Detection, Measurement and Classification of Discontinuities of Signals Captured with Noise

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Thank you for giving me the chance to review the paper. I carefully review the paper and here are my comments:.

1. Clarity and Organization: The manuscript aims to introduce an algorithm for detecting, measuring, and classifying discontinuities in noisy signals, a subject with significant potential applications. However, the paper suffers from a lack of clear organization and cohesiveness. Key concepts are introduced without adequate background, making it challenging for readers unfamiliar with the subject to follow the discourse.

2.  

3. Technical Depth and Novelty: While the manuscript proposes a new algorithm adapted from Harten's subcell-resolution approximation, it fails to adequately differentiate this approach from existing methods. The technical sections lack depth, and there is insufficient discussion on how this approach improves upon or differs significantly from existing methodologies.

4. Data and Methodology: The paper presents an application related to heart rate measurements in sports, yet there is a noticeable absence of detailed methodology on how the data was collected, processed, and analyzed. This omission raises questions about the reproducibility and reliability of the findings. The simulation is not enough, real data not enough.
   
   
   

5. Statistical Analysis and Validation: The statistical analysis presented lacks rigor. The manuscript would benefit from a more thorough statistical treatment of the data, including validation of the algorithm's performance against established benchmarks or controlled datasets.

6. Literature Review: The literature review in the manuscript is not comprehensive. It fails to situate the study within the broader context of current research in the field. A more extensive review of related work would help demonstrate the manuscript's contribution to the field. Only four references?

7.  
8.  
9. In summary, while the topic is of interest and could contribute to the field, the manuscript in its current form has several critical areas that need addressing. A thorough revision considering the above points is recommended before it can be considered for publication

Author Response

First, we would like to express our gratitude to the referees for their improvement suggestions on the article. We have attempted to present a new presentation following their recommendations. Initially, we have enhanced the abstract, emphasizing the advantages of the new proposal. The introduction has been completely revised, starting with a motivation for the addressed problem. Subsequently, we present our proposal, review various related works, discuss the advantages of our algorithm, and finally, introduce the application we aim to address. Before delving into our proposal, we have added a new section to provide a better explanation of the algorithm's framewrok. Additionally, we have expanded explanations of all tools and ideas contributing to the algorithm. In the initial phase of our algorithm, the ENO-SR method undergoes a meticulous adaptation to account for dynamic changes in divided differences, emphasizing decentering only in instances where variations are not attributed to noise. This nuanced adjustment enhances the method's reliability in handling potential irregularities in the data. Subsequently, a thorough examination of possible discontinuities is conducted with a specific focus on scenarios where the discontinuity is positioned at a node or within an interval. The insights derived from this analysis are systematically cataloged, encapsulating essential constraints that guide the formulation of our algorithm presented. While the algorithm imposes a notable number of constraints, numerical examples reveal its exceptional resilience in accommodating substantial levels of noise. This adaptability positions the algorithm as a robust solution, demonstrating superior performance compared to similar methodologies in real-world scenarios. In essence, the journey from refining the ENO-SR method to algorithm formulation involves meticulous consideration of divided differences, a comprehensive analysis of discontinuities, and the systematic integration of constraints, resulting in a good alternative as we can see in the numerical experiments. We observe the ability to identify corners and jumps even when perturbing the signal with greater noise than that found in the references we include. In the conclusions, we have added some lines for future work and increased the number of references to 18, which have been incorporated throughout the paper.

Reviewer 2 Report

Comments and Suggestions for Authors

1. The introduction is practically absent and is written improperly. Instead of reviewing the literature to indicate the relevance of the research topic, authors actually use the introduction as a problem statement. It is necessary to review the work on this topic. Identify the unsolved tasks. Find the place of their research. And then make a problem statement. And I would recommend setting the task in a separate section. 

2. Clearly state the purpose of your work.

3. The algorithm (table 3), which is the key to the work, is not sufficiently commented. Describe its advantages over existing algorithms that you have considered. Do a comparative analysis. Specify the limitations of your algorithm. 

4. The numerical experiment is described poorly. Where are the source data taken from? Describe the production in detail. You constantly operate the words «Very big noise». You can quantify the term, for example by the signal/noise ratio. Does your method work well in the full frequency range or does it have advantages for a particular frequency range? 

5. In conclusion, you write about certain devices. They use your algorithm? Why are they not mentioned in the text of the work?

 

The work as presented resembles a draft from different ideas. The relationship between the ideas is not yet available. It is necessary to put this material in order. It needs deep processing.

Author Response

First, we would like to express our gratitude to the referees for their improvement suggestions on the article. We have attempted to present a new presentation following their recommendations. Initially, we have enhanced the abstract, emphasizing the advantages of the new proposal. The introduction has been completely revised, starting with a motivation for the addressed problem. Subsequently, we present our proposal, review various related works, discuss the advantages of our algorithm, and finally, introduce the application we aim to address. Before delving into our proposal, we have added a new section to provide a better explanation of the algorithm's framewrok. Additionally, we have expanded explanations of all tools and ideas contributing to the algorithm. In the initial phase of our algorithm, the ENO-SR method undergoes a meticulous adaptation to account for dynamic changes in divided differences, emphasizing decentering only in instances where variations are not attributed to noise. This nuanced adjustment enhances the method's reliability in handling potential irregularities in the data. Subsequently, a thorough examination of possible discontinuities is conducted with a specific focus on scenarios where the discontinuity is positioned at a node or within an interval. The insights derived from this analysis are systematically cataloged, encapsulating essential constraints that guide the formulation of our algorithm presented. While the algorithm imposes a notable number of constraints, numerical examples reveal its exceptional resilience in accommodating substantial levels of noise. This adaptability positions the algorithm as a robust solution, demonstrating superior performance compared to similar methodologies in real-world scenarios. In essence, the journey from refining the ENO-SR method to algorithm formulation involves meticulous consideration of divided differences, a comprehensive analysis of discontinuities, and the systematic integration of constraints, resulting in a good alternative as we can see in the numerical experiments. We observe the ability to identify corners and jumps even when perturbing the signal with greater noise than that found in the references we include. In the conclusions, we have added some lines for future work and increased the number of references to 18, which have been incorporated throughout the paper.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

I have no further comments. 

Author Response

Letter to the reviewers

Reviewer 1

Reviewer: I have no further comments. 

Answer: Thanks

Reviewer 2

Reviewer: The revised version of the article is better

Answer: Thanks

Reviewer: I still do not understand the purpose of the paper.

Answer: The purpose of our paper is to introduce an algorithm for the detection of discontinuities that allows us, on the one hand, to find discontinuities (jumps) in signals disturbed by high levels of noise (more than those found in the literature), and on the other hand, to be able to identify discontinuities in derivatives as well (high gradients, corners). As a secondary objective, we propose the use of the algorithm in a particular practical application.

Since the practical application may not be known to many potential readers, a comprehensive explanation of it is provided. It is emphasized that our goal is not to verify the accuracy of the data; this aspect has already been validated in several previous works focused on the same application. We only like to apply the algorithm to the data and explain how the information obtained by the algorithm can help the coach team.

We regret if we were not clear enough, and we acknowledge that this may have introduced confusion in the reading.

Reviewer: The abstract and the introduction only talk about the algorithm, which is presented in Table 3.

Answer: I put in red the paragraphs in both abstract and introduction where we introduce the application.  

Reviewer: However, in section 5, obscure portable measurement devices appear. And the goal becomes to evaluate the accuracy of their measurements. But it has nothing to do with the algorithm. To estimate the accuracy of a measuring instrument, build its metrological model. Estimate the methodological error. Then apply your algorithm and prove that it has decreased. So far, my opinion that the work is a draft has not changed.

Answer: In the review papers [9, 10], we can see that these devices are well-established. It is not our goal.

Our intention only is to check that the algorithm can detect different exercise zones (rest, activation, effort, recovery). This information is embedded in the signals provided by the devices. The signals are contaminated with noise and contain discontinuities which delineate the different exercise zones. Therefore, it is as an example of the type of signals for which the algorithm has been designed.

In practice, the exercise zones are currently differentiated manually and retrospectively. What we propose is to use algorithms like the one suggested to perform this task automatically and in real-time. As a practical application in sports, we could, for example three utilities are: enhance team game rotations (ensuring that the player is sufficiently recovered after a substitution while simultaneously ensuring that players on the court are not entering fatigue), observe the evolution of physical conditioning through slope analysis (decreasing slopes associated with the activation phase and increasing those of the recovery phase), and detect possible cardiovascular anomalies associated with abnormally high heart rate levels.

We have included in red how we have modified the explanation of the section 5.

Reviewer: Moreover, errors have appeared that were not present in the original version.

Answer: We have reviewed and corrected possible typos in the article.

Reviewer 2 Report

Comments and Suggestions for Authors

The revised version of the article is better than the previous one. However, in my opinion, it is not sufficient for publication. In fact, the authors have revised mainly the introduction. It became much better, but other issues remained. I still do not understand the purpose of the paper. The abstract and the introduction only talk about the algorithm, which is presented in Table 3. However, in section 5, obscure portable measurement devices appear. And the goal becomes to evaluate the accuracy of their measurements. But it has nothing to do with the algorithm. To estimate the accuracy of a measuring instrument, build its metrological model. Estimate the methodological error. Then apply your algorithm and prove that it has decreased. So far, my opinion that the work is a draft has not changed. Moreover, errors have appeared that were not present in the original version. For example, on page 6 in the second paragraph, instead of Sj (which was in the original version), the authors write j. This is clearly an error. Formula (4) in the original version was absorbed by the text and a line of words without spaces appeared in italics. The same line appears in the penultimate paragraph on page 8. It is very difficult to read the revised version because the authors have not highlighted the corrections in the text of the paper. The article still needs a deep revision.

Author Response

Letter to the reviewers

Reviewer 1

Reviewer: I have no further comments. 

Answer: Thanks

Reviewer 2

Reviewer: The revised version of the article is better

Answer: Thanks

Reviewer: I still do not understand the purpose of the paper.

Answer: The purpose of our paper is to introduce an algorithm for the detection of discontinuities that allows us, on the one hand, to find discontinuities (jumps) in signals disturbed by high levels of noise (more than those found in the literature), and on the other hand, to be able to identify discontinuities in derivatives as well (high gradients, corners). As a secondary objective, we propose the use of the algorithm in a particular practical application.

Since the practical application may not be known to many potential readers, a comprehensive explanation of it is provided. It is emphasized that our goal is not to verify the accuracy of the data; this aspect has already been validated in several previous works focused on the same application. We only like to apply the algorithm to the data and explain how the information obtained by the algorithm can help the coach team.

We regret if we were not clear enough, and we acknowledge that this may have introduced confusion in the reading.

Reviewer: The abstract and the introduction only talk about the algorithm, which is presented in Table 3.

Answer: I put in red the paragraphs in both abstract and introduction where we introduce the application.  

Reviewer: However, in section 5, obscure portable measurement devices appear. And the goal becomes to evaluate the accuracy of their measurements. But it has nothing to do with the algorithm. To estimate the accuracy of a measuring instrument, build its metrological model. Estimate the methodological error. Then apply your algorithm and prove that it has decreased. So far, my opinion that the work is a draft has not changed.

Answer: In the review papers [9, 10], we can see that these devices are well-established. It is not our goal.

Our intention only is to check that the algorithm can detect different exercise zones (rest, activation, effort, recovery). This information is embedded in the signals provided by the devices. The signals are contaminated with noise and contain discontinuities which delineate the different exercise zones. Therefore, it is as an example of the type of signals for which the algorithm has been designed.

In practice, the exercise zones are currently differentiated manually and retrospectively. What we propose is to use algorithms like the one suggested to perform this task automatically and in real-time. As a practical application in sports, we could, for example three utilities are: enhance team game rotations (ensuring that the player is sufficiently recovered after a substitution while simultaneously ensuring that players on the court are not entering fatigue), observe the evolution of physical conditioning through slope analysis (decreasing slopes associated with the activation phase and increasing those of the recovery phase), and detect possible cardiovascular anomalies associated with abnormally high heart rate levels.

We have included in red how we have modified the explanation of the section 5.

Reviewer: Moreover, errors have appeared that were not present in the original version.

Answer: We have reviewed and corrected possible typos in the article.

Round 3

Reviewer 2 Report

Comments and Suggestions for Authors

The authors have improved the article. I believe that it can be published.