This is kind of a new Fourier harmonic analysis of a aprticular Ap event which b itself is certainly interesting. As such it is a technical paper of how to analyse irreegularl distributed data to make them a continuum and represent it as a function which can be smoothl represented as a Fourir seires within the interval of observation.

This is all ok. There is nothing to against the method in as far as it is new or new in parts because Fourier analysis is, of course, an old methodology to analyse data. I have not gone into the literature to check whether similar mehtods have also been applied, but this is not important. The authors show that their representation works even in takeingg its inverse to reconstruct the data.

All that is ok. What is, however, missing, is the physical meaning, the insight gained by formally appling such an analysis. The paper is lacking that completely. It stops at an intermediate formal point. One may ask: and so what? What should one do with that? What is the result? Cleaning a road which nobody is using makes lilttle sense. The authors shuld absolutely add what the physical meaning of their method is even applied to the event they are using it. Without such an effort, result, information I cannot accept the paper . 

This manuscript applies Fast Fourier Transform (FFT) techniques to analyze the geomagnetic Ap index. The authors examine amplitude and phase coefficients over three selected time intervals. While the topic is potentially interesting, several major issues must be addressed before the work can be considered further.

1. The abstract claims that the study analyzes the Dst index, but the manuscript contains no such analysis. It also states that the spectral content prior to the substorm growth phase is examined, yet no analysis relating to the substorm growth phase appears in the paper.
2. A substantial portion of Section 2 simply reproduces standard FFT formulations. Since these are well-established and widely known, it is unnecessary to present them in such detail. Moreover, the expressions for a_nl​ and b_nl​ are mathematically equivalent to the formulation in terms of C_{nl}​ and ϕ_nl​. Because only C_{nl}​ and ϕ_nl​.are used in the subsequent analysis, the extensive derivations of unused quantities are redundant.
3. Line 101. The statement about “linear interpolation” is unclear. It is not clear what type interpolation has been performed, how the interpolation modifies the sampling rate, or how the Nyquist frequency is affected. This requires explicit clarification.
4. Line 114-115. “In other words, all coefficients and phases are calculated in (3)–(5) for every three-hour interval”. It is unclear whether a moving time-window is used, what the total window length is (e.g., 27 days?), and how the three-hour stepping is implemented. This should be explained precisely.
5. Figure 1, The inverse FFT reconstruction of Ap is a routine check applicable to any FFT analysis. It does not provide new insight into either the method or the dataset. This figure should be removed or moved to supplementary material.
6. Standard practice in space-physics FFT analysis is to express coefficients as functions of frequency ω (or period), not as a function of index n. The physical meaning of n in Figures 2–6 is not immediately obvious, and readers cannot interpret the results without knowing the corresponding frequencies or periods.
7. It is very hard to interpreted Fig.2, Fig.3. If the goal is to relate coefficient variations to substorms or magnetic storms, the relevant geomagnetic indices (e.g., AL/AE for substorms or Dst for storms) should be plotted alongside the spectral coefficients on the same timescale. Without this, interpretation is very limited.
8. Fig.5 and Fig.6. The manuscript does not justify why phase is normalized by n, nor does it explain the near-linear trend seen in the figures. This raises concerns that the behavior might be an artifact of the analysis method rather than a physical signal.
9. A major issue is the absence of contextual background on the Ap/Kp indices. Ap is the linearized form of Kp and provides a widely used measure of magnetospheric convection strength (e.g., Thomsen 2004; Rowland & Wygant 1998; Wang et al. 2025). Large-scale magnetospheric convection is driven by dayside and nightside magnetic reconnection (e.g., Siscoe & Huang 1985; Cowley & Lockwood 1992; Dai et al. 2024; Zhu et al. 2024, 2025) and penetrates deep into the inner magnetosphere (e.g., Wygant et al. 1998; Dai et al. 2015; Thaller et al. 2015).
   
   These previous studies should be discussed to establish the physical context and significance of analyzing the Ap/Kp indices.

Thomsen, M. F. (2004). Why Kp is such a good measure of magnetospheric convection. Space Weather, 2(11), S11004. https://doi.org/10.1029/2004SW000089

Rowland, D. E., & Wygant, J. R. (1998). Dependence of the large‐scale, inner magnetospheric electric field on geomagnetic activity. Journal of Geophysical Research, 103(A7), 14959–14964. https://doi.org/10.1029/97JA03524

Wang, X., et al. (2025). Inner magnetospheric convection electric fields and corresponding geomagnetic indices during high-speed solar wind streams. Space Weather, 23, e2025SW004548. https://doi.org/10.1029/2025SW004548

Cowley, S. W. H., & Lockwood, M. (1992). Excitation and decay of solar-wind–driven flows in the magnetosphere–ionosphere system. Annales Geophysicae, 10(1–2), 103–115.

Dai, L., et al. (2015). Near-Earth injection of MeV electrons associated with intense dipolarization electric fields: Van Allen Probes observations. Geophysical Research Letters, 42(15), 6170–6179. https://doi.org/10.1002/2015GL064955

Dai, L., et al. (2024). Global-scale magnetosphere convection driven by dayside magnetic reconnection. Nature Communications, 15(1), 639. https://doi.org/10.1038/s41467-024-44992-y

Siscoe, G. L., & Huang, T. S. (1985). Polar cap inflation and deflation. Journal of Geophysical Research, 90(A1), 543–547. https://doi.org/10.1029/JA090iA01p00543

Thaller, et al. (2015). Van Allen Probes investigation of the large-scale duskward electric field and its role in ring current formation and plasmasphere erosion in the 1 June 2013 storm. Journal of Geophysical Research: Space Physics, 120(6), 4531–4543. https://doi.org/10.1002/2014JA020875

Wygant, J., et al. (1998). Experimental evidence on the role of the large spatial-scale electric field in creating the ring current. Journal of Geophysical Research, 103(A12), 29527–29544. https://doi.org/10.1029/98JA01436

Zhu, M., et al. (2025). Response of magnetospheric convection to the southward turning of the IMF in fast and slow solar wind streams. Journal of Geophysical Research: Space Physics, 130, e2025JA034529. https://doi.org/10.1029/2025JA034529

Zhu, M.,et al. (2024). The influence of ionospheric conductance on magnetospheric convection during southward IMF. Journal of Geophysical Research: Space Physics, 129(9), e2024JA032607. https://doi.org/10.1029/2024JA032607