could possibly isolate multiple modes whose summed activities across time (i.e., in the grand mean spectrum) happened to cancel each other out at frequencies of interest. Here, FOOOF would not find any evidence of them."

https://eeglab.org/plugins/imat/

[EugenMasherov]

(Warning: the following is an extreme, provocative point of view; it is expressed precisely to elicit criticism, even the harshest.) A periodic process is one about which we know everything over an infinite period of time, knowing a single, infinitely repeating period. A sinusoidal periodic process is one that we can continue to infinity, knowing only three points (from which we can evaluate the difference equation that all process values follow). It follows, then, that a periodic process is one that poorly or not at all transfers information. "Aperiodic" processes can be information-dense, and the closer they are to white noise, the more information-dense they are (deviations from a flat spectrum can be related, for example, to the fact that the higher the frequency, the greater the energy consumption, and the maximum information flow for a given energy limit, with a certain dependence of energy consumption on frequency, can be 1/f). That is, it makes sense to speak not of "aperiodic" and "periodic" processes, but of "informational" and "non-informational" signals (the latter, however, have physiological significance and are associated with the transmission of information, so they should be considered in connection with "aperiodic"). The fact that we are primarily discussing sinusoidal signals is partly due to the fact that a sinusoid is beautiful to our eyes and easily recognized, as well as being quite simple to evaluate using Fourier, and partly due to the fact that many such signals are pathological (delta activity primarily, although it is not always pathological), having clinical significance. "Aperiodic" signals are more difficult to analyze by the eye, requiring rather non-trivial mathematical processing. Therefore, they attracted attention later (although in early works, where correlation analysis, rather than Fourier, was used, aperiodic signals were given attention). I don't want to say that we should abandon the study of periodic signals, but "aperiodic" signals are the most important object of research, and they need to be studied from the point of view of the generation mechanism, which will perhaps also clarify "periodic" signals. вт, 19 мая 2026 г. в 06:42, Makoto Miyakoshi ***@***.***>:

…

Hi @MarjanZamani1990 <https://github.com/MarjanZamani1990> After thinking more carefully about the problem, I think I may have initially underestimated how intertwined the periodic and aperiodic components are. In fact, I have been against the use of the name periodic vs. aperiodic to refer to alpha peak vs. 'background slope' of PSD. Alpha = periodic is rather ok. The problem is the aperiodic: I can make a smooth 1/f slope from multiple sinusoids. Are they not periodic? now it seems more likely that their relationship is much more coupled and possibly even generative rather than simply additive. I'm curious to know what you realized. — Reply to this email directly, view it on GitHub <#13?email_source=notifications&email_token=B2DLTZFMZRRS24V7K3AUPPD43PJZDA5CNFSNUABIM5UWIORPF5TWS5BNNB2WEL2ENFZWG5LTONUW63SDN5WW2ZLOOQXTCNRZG4YDGMZSUZZGKYLTN5XKOY3PNVWWK3TUUVSXMZLOOSWGM33PORSXEX3DNRUWG2Y#discussioncomment-16970332>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/B2DLTZAUWINPF534X24LKX343PJZDAVCNFSM6AAAAACSNKWJTWVHI2DSMVQWIX3LMV43URDJONRXK43TNFXW4Q3PNVWWK3TUHMYTMOJXGAZTGMQ> . Triage notifications on the go with GitHub Mobile for iOS <https://apps.apple.com/app/apple-store/id1477376905?ct=notification-email&mt=8&pt=524675> or Android <https://play.google.com/store/apps/details?id=com.github.android&referrer=utm_campaign%3Dnotification-email%26utm_medium%3Demail%26utm_source%3Dgithub>. You are receiving this because you commented.Message ID: ***@***.***>

[MakotoMiyakoshi]

Hi @EugenMasherov,

I agree.

Part of the problem is that we do not know what model we should make to study so-called 'aperiodic' signals. There are whole bunch of random non-linear metrics. Among these, I think 1/f-ness is one of the most successful and accessible one, quickly gaining popularity in the past 5 years.