**5. Conclusion**

In this paper, we investigated scaling and time-frequency properties of PM10 data in Hilbert frame. The performances obtained in the Hilbert space are compared with those achieved in the Fourier space. Firstly, with the Hilbert spectral analysis (HSA), a power law behavior is clearly observed on the frequency range 2*:*<sup>09</sup> <sup>10</sup><sup>7</sup> ⩽*f*⩽4*:*57 <sup>10</sup><sup>5</sup> Hz which corresponds to time scales 6*:*1 hours⩽*T*⩽55*:*4 days with an estimated spectral exponent *β<sup>h</sup>* = 1.02 0.10. As HSA methodology has a very local ability in both physical and spectral spaces, the influence of intermittent dust events with huge fluctuations is included in the amplitude-frequency space which is not the case in Fourier spectrum. Thereafter, PM10 data are illustrated in time-frequency representations with the Hilbert spectrum and spectrogram. The results provide the evidence that HS-based TFR performs better than SPEC. The higher resolution in TFR offers better fluctuations of PM10 energy for *f* < 1μ Hz. This is due to the fact that it is impossible to increase the TF resolution at the desired level in SPEC. The major asset of HS is that the time resolution can be as precise as the sampling period and the frequency resolution depends on the choice up to the Nyquist limit. In addition, contrary to SPEC which introduces a noticeable amount of cross-spectral energy terms during the use of window function with overlapping, HS is fully adaptive to datasets due to the decomposition of the signals. These first results suggest a substantial possibility to perform a profound dynamical analysis of PM10 concentrations for the Caribbean area in order to quantify the origin and the threshold pollution.
