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A Signal Complexity-Based Approach for AM–FM Signal Modes Counting

Author

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  • Vittoria Bruni

    (Department of Basic and Applied Sciences for Engineering, Sapienza University of Rome, via Antonio Scarpa 16, 00161 Rome, Italy
    Institute for the Applications of Calculus, National Research Council, via dei Taurini 19, 00185 Rome, Italy
    These authors contributed equally to this work.)

  • Michela Tartaglione

    (Department of Basic and Applied Sciences for Engineering, Sapienza University of Rome, via Antonio Scarpa 16, 00161 Rome, Italy
    These authors contributed equally to this work.)

  • Domenico Vitulano

    (Department of Basic and Applied Sciences for Engineering, Sapienza University of Rome, via Antonio Scarpa 16, 00161 Rome, Italy
    Institute for the Applications of Calculus, National Research Council, via dei Taurini 19, 00185 Rome, Italy
    These authors contributed equally to this work.)

Abstract

Frequency modulated signals appear in many applied disciplines, including geology, communication, biology and acoustics. They are naturally multicomponent, i.e., they consist of multiple waveforms, with specific time-dependent frequency (instantaneous frequency). In most practical applications, the number of modes—which is unknown—is needed for correctly analyzing a signal; for instance for separating each individual component and for estimating its instantaneous frequency. Detecting the number of components is a challenging problem, especially in the case of interfering modes. The Rényi Entropy-based approach has proven to be suitable for signal modes counting, but it is limited to well separated components. This paper addresses this issue by introducing a new notion of signal complexity. Specifically, the spectrogram of a multicomponent signal is seen as a non-stationary process where interference alternates with non-interference. Complexity concerning the transition between consecutive spectrogram sections is evaluated by means of a modified Run Length Encoding. Based on a spectrogram time-frequency evolution law, complexity variations are studied for accurately estimating the number of components. The presented method is suitable for multicomponent signals with non-separable modes, as well as time-varying amplitudes, showing robustness to noise.

Suggested Citation

  • Vittoria Bruni & Michela Tartaglione & Domenico Vitulano, 2020. "A Signal Complexity-Based Approach for AM–FM Signal Modes Counting," Mathematics, MDPI, vol. 8(12), pages 1-33, December.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:12:p:2170-:d:457160
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    References listed on IDEAS

    as
    1. Bruni, Vittoria & Tartaglione, Michela & Vitulano, Domenico, 2020. "An iterative approach for spectrogram reassignment of frequency modulated multicomponent signals," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 176(C), pages 96-119.
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    5. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 1.
    6. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 4.
    7. Peter D. Grünwald, 2007. "The Minimum Description Length Principle," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262072815, April.
    8. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 3.
    9. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 2.
    10. Vittoria Bruni & Michela Tartaglione & Domenico Vitulano, 2019. "A Fast and Robust Spectrogram Reassignment Method," Mathematics, MDPI, vol. 7(4), pages 1-20, April.
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