Sity of Montenegro, 81000 Podgorica, Montenegro; [email protected] (I.S.); [email protected] (M.D.) Faculty of Engineering, University of Rijeka, 51000 Rijeka, Croatia Gipsa-Lab, UniversitGrenoble Alpes, 38400 Grenoble, France; [email protected] Faculty of Computer Science and Engineering, University Ss. Cyril and Methodius, 1000 Skopje, North Macedonia; [email protected] Correspondence: [email protected] (M.B.); [email protected] (J.L.)Citation: Brajovi, M.; Stankovi, I.; c c Lerga, J.; Ioana, C.; Zdravevski, E.; Dakovi, M. Multivariate c Decomposition of Acoustic signals in Dispersive Channels. Mathematics 2021, 9, 2796. https://doi.org/ 10.3390/math9212796 Academic Editor: Jo Nuno Prata Received: 23 September 2021 Accepted: 28 October 2021 Published: four NovemberAbstract: We present a signal decomposition process, which separates modes into person components while preserving their integrity, in effort to tackle the challenges related to the Tenidap MedChemExpress characterization of modes in an acoustic dispersive environment. With this strategy, every single mode is usually analyzed and processed individually, which carries opportunities for new insights into their characterization possibilities. The proposed methodology is determined by the eigenanalysis with the autocorrelation matrix of the analyzed signal. When eigenvectors of this matrix are properly linearly combined, each signal element could be separately reconstructed. A proper linear mixture is determined according to 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 outcomes support the theory and indicate the applicability of the proposed methodology in the decomposition of acoustic signals in dispersive channels. Keywords and phrases: concentration measures; dispersive channels; multivariate signals; non-stationary signals; multicomponent signal decomposition1. Introduction Signals with time-varying spectral content, known as non-stationary signals, are analyzed applying time-frequency signal (TF) signal evaluation [17]. Some generally utilised TF representations involve short-time Fourier transform (STFT) [1,3], pseudo-Wigner distribution (WD) [1,9,12], and S-method (SM) [3]. Time-scale, multi-resolution analysis working with the wavelet transform is an more strategy to characterize non-stationary signal behavior [4]. Different representations are primarily applied in the instantaneous frequency (IF) estimation and related applications [85], given that they concentrate the energy of a signal element at and around the respective instantaneous frequency. Concentration measures give a quantitative description with the signal concentration inside the provided representation domain [18], and may be utilized to assess the region with the time-frequency plane covered by a signal element. In order to characterize multicomponent signals, it is actually very prevalent to perform signal decomposition, which assumes that each and every person element is extracted for MCC950 References separate evaluation, like for the IF estimation. Decomposition strategies for multicomponent signals are really efficient if components do not overlap in the time-frequency plane [196]. The technique initially presented in [26] can be used to totally extract every component by using an intrinsic relation amongst the PWD and the SM. Inside the evaluation of multicomponent signals, it’s, nevertheless, prevalent that numerous components partially overla.
