Generalized Hurst Hypothesis: Description of Time-Series in Communication Systems
Round 1
Reviewer 1 Report
The editor / the authors
The article presents considerations on the application of the method generalized Hurst laws to obtain a new set of reduced parameters in data related to communication systems. Three hypotheses were analyzed for trendless sequences/long-time series. The article contains four chapters and a three-part appendix.
The article is interesting but contains some ambiguities.
- In chapter Introduction, although the article concerns the application to communication systems, only one article in this field was referred - [15]. This part should be expanded or commented on the small number of articles on communication on this issue.
- The sentence starting with "In this paper" (Line 34) should start with a separate paragraph concerning the topic of the article and the news obtained by the authors. In general, this part of the chapter is poorly structured
- Figures 1, 2, 3 should be of similar size to allow a more convenient comparison of the value and aesthetics of the article.
Author Response
Please see the attachment.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Authors present an extension of Hurst law model to include more additive terms with different exponents.
But the purpose of the paper is not clear, and neither is the title: "generalized Hurst" is too broad, and "description of time series in communication systems" is even more. In fact, some examples are about audio signals.
What is the purpose of the paper? to show that a system can be described by a set of parameters for classification purposes? why could be useful this? In communications it is more important to identify the channel response, maximize SNR, etc.
At least some explanations relating the Hurst model to the basic Communication parameters is needed (what kind of noise is your first, second or third model better to describe or fitted?; what about the spectrum or correlation function?; are you considering the TLS as the input noise or the convolution of the input noise with the impulse response of the system/channel?)
In the examples authors talk about the phase. They explain the complex conjugate relationship; this is probably related to the transfer function of the channel or the real nature of the input? Any thoughts about that? When you show the results for the phase, please include the maths to make clear the phase noise definition you use in figure 2.
Minor comment: please, specify the definition of R and S functions. It is the core of the Hurst and it is not defined in the paper.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Reviewer 3 Report
1. Equation 1 does not describe what R (x) and S (x) are.
2. The title indicates the interest in communication systems. However, we do not know what it means in practice that a given system meets a certain hypothesis and is described by a generalized form of the Hurst law.
3. Why is it significant that the system is described in a specific form of generalized Hurst law?
4. The authors dealt with a similar subject in the following articles:
Nigmatullin, R. R., & Vorobev, A. S. (2019). The “Universal” Set of Quantitative Parameters for Reading of the Trendless Sequences. Fluctuation and Noise Letters, 18 (04) Nigmatullin, Raoul & Dorokhin, Semyon & Ivchenko, Alexander. (2020). A Novel Approach to Radiometric Identification. 10.3233 / FAIA200806.
These articles are not mentioned in References. It would be necessary to show how they differ from the current article.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
The revised article takes into account my comments. Good luck to the authors.
Reviewer 2 Report
I like the new version of the paper and specially the response to my comments. It is intriguing the complex conjugate issue
