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  1. Author Response*

    Reviewer 2 (Public Review):

    1. The periodic components of the simulated power did not overlap as is often seen in empirical data, they were confined to 1-40 Hz (e.g. no gamma activity was simulated), and the simulations did not include a knee in the aperiodic component. This means that it Is unclear whether SPRiNT would work as well in more complex or excessively noisy datasets. The non-sinusoidal waveform shape of the periodic component in the rodent data reiterates this concern.

    We are grateful that the Reviewer raised these important considerations about the practical value of SPRiNT in more complex data scenarios.

    We wish to clarify that in the simulations reported, although two simultaneous periodic components would not share the same centre frequency, a substantial number of realizations of the simulations made these components overlap with centre frequencies separated by less than 5 Hz (6% of all simultaneously simulated peaks; n = 8166). We now provide an example of two overlapping spectral peaks in the revised version of Figure 3 – figure supplement 1C.

    In preparing the revised manuscript, we also studied how the spectral overlap of periodic components would determine the peak detection rate: we found that the peak detection rate increases with the separation between two consecutive peaks along the frequency spectrum, but that it is independent of the presence of other peaks if they are at least 8 Hz apart from each other (Figure 3 – figure supplement 1D).

    As correctly mentioned by the Reviewer, the original synthesized data did not comprise components beyond a maximum frequency of 40 Hz, nor did they include a knee in their aperiodic component. In the revised manuscript, we now report new results obtained from the analysis of 1000 synthesized time series that comprise two periodic components (including one periodic component between 30-80 Hz) and a knee in their aperiodic component (Figure 3 – figure supplement 2). The relevant additions to the Methods section are pasted below:

    "We also simulated 1000 time series with aperiodic activity featuring a static knee (Figure 3 – figure supplement 2). Aperiodic exponents were initialized between 0.8-2.2 Hz-1. Aperiodic offsets were initialized between -8.1 and -1.5 a.u., and knee frequencies were set between 0 and 30 Hz. Within the 12-36 s time segment into the simulated time series (onset randomized), the aperiodic exponent and offset underwent a linear shift and a random magnitude in the range of -0.5 to 0.5 Hz-1 and -1 to 1 a.u., respectively. The duration of the linear shift was randomly selected for each simulated time series between 1 and 20 s; the knee frequency was constant for each simulated time series. We added two oscillatory (rhythmic) components (amplitude: 0.6-1.6 a.u.; standard deviation: 1-2 Hz) of respective peak centre frequencies between 3-30 Hz and between 30-80 Hz, with the constrain of minimum peak separation of at least 2.5 peak standard deviations. The onset of each periodic component was randomly assigned between 5-25 s, with an offset between 35-55 s. (Lines 773 to 784)"

    We analyzed these data with SPRiNT within the 1-100 Hz frequency range. These new results indicate that SPRiNT performs in a satisfactory manner on data with components distributed over a broader frequency range, with a knee in their aperiodic component.

    Below are the related edits to the revised Results section:

    "SPRiNT did not converge to fit aperiodic exponents in the range [-5, 5] Hz-1 only on rare occasions (<2% of all time points). We removed these data points from further analysis. The simulated aperiodic exponents and offsets were recovered with MAEs of 0.22 and 0.42, respectively; static knee frequencies were recovered with a MAE of 3.55x104 (inflated by large outliers in absolute error; median absolute error = 11.72). Overall, SPRiNT detected the peaks of the simulated periodic components with 56% sensitivity and 99% specificity. The spectral parameters of periodic components were recovered with equivalent performances in the lower (3-30 Hz) and respectively, higher (30-80 Hz) frequency ranges: MAEs for centre frequency (0.32, resp. 0.32), amplitude (0,27, resp. 0.22), and standard deviation (0,35, resp. 0.29). (Lines 244 to 252)"

    We also now discuss possible limitations in the Discussion:

    "Finally, SPRiNT’s performances were slightly degraded when spectrograms comprised an aperiodic knee (Figure 3 – figure supplement 2). This is due to the specific challenge of estimating knee parameters. Nevertheless, the spectral knee frequency is related to intrinsic neuronal timescales and cortical microarchitecture (Gao et al., 2021), which are expected to be stable properties within each individual and across a given recording. Thus, we recommend estimating (and reporting) aperiodic knee frequencies from the power spectrum of the data with specparam, and specifying the estimated value as a SPRiNT parameter. (Lines 480 to 486)"

    The Reviewer’s point on non-sinusoidal waveform shapes is also well taken, but we would like to emphasize that they challenge all current methods, including but not specific to SPRiNT or specparam (Donoghue et al., 2021). Indeed, SPRiNT and specparam perform a parametric decomposition of the spectrally transformed data, regardless of whether periodic components of a true sinusoidal nature are present. Non-sinusoidal periodic time series, such as the sawtooth waveforms observed in the rodent data analyzed in the manuscript, comprise spectral peaks as harmonic components (here of a theta-band fundamental rhythm). For this reason, we opted to focus our analyses and discussion of these data to the temporal dynamics of their aperiodic components.

    1. Furthermore, the SPRiNT and specparam parameters were fixed and arbitrary, and it is unclear how robust the current results are with respect to changes in these parameters.

    Here too, we appreciate the Reviewer’s insight and concern.

    We explored a subset of the simulations with SPRiNT using alternative settings for STFT (Figure 2 – figure supplement 3) and observed overall satisfactory performances. We now report the relevant results in an addition to the Supplemental Materials, as pasted below:

    "SPRiNT settings for higher temporal resolution (time range: 1-59 s, in 0.25 s steps; frequency range: 1-40 Hz, in 1 Hz steps) provided slightly larger estimation errors of exponent (MAE = 0.15) and offset (MAE = 0.20) relative to original settings (exponent, offset MAE = 0.11, 0.14, respectively). Alpha peaks were recovered with slightly lower sensitivity (98% at time bins with maximum peak amplitude; original 99%) and specificity (9% spurious detections; original 4%), and with greater errors in centre frequency (MAE = 0.43), amplitude (MAE = 0.24), and bandwidth (MAE = 0.53) compared to original settings (centre frequency, amplitude, bandwidth MAE = 0.33, 0.20, 0.42, respectively). Down-chirping beta oscillations were detected with lower sensitivity (93% sensitivity at time bins with maximum peak amplitude, original 98%; 86% specificity, original 98%), and with greater errors in centre frequency (MAE = 0.57), amplitude (MAE = 0.22), and bandwidth (MAE = 0.57) compared to original settings (centre frequency, amplitude, bandwidth MAE = 0.43, 0.17, 0.48, respectively). SPRiNT settings for higher frequency resolution (time range: 2-58 s, in 0.5 s steps; frequency range: 1-40 Hz, in 0.5 Hz steps) provided comparable estimation errors of exponent (MAE = 0.13) and offset (MAE = 0.16) relative to original settings (exponent, offset MAE = 0.11, 0.20, respectively). Alpha peaks were recovered with similar sensitivity (99% at time bins with maximum peak amplitude; original 99%) but lower specificity (21% spurious detections; original 4%), and with comparable errors in centre frequency (MAE = 0.35), amplitude (MAE = 0.23), and bandwidth (MAE = 0.41) to original settings (centre frequency, amplitude, bandwidth MAE = 0.33, 0.20, 0.42, respectively). Down-chirping beta oscillations were detected with comparable sensitivity (99% sensitivity at time bins with maximum peak amplitude, original 98%) but lower specificity (78%, original 98%), and with greater errors in centre frequency (MAE = 0.50), amplitude (MAE = 0.21), and bandwidth (MAE = 0.59) relative to original settings (centre frequency, amplitude, bandwidth MAE = 0.43, 0.17, 0.48, respectively). (Lines 1190 to 1213)"

    We now provide in the Discussion practical recommendations for setting the methods parameters, which will depend on the specific objectives of a given study. We saw the rationale for the settings used in the manuscript as guidelines to future users. We believe the specific recommendations added will be of greater practical value of the manuscript.

    Reviewer 3 (public Review):

    1. Based on the simulated data, SPRiNT seems to be very efficient and robust, and it is also superior to the wavelet-specparam approach. However, while the simulations are very extensive, I find that they are constructed in a manner that may induce biases as the comparison is conducted between SPRiNT and a single, fixed wavelet-based approach. Like any spectral analysis technique, wavelets possess their own trade-off between temporal and frequency resolutions. As the wavelet analyses are conducted using a fixed set of parameters, it may be that some of the differences between the methods stem from how well they are suited for detecting the simulated activity that is constructed using a certain standard deviation of their oscillatory frequencies. It would be valuable to evaluate whether changing the wavelet-analysis parameters or the width of the simulated oscillations would change how the alternative methods compare. It is of course clear that the STFT based approach would remain computationally superior, but it would be interesting to see whether the other differences would remain as robust after the above more detailed evaluation of the methods. Related to the method comparison, it also appears that the outlier removal within SPRiNT markedly improves the quantification of the periodic components. This matter could be discussed more within the manuscript.

    We appreciate the concerns expressed by this Reviewer regarding our choice of wavelet parameters.

    To respond to the concerns expressed, we have performed new analyses with the wavelet-specparam approach with a diversity of alternative time-frequency resolutions: FWHM of 2s at 1 Hz, and FWHM of 4s at 1 Hz (Figure 2 – Figure supplement 2).

    The changes observed remain qualitatively moderate, and the performances below those obtained with SPRiNT. The new results are displayed in Figure 2 – figure supplement 2 and described in the following revisions to Supplemental Materials:

    "Wavelet settings of finer resolution in time and coarser in frequency (time range: 3-57 s, in 0.005 s steps; central frequency = 1 Hz, FWHM = 2 s; frequency range: 1-40 Hz, in 1 Hz steps) yielded lower estimation errors of exponent (MAE = 0.12) and offset (MAE = 0.35) compared to original settings (exponent, offset MAE = 0.19, 0.78). Alpha peaks were recovered with higher sensitivity (97% at time bins with maximum peak amplitude, original 95%) and specificity (32% spurious detections, original 47%), although with greater errors in centre frequency (MAE = 0.61), amplitude (MAE = 0.25), and bandwidth (MAE = 0.94) compared to original settings (centre frequency, amplitude, bandwidth MAE = 0.41, 0.24, 0.64, respectively). Down-chirping beta oscillations were detected with lower sensitivity (29% sensitivity at time bins with maximum peak amplitude, original 62%) but higher specificity (97%, original 90%), and with greater errors in centre frequency (MAE = 0.63), amplitude (MAE = 0.17), and bandwidth (MAE = 1.59) relative to original settings (centre frequency, amplitude, bandwidth MAE = 0.58, 0.16, 1.05, respectively). When wavelet settings prioritized resolution in frequency over time (time range: 4-56 s, in 0.005 s steps; central frequency = 1 Hz, FWHM = 4 s; frequency range: 1-40 Hz, in 1 Hz steps) relative to original settings, the errors in estimates of exponent (MAE = 0.16) and offset (MAE = 0.47) parameters were reduced (original exponent, offset MAE = 0.19, 0.78, respectively). Alpha peaks were recovered with higher sensitivity (99% at time bins with maximum peak amplitude, original 95%) and similar specificity (46% spurious detections, original 47%), although with larger errors in centre frequency (MAE = 0.33), amplitude (MAE = 0.20), and bandwidth (MAE = 0.43) compared to original settings (centre frequency, amplitude, bandwidth MAE = 0.41, 0.24, 0.64, respectively). In contrast, down-chirping beta oscillations were detected with slightly higher sensitivity (79% at time bins with maximum peak amplitude, original 62%) and specificity (91%, original 90%), and with lower errors on centre frequency (MAE = 0.37), amplitude (MAE = 0.14), and bandwidth (MAE = 0.71) compared to original settings (centre frequency, amplitude, bandwidth MAE = 0.58, 0.16, 1.05, respectively). (Lines 1155 to 1179)"

    We now discuss the outlier peak removal process and its benefits/drawbacks more extensively in the revised Discussion. The relevant section is pasted below:

    "SPRiNT’s optional outlier peak removal procedure increases the specificity of detected spectral peaks by emphasizing the detection of periodic components that develop over time. This feature is controlled by threshold parameters that can be adjusted along the time and frequency dimensions. So far, we found that applying a semi-conservative threshold for outlier removal (i.e., if less than 3 more peaks are detected within 2.5 Hz and 3 s around a given peak of the spectrogram) reduced the false detection rate by 50%, without affecting the true detection rate substantially (a <5% reduction; Figure 3 and Figure 3 – figure supplement 3). Setting these threshold parameters too conservatively would reduce the sensitivity of peak detection. (Lines 487 to 494)"

    1. As for the investigation of real data, there are a few aspects that in my opinion could be investigated more thoroughly. Based on the findings it appears that the fine-grained time-resolved parametrization yields added value, especially in eyes-open rest where the fluctuation of alpha center frequency dissociates the different age groups, whereas the other time-resolved findings are not as unambiguously supportive of the need for fine-grained time-resolved analysis. Regarding the first point (fluctuation of alpha center frequency), the finding that the amount of fluctuation within the alpha frequency is distinct across age groups is very interesting. On the methodological, an open question is whether SPRiNT is required for making this observation. That is, is this effect observed only when applying the specparam-based parametrization (and outlier removal) after STFT or would the same observation have been made simply by estimating the fluctuations directly from the STFT based spectral estimates? As for using SPRiNT to determine the properties of aperiodic activity, presently it is not clear whether the approach yields added value compared to the more direct use of specparam. That is, the present findings show that the mean aperiodic slope dissociates both different age groups and resting-state conditions (eyes-open vs. -closed). It would be appropriate to test whether the same observation would be made by using specparam in the more standard way by first obtaining one spectral estimate across the whole one-minute time windows and then parametrizing this estimate. This type of testing would yield insights into whether there is a difference between SPRiNT that builds on dynamic but noisier spectral estimates and that allows the outlier removal and the standard approach benefiting from more stable spectral estimates for the present data and possibly for other questions. As for the rodent movement data, the evidence is clear that the aperiodic exponent differs between resting and movement state. However, the fundamental meaning of the change of the exponent at transition points is not explored. Does this change simply reflect the speed of the animal/amount of movement that changes across the time period prior and post rest and movement onsets? That is, does the transition curve align with the movement curve or does it represent something more complex? This aspect could be evaluated and discussed more extensively. Together, the above additional evaluations would be beneficial for determining whether there is value in looking at aperiodic activity in a time-resolved manner and whether a fine-grained analysis is needed or would a more static analysis takes into account the fact tasks/states fare equally or even in a superior manner.

    We appreciate all concerns raised here by the Reviewer. We intended to report that age-related changes of spectral features in healthy aging (Cellier et al., 2021; Donoghue et al., 2020; Hill et al., 2022; Ostlund et al., 2022; Schaworonkow & Voytek, 2021) can be replicated using summary statistics of SPRiNT outcomes. Our intention was not to showcase these effects as novel. To clarify our purpose and the novelty in the proposed approach, we have revised Figure 4 accordingly and now emphasize the genuine novel aspects of our findings from the time-resolved parameterization of the spectrogram.

    We further investigated the benefits of using SPRiNT to detect age-related changes in the temporal variability of alpha-peak frequency. Using STFT, we replicated the same effect trends whereby older individuals exhibit greater temporal variability of alpha-peak frequency. One asset from the SPRiNT approach is the interpretability of the effect because it detects genuine peak components in the spectrogram and correct their parameters from possible confounds from concurrent aperiodic components. Individual alpha peak frequency derived from STFT is based on instantaneous fluctuations of signal power in the alpha band, regardless of the actual presence of a periodic component.

    As for apparent discrepancies between the SPRiNT and specparam outcomes, we found that only the specparam-derived alpha amplitude, not SPRiNT’s, was predictive of age group. Please see our response to Reviewer 1’s first comment for a detailed interpretation of this outcome.

    Concerning the rodent data, we followed this Reviewer’s suggestion of determining whether aperiodic exponent was related to movement speed at the transitions between movement and rest (and vice versa). Indeed, we found that variability in aperiodic exponent proximal to transitions between movement and rest was partially explained by instantaneous movement speed (see Figure 5 – figure supplement 3). Below, we have revised the Results and Discussion sections accordingly:

    "We tested whether changes in aperiodic exponent proximal to transitions of movement and rest were related to movement speed and found a negative linear association in both subjects for both transition types (EC012 transitions to rest: β = -9.6x10-3, SE = 4.7x10-4, 95% CI [-1.1x10-2 -8.6x10-3], p < 0.001, R2 = 0.29; EC012 transitions to movement: β = -7.3x10-3, SE = 4.3x10-4, 95% CI [-8.1x10-3 -6.4x10-3], p < 0.001, R2 = 0.18; EC013 transitions to rest: β = -1.1x10-2, SE = 2.3x10-4, 95% CI [-1.2x10-2 -1.1x10-2], p < 0.001, R2 = 0.32; EC013 transitions to movement: β = -1.2x10-2, SE = 3.2x10-4, 95% CI [-1.3x10-2 -1.2x10-2], p < 0.001, R2 = 0.26; Figure 5 – figure supplement 3). (Lines 403-410)"

    Changes in aperiodic exponent were partially explained by movement speed (Figure 5 – figure supplement 3), which could reflect increased processing demands from additional spatial information entering entorhinal cortex (Keene et al., 2017) or increased activity in cells encoding speed directly (Iwase et al., 2020). (Lines 556-560)

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  2. Evaluation Summary:

    The paper addresses the highly timely questions of how to quantify aperiodic and periodic neural activity. This was done by extending previous work by embracing time-resolved parametrization of both simulated, noninvasive EEG and intracranial data. The new approach is termed Spectral Parametrization Resolved in Time (SPRiNT) and the paper shows that the slope of aperiodic activity is linked with both behaviour and age. The method thus demonstrates the importance of evaluating the state-dependence of aperiodic activity and dynamic properties of oscillatory components in a time-resolved manner.

    (This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #2 and Reviewer #3 agreed to share their name with the authors.)

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  3. Reviewer #1 (Public Review):

    Until recently EEG/MEG research has been primarily focused on the analysis of neural oscillations and evoked responses. A noise component i.e. 1/f or aperiodic part of the spectrum was mostly considered as a nuisance. Recently, however, this aperiodic part was recognized as an important and neurophysiologically meaningful form of neural activity reflecting a balance between excitation and inhibition. Yet estimation of such aperiodic component has been performed for relatively long recordings. Recognizing that brain states are dynamic and that both periodic and aperiodic components can change quickly in time, the authors introduced an approach (SPRiNT) allowing estimation of these components in a time-resolved manner, which provides parameters for consecutive time segments. This study includes a large number of simulations and analyses of real data including EEG recordings from a large number of healthy participants and LFP recordings from rats. In the case of EEG recordings, the authors show how parameters extracted with SPRiNT differ between young and elderly participants and between eyes-closed and eyes-open conditions. In LFP recordings neural activity is used to define periods of rest from the motor activity. In general, the study is performed on a good technical level, contains adequate statistical treatment of the data and the obtained results are interpreted in agreement with the current neurophysiological understanding of the periodic and aperiodic parts of electrophysiological signals. The method will be important for the analysis of neural data where transient neural states are likely to be present, for instance during different sensory, motor and cognitive tasks.

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  4. Reviewer #2 (Public Review):

    This paper describes a new tool for decomposing neural data into periodic and aperiodic spectral components. Traditionally the aperiodic (1/f) component has been viewed as noise that is static over time, but recently it has become clear that it is physiologically meaningful and variable. Ignoring its parameters and temporal variation thereof can lead to misinterpretation of the periodic components. The authors build on a recent parameterisation approach (Donoghue et al., 2020) to make it temporally resolved, and more robust to transient periodic components.

    Using this new method, the authors show that SPRiNT outperforms the original static method based on realistic simulations, and further show that its performance in detecting periodic components is generally high, though it struggles to detect low-frequency components (e.g. delta activity), and it underestimates the number of periodic components when more than two were simulated. Using SPRiNT in empirical data, the authors show that changes in periodic and aperiodic parameters correlate with participants' age and behaviour in humans and that aperiodic dynamics are related to movement in rodents. Because this method gives a richer and more accurate description of neural dynamics, it has the potential to be widely adopted by the field.

    Strengths:
    By transforming the static parameterisation method into a time-resolved one, the authors break down the assumption of temporal stationarity of a/periodic components, an assumption that is challenged by empirical data. The authors use a rigorous set of simulations to support this claim, and moreover, they show that their method gives a richer description of empirical data than what is traditionally used in the field.
    Furthermore, the proposed method is simple in use and computationally efficient. The source code is readily available in Brainstorm and as MATLAB standalone function and has the potential to be widely used.
    The results presented by the authors are transparent and the conclusions are supported by multiple pieces of evidence, e.g. both frequentist statistics and a post hoc Bayes factor analysis are presented, and the supplemental material presents additional evidence.

    Weaknesses:
    While the simulations in this paper support the claim that the presented method can parameterise time-varying a/periodic components, the simulations are not exhaustive. The periodic components of the simulated power did not overlap as is often seen in empirical data, they were confined to 1-40 Hz (e.g. no gamma activity was simulated), and the simulations did not include a knee in the aperiodic component. This means that it Is unclear whether SPRiNT would work as well in more complex or excessively noisy datasets. The non-sinusoidal waveform shape of the periodic component in the rodent data reiterates this concern. Furthermore, the SPRiNT and specparam parameters were fixed and arbitrary, and it is unclear how robust the current results are with respect to changes in these parameters.

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  5. Reviewer #3 (Public Review):

    The authors developed a novel method (Spectral Parametrization Resolved in Time, SPRiNT) intended for conducting time-resolved parametrization of both periodic and aperiodic neural activity. The method builds largely on the specparam/fooof-toolbox (fitting oscillations & one over f) and extends it by implementing a short-time Fourier transform (STFT) based approach for estimating time-resolved periodograms which are followed by the parametrization of neural activity via specparam and elimination of outlier spectral peaks. SPRiNT is then tested using simulated data against an alternative wavelet-based approach for conducting time-resolved parametrization of aperiodic and periodic activity as well applied to both resting-state human EEG data and intracranial data from rodents to evaluate the value of inspecting spectral parametrization in a dynamic manner. The question addressed by the study is very timely as there is an increasing interest in the role of aperiodic neural activity as well as detailed aspects of oscillatory components across a wide range of neuroscientific questions that have so far been primarily approached via static estimates of the spectral components. Based on the simulations, SPRiNT appears to be very efficient and superior at least compared to the one alternative method, opening the possibility for other researchers to investigate the role of aperiodic and periodic neural activity in a time-resolved manner. The method is applied to two sets of real recorded data, a resting-state EEG data collected from adults of different age groups (20-40 and 55-80 years) and intracranial data from two rodents during resting and movement conditions. The analyses on real data show that the slope of aperiodic activity varies across tasks/states and that the variability of the frequency of alpha oscillations dissociates individuals based on their age group. The analyses on real data thus show that at least for periodic data it is important to consider the fluctuations of the oscillatory parameters within extended periods of individual tasks. However, for aperiodic components, the evidence for this is not very strong. The work shows that the slope of aperiodic components changes at the transition from movement to resting condition but based on the reported findings it is not clear whether this represents more than just a gradual change in the amount of movement of the rodents. As for the comparison of SPRiNT to alternative approaches, the conducted testing against alternative methods does not unambiguously demonstrate its value in examining time-resolved properties of periodic and aperiodic components. This holds both for using SFTM vs. wavelets, using specparam based parametrization vs. direct estimates from STFT analyses, and using SPRiNT vs. basing the parametrization on a single spectral estimate across the whole duration of a task/state. The work thus 1) presents a novel approach for enhancing the study of a timely neuroscientific question that aims to facilitate the investigation of a broad range of related questions within the field, 2) shows that the dynamic properties of cortical oscillations within a uniform task can be a relevant marker of neural activity for dissociating different subject groups, and 3) yields added evidence on the importance of investigating the task- and state-dependence of aperiodic activity. However, the present level of testing of SPRiNT and evaluation of the observations do not fully allow one to evaluate the impact of the method and to determine the importance of investigating the different neural components (periodic vs. aperiodic) in a time-resolved manner.

    In my opinion, the study could be improved particularly by extending the comparison of SPRiNT to alternative approaches as well by a more thorough discussion of the observations, especially as regards the value of time-resolved analysis of aperiodic vs periodic neural activity.

    Specific comments

    1. Based on the simulated data, SPRiNT seems to be very efficient and robust, and it is also superior to the wavelet-specparam approach. However, while the simulations are very extensive, I find that they are constructed in a manner that may induce biases as the comparison is conducted between SPRiNT and a single, fixed wavelet-based approach. Like any spectral analysis technique, wavelets possess their own trade-off between temporal and frequency resolutions. As the wavelet analyses are conducted using a fixed set of parameters, it may be that some of the differences between the methods stem from how well they are suited for detecting the simulated activity that is constructed using a certain standard deviation of their oscillatory frequencies. It would be valuable to evaluate whether changing the wavelet-analysis parameters or the width of the simulated oscillations would change how the alternative methods compare. It is of course clear that the STFT based approach would remain computationally superior, but it would be interesting to see whether the other differences would remain as robust after the above more detailed evaluation of the methods. Related to the method comparison, it also appears that the outlier removal within SPRiNT markedly improves the quantification of the periodic components. This matter could be discussed more within the manuscript.

    2. As for the investigation of real data, there are a few aspects that in my opinion could be investigated more thoroughly. Based on the findings it appears that the fine-grained time-resolved parametrization yields added value, especially in eyes-open rest where the fluctuation of alpha center frequency dissociates the different age groups, whereas the other time-resolved findings are not as unambiguously supportive of the need for fine-grained time-resolved analysis. Regarding the first point (fluctuation of alpha center frequency), the finding that the amount of fluctuation within the alpha frequency is distinct across age groups is very interesting. On the methodological, an open question is whether SPRiNT is required for making this observation. That is, is this effect observed only when applying the specparam-based parametrization (and outlier removal) after STFT or would the same observation have been made simply by estimating the fluctuations directly from the STFT based spectral estimates? As for using SPRiNT to determine the properties of aperiodic activity, presently it is not clear whether the approach yields added value compared to the more direct use of specparam. That is, the present findings show that the mean aperiodic slope dissociates both different age groups and resting-state conditions (eyes-open vs. -closed). It would be appropriate to test whether the same observation would be made by using specparam in the more standard way by first obtaining one spectral estimate across the whole one-minute time windows and then parametrizing this estimate. This type of testing would yield insights into whether there is a difference between SPRiNT that builds on dynamic but noisier spectral estimates and that allows the outlier removal and the standard approach benefiting from more stable spectral estimates for the present data and possibly for other questions. As for the rodent movement data, the evidence is clear that the aperiodic exponent differs between resting and movement state. However, the fundamental meaning of the change of the exponent at transition points is not explored. Does this change simply reflect the speed of the animal/amount of movement that changes across the time period prior and post rest and movement onsets? That is, does the transition curve align with the movement curve or does it represent something more complex? This aspect could be evaluated and discussed more extensively. Together, the above additional evaluations would be beneficial for determining whether there is value in looking at aperiodic activity in a time-resolved manner and whether a fine-grained analysis is needed or would a more static analysis fact takes into account the tasks/states fare equally or even in a superior manner.

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