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

Vittoria Bruni, Michela Tartaglione and Domenico Vitulano
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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
Michela Tartaglione: Department of Basic and Applied Sciences for Engineering, Sapienza University of Rome, via Antonio Scarpa 16, 00161 Rome, Italy
Domenico Vitulano: Department of Basic and Applied Sciences for Engineering, Sapienza University of Rome, via Antonio Scarpa 16, 00161 Rome, Italy

Mathematics, 2020, vol. 8, issue 12, 1-33

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.

Keywords: multicomponent signals; modes’ number; local number; interfering AM–FM signals; non-separable modes; overlapping components; signal complexity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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