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Analyzing spectral peak distribution of coupled signals using Fourier transform theory

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Abstract

Higher-order cumulants have a greater ability to mechanically reduce the impact of Gaussian noise, whether it is white or colored. As a consequence, higher-order statistical cumulants are gaining more attention in signal processing. Bispectral peaks arise due to phase coupling, and the distribution of these spectral peaks follows a special law. To analyze the distribution of these spectral peaks, this study adopted the method of harmonic decomposition. Based on Fourier transform theory, the harmonic frequencies where phase coupling occurs are calculated. By conducting a third-order cumulant analysis of the harmonics, the position of the spectral peak can be obtained. Then, using trigonometric functions, the methods of amplifying, reducing, and increasing the spectral peaks were discussed and verified through experiments. Since the collected vibration signal can be regarded as a function that satisfies the Fourier transform conditions, the above theoretical analysis can be applied to the analysis of various actual collected signals. Currently, bispectrum is generally used in actual applications to distinguish signal states by showing different peaks of the signal in different states. However, this application often encounters situations where the bispectrum in different states is difficult to distinguish. The experimental results showed that the methods of amplifying, reducing, and increasing the spectral peaks were helpful in strengthening the practical application effects of the bispectrum.

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Acknowledgements

This paper was supported by the Research Start-up Fund for high-level talents of FuZhou University of International Studies and Trade (FWKQJ202006) and 2022 Guiding Project of Fujian Science and Technology Department (2022H0026).

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Authors and Affiliations

  1. School of Big Data, Fuzhou University of International Studies and Trade, Fuzhou, China

    Wu Wenbing & Yuan Xiaojian

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  1. Wu Wenbing
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  2. Yuan Xiaojian
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Contributions

WW agreed on the content of the study and methodology. WW and YX collected all the data for analysis and completed the analysis based on agreed steps. The results and conclusions were discussed and written together. The author read and approved the final manuscript.

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Correspondence to Yuan Xiaojian.

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Wenbing, W., Xiaojian, Y. Analyzing spectral peak distribution of coupled signals using Fourier transform theory. Indian J Phys 97, 4509–4519 (2023). https://doi.org/10.1007/s12648-023-02728-6

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