Sity of Montenegro, 81000 Podgorica, Montenegro; [email protected] (I.S.); [email protected] (M.D.) Faculty of Engineering, University of

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 system 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/ ten.3390/math9212796 Academic Editor: Jo Nuno Prata Received: 23 September 2021 Accepted: 28 October 2021 Published: four NovemberAbstract: We present a signal decomposition procedure, which separates modes into person elements even though preserving their integrity, in work to tackle the challenges related to the characterization of modes in an acoustic dispersive environment. With this method, every single mode may be analyzed and processed individually, which carries opportunities for new insights into their characterization possibilities. The proposed methodology is according to the eigenanalysis on the autocorrelation matrix on the analyzed signal. When eigenvectors of this matrix are effectively linearly combined, every single signal component can be separately reconstructed. A suitable linear combination is determined according to the minimization of concentration measures calculated exploiting time-frequency representations. Within this paper, we engage a steepest-descent-like algorithm for the minimization procedure. Numerical outcomes help the theory and indicate the applicability with the proposed methodology within the decomposition of acoustic signals in dispersive channels. Search Seclidemstat Seclidemstat 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 employing time-frequency signal (TF) signal evaluation [17]. Some commonly 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 evaluation using the wavelet transform is an more method to characterize non-stationary signal behavior [4]. A variety of representations are mainly applied inside the instantaneous frequency (IF) estimation and associated applications [85], considering the fact that they concentrate the power of a signal element at and about the respective instantaneous frequency. Concentration measures deliver a quantitative description of the signal concentration within the provided representation domain [18], and may be made use of to assess the area on the time-frequency plane covered by a signal component. So that you can characterize multicomponent signals, it is very prevalent to perform signal decomposition, which assumes that every individual element is extracted for separate evaluation, for example for the IF estimation. Decomposition tactics for multicomponent signals are rather efficient if elements don’t overlap inside the time-frequency plane [196]. The approach originally presented in [26] is often utilised to fully extract every element by utilizing an intrinsic relation Decanoyl-L-carnitine site between the PWD and the SM. Inside the evaluation of multicomponent signals, it is actually, on the other hand, widespread that several components partially overla.