On the decomposition of multichannel nonstationary multicomponent signals

Stanković, Ljubiša; Brajović, Miloš; Daković, Miloš; Mandic, Danilo P.

doi:10.1016/j.sigpro.2019.107261

Cited by 26 publications

(22 citation statements)

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“…These approaches include both Hilbert vibrational decomposition and Kalman filter-based approaches [27], [33]- [35] along with sparsity-promoting decompositions [24], [25]. Wigner distributionbased approaches show great promise for decomposing multicomponent signals with modes that have crossover between frequencies [36].…”

Section: Introductionmentioning

confidence: 99%

Extraction of Instantaneous Frequencies and Amplitudes in Nonstationary Time-Series Data

et al. 2021

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Time-series analysis is critical for a diversity of applications in science and engineering. By leveraging the strengths of modern gradient descent algorithms, the Fourier transform, multi-resolution analysis, and Bayesian spectral analysis, we propose a data-driven approach to time-frequency analysis that circumvents many of the shortcomings of classic approaches, including the extraction of nonstationary signals with discontinuities in their behavior. The method introduced is equivalent to a nonstationary Fourier mode decomposition (NFMD) for nonstationary and nonlinear temporal signals, allowing for the accurate identification of instantaneous frequencies and their amplitudes. The method is demonstrated on a diversity of time-series data, including on data from cantilever-based electrostatic force microscopy to quantify the time-dependent evolution of charging dynamics at the nanoscale.

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Section: Introductionmentioning

confidence: 99%

Extraction of Instantaneous Frequencies and Amplitudes in Nonstationary Time-Series Data

et al. 2021

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“…In the multivariate (multichannel) framework, it is assumed that the signals are acquired using multiple sensors, [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44]. The sensors modify component amplitudes and phases.…”

Section: Introductionmentioning

confidence: 99%

“…It was previously shown that WD-based decomposition is possible if signals are available in the multivariate form [28][29][30]. Moreover, the decomposition can be performed by directly engaging the eigenanalysis of the auto-correlation matrix, calculated for signals in the multivariate form [31][32][33][34]. It should also be noted that the problem of multicomponent signal decomposition has some similarities with the blind source separation [45][46][47][48].…”

Section: Introductionmentioning

confidence: 99%

“…We aim at solving this notoriously difficult practical problem by exploiting the interdependencies of multiply acquired signals: such signals can be considered as multivariate and are subject to slight phase changes across various channels, occurring due to different sensing positions and due to various physical phenomena, such as water ripples, uneven seabed, and changes in the seabed substrate. As each eigenvector of the autocorrelation matrix of the input signal represents a linear combination of the signal components [31,33], slight phase changes across the various channels are actually favorable for forming an undetermined set of linearly independent equations relating the eigenvectors and the components. Moreover, we have previously shown that each component is a linear combination of several eigenvectors corresponding to the largest eigenvalues, with unknown weights [31] (the number of these eigenvalues is equal to the number of signal components).…”

Section: Introductionmentioning

confidence: 99%

“…As each eigenvector of the autocorrelation matrix of the input signal represents a linear combination of the signal components [31,33], slight phase changes across the various channels are actually favorable for forming an undetermined set of linearly independent equations relating the eigenvectors and the components. Moreover, we have previously shown that each component is a linear combination of several eigenvectors corresponding to the largest eigenvalues, with unknown weights [31] (the number of these eigenvalues is equal to the number of signal components). Among infinitely many possible combinations of eigenvectors, the aim is to find the weights producing the most concentrated combination, as each individual signal compo-nent (mode) is more concentrated than any linear combination of components, as discussed in detail in [31].…”

Section: Introductionmentioning

confidence: 99%

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Multivariate Decomposition of Acoustic Signals in Dispersive Channels

et al. 2021

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We present a signal decomposition procedure, which separates modes into individual components while preserving their integrity, in effort to tackle the challenges related to the characterization of modes in an acoustic dispersive environment. With this approach, each mode can be analyzed and processed individually, which carries opportunities for new insights into their characterization possibilities. The proposed methodology is based on the eigenanalysis of the autocorrelation matrix of the analyzed signal. When eigenvectors of this matrix are properly linearly combined, each signal component can be separately reconstructed. A proper linear combination is determined based on the minimization of concentration measures calculated exploiting time-frequency representations. In this paper, we engage a steepest-descent-like algorithm for the minimization process. Numerical results support the theory and indicate the applicability of the proposed methodology in the decomposition of acoustic signals in dispersive channels.

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Successive multivariate variational mode decomposition

Liu

2022

Multidim Syst Sign Process

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On the decomposition of multichannel nonstationary multicomponent signals

Cited by 26 publications

References 50 publications

Extraction of Instantaneous Frequencies and Amplitudes in Nonstationary Time-Series Data

Extraction of Instantaneous Frequencies and Amplitudes in Nonstationary Time-Series Data

Multivariate Decomposition of Acoustic Signals in Dispersive Channels

Successive multivariate variational mode decomposition

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