The manuscript is discussing two approaches on modal indetification of systems with a complex response or damping. Although, the abstract clearly indicates the aim of research as well as its purposefulness and expected outcomes, it is too short, and does not properly reflect the obtained results. The title of the manuscipt is adequate with a proper balance between informativity and generality. The references are adequately selected with respect to the broadness of the investigated topic and the length of the manuscript. The introduction contains clear and concise background on appearance of wavelet theory as well as first engineering applications, in particular in modal analysis. Then, the authors presented their research problem, proposing two methods for modal parameter identification using continuous wavelet transform. In section 1.2 the authors presented a theoretical backgroud on the construction and properties of the continuous wavelet transform and the properties of two selected complex-valued wavelets considered by the authors in the following study. By this introduction and further explanation of their properties and possible effect of their application the authors validated the purposefulness of selection of the studied problem. The authors presented the process of selection of the studies subject in a solid and clear way. The presentation of the mathematical side of the investigated problem is concise and clear with all steps of a mindflow and all variables described. Due to the theoretical character of this manuscript the validity, reliability and reproducibility of the study has also purely theoretical character, hovewer it is well grounded in all the mentioned issues. The part with results is followed with a short introduction to the problem of modal indentification of systems, including the main assumptions and limitations. In the section 1.3 the authors defined a function describing a signal used further for the processing, which can be considered as data representation. In two further subsections the authors presented the results for two methods of modal identification using continuous wavelet transform considered in this study. The presented results are theoreticaly justified by showing the effectiveness of modal identification of particular harmonics using both approaches with addressing these approaches to the property of a system (level of noise). Finally, the authors addressed to the reference (another paper of the first author), where the experimental validation of this approach was performed on signals from a real system, however no details were given in the following manuscript. This validation step is significant from the point of view of a practical application of the presented approaches, and, in my opinion, should be briefly presented in the following manuscript. In the part with discussion and conclusions the authors pointed on the way of emphasizing the maxima of the singularities analysis function, which is an effect of application of the proposed approach and which allows for easier modal identification of systems, especially in the cases with neighboring poles. The results of this study has a practical importance due to a possibility of modal identification of systems with lower uncerntainty. Although, the authors did not provided any comparisons to other studies, the validation study on a real object cited in the part of the manuscript makes it relevant for practical applications. No limitations of applicability were given in this part, however, such limitations were discussed during description of particular methods and discussion of the results in subsections 1.3.1 and 1.3.2.

Despite the overall good quality of the manuscript several issues need to be expained or corrected.

1) Selected references are quite old, which from the one point of view is good, since the authors cited necessary references to define a research problem, while from the other hand, lack of recent references may indicate an insufficiently performed literature review.

2) The authors presented a literature survey in the area of modal identification, however no clear statements on originality and open problems are given.

3) One remark is necessary in terms of used symbols. The type of symbols used for the Laplace transfrom is not appropriate in the light of accepted practices. The style of symbols used by the authors for this purpose is reserved for noting algebras or number spaces (in particular H is reserved for the hypercomplex vector space of quaternions). This ambigiuty is present in the manuscript, e.g. in the first sentence of the subsection 1.3.2. I suggest to change this symbol to uppercase italic L, which is commonly used for noting the Laplace transform. Although, the notation varies from journal to journal, and the most of symbols can be used interchangeably, in the case of the Laplace transform the notation in the mentioned format is unified and need to be used appropriately.

4) The figures representing results are important and necessary, however, in order to improve their readability it is necessary to introduce several corrections. In particular, in Fig. 1.1there is lack of description of a horizontal axes in both plots and lack of colorbar for the results presented in the second (right) plot in this figure. Additionally, no legends were added in Fig. 1.2, which make it unreadable without explanation in text.

5) The discussion and conclusions in this manuscript are not placed in a separate section, which makes it difficult to follow. They are presented on page 9 just before the reference list.