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

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...

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Bibliographic Details
Published inMathematics (Basel) Vol. 8; no. 12; p. 2170
Main Authors Bruni, Vittoria, Tartaglione, Michela, Vitulano, Domenico
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.12.2020
Subjects
Acoustic noise
Acoustics
Complexity
Decomposition
Estimation
Gravitational waves
Interference
interfering AM–FM signals
local number
Methods
modes’ number
multicomponent signals
non-separable modes
overlapping components
Signal processing
Stationary processes
Time dependence
Waveforms
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math8122170