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Nonstationary signal decomposition for dummies [article]

Antonio Cicone
2017 arXiv   pre-print
How can I decompose a nonstationary signal? What are the advantages of using the most recent methods available in the literature versus using classical methods like (short time) Fourier transform or wavelet transform? This paper tries to address these and other questions providing the reader with a brief and self contained survey on what and how to tackle the decomposition of nonstationary signals.
arXiv:1710.04844v1 fatcat:ueygcwwstrcfvgn5swju7tsgpm

A note on the Joint Spectral Radius [article]

Antonio Cicone
2015 arXiv   pre-print
A brief summary on the properties of the so called Joint Spectral Radius
arXiv:1502.01506v1 fatcat:xmneo25uwnbqzlm2a4su5wpk5i

Linear dynamical systems on graphs [article]

Antonio Cicone and Nicola Guglielmi and Vladimir Protasov
2016 arXiv   pre-print
We consider linear dynamical systems with a structure of a multigraph. The vertices are associated to linear spaces and the edges correspond to linear maps between those spaces. We analyse the asymptotic growth of trajectories (associated to paths along the multigraph), the stability and the stabilizability problems. This generalizes the classical linear switching systems and their recent extensions to Markovian systems, to systems generated by regular languages, etc. We show that an arbitrary
more » ... ystem can be factorized into several irreducible systems on strongly connected multigraphs. For the latter systems, we prove the existence of invariant (Barabanov) multinorm and derive a method of its construction. The method works for a vast majority of systems and finds the joint spectral radius (Lyapunov exponent). Numerical examples are presented and applications to the study of fractals, attractors, and multistep methods for ODEs are discussed.
arXiv:1607.00415v1 fatcat:topuxj5gy5agxjb37jvplagfiu

Lifted polytope methods for stability analysis of switching systems [article]

Raphael M. Jungers, Nicola Guglielmi, Antonio Cicone
2012 arXiv   pre-print
We describe new methods for deciding the stability of switching systems. The methods build on two ideas previously appeared in the literature: the polytope norm iterative construction, and the lifting procedure. Moreover, the combination of these two ideas allows us to introduce a pruning algorithm which can importantly reduce the computational burden. We prove several appealing theoretical properties of our methods like a finiteness computational result which extends a known result for
more » ... sets of matrices, and provide numerical examples of their good behaviour.
arXiv:1207.5123v1 fatcat:w6f7kl7t7nh4xfd7bzkjtvtub4

Convergence analysis of Adaptive Locally Iterative Filtering and SIFT method [article]

Antonio Cicone, Hau-Tieng Wu
2020 arXiv   pre-print
ACKNOWLEDGEMENTS Antonio Cicone is a member of the Italian "Gruppo Nazionale di Calcolo Scientifico" (GNCS).  ... 
arXiv:2005.04578v1 fatcat:ahy4xtehdffx5drpu7nrpg7uc4

Conjectures on spectral properties of ALIF algorithm [article]

Giovanni Barbarino, Antonio Cicone
2020 arXiv   pre-print
Acknowledgements Antonio Cicone is a member of the Italian "Gruppo Nazionale di Calcolo Scientifico" (GNCS) of the Istituto Nazionale di Alta Matematica "Francesco Severi" (INdAM).  ... 
arXiv:2009.00582v1 fatcat:xfxohcbp3vaqpnuxy5t2raurbu

Iterative Filtering as a direct method for the decomposition of non-stationary signals [article]

Antonio Cicone
2018 arXiv   pre-print
The Iterative Filtering method is a technique developed recently for the decomposition and analysis of non-stationary and non-linear signals. In this work we propose two alternative formulations of the original algorithm which allows to transform the Iterative Filtering method into a direct technique, making the algorithm closer to an online algorithm. We present a few numerical examples to show the effectiveness of the proposed approaches.
arXiv:1811.03536v1 fatcat:vsghi3jozra35gnheygfiaz6em

Multidimensional Iterative Filtering method for the decomposition of high-dimensional non-stationary signals [article]

Antonio Cicone, Haomin Zhou
2015 arXiv   pre-print
Cicone, J. Liu, and H. Zhou, Adaptive local iterative filtering for signal decomposition and instantaneous frequency analysis, arXiv:1411.6051, 2014.  ... 
arXiv:1507.07173v1 fatcat:pzyxm3ei6rgfjh7nfqhhm75m2y

A sub-optimal solution for optimal control of linear systems with unmeasurable switching delays [article]

Antonio Cicone, Alessandro D'Innocenzo, Nicola Guglielmi, Linda Laglia
2015 arXiv   pre-print
We consider the optimal control design problem for discrete-time LTI systems with state feedback, when the actuation signal is subject to unmeasurable switching propagation delays, due to e.g. the routing in a multi-hop communication network and/or jitter. In particular, we set up a constrained optimization problem where the cost function is the worst-case L_2 norm for all admissible switching delays. We first show how to model these systems as pure switching linear systems, and as main
more » ... tion of the paper we provide an algorithm to compute a sub-optimal solution.
arXiv:1509.03351v1 fatcat:mgrwxepeq5bwbjn5v4ratql7cq

Google PageRanking problem: The model and the analysis

Antonio Cicone, Stefano Serra-Capizzano
2010 Journal of Computational and Applied Mathematics  
MSC: 65F10 65F15 65Y20 15A18 15A21 15A51 Keywords: Google matrix PageRanking Surfing model Rank-one perturbation Brauer's Theorem Jordan canonical form Principle of biorthogonality Extrapolation formulae a b s t r a c t The spectral and Jordan structures of the Web hyperlink matrix G(c) = cG+(1−c)ev T have been analyzed when G is the basic (stochastic) Google matrix, c is a real parameter such that 0 < c < 1, v is a nonnegative probability vector, and e is the all-ones vector. Typical studies
more » ... ve relied heavily on special properties of nonnegative, positive, and stochastic matrices. There is a unique nonnegative vector y(c) such that y(c) T G(c) = y(c) T and y(c) T e = 1. This PageRank vector y(c) can be computed effectively by the power method. We consider a square complex matrix A and nonzero complex vectors x and v such that Ax = λx and v * x = 1. We use standard matrix analytic tools to determine the eigenvalues, the Jordan blocks, and a distinguished left λ-eigenvector of A(c) = cA + (1 − c)λxv * as a function of a complex variable c. If λ is a semisimple eigenvalue of A, there is a uniquely determined projection N such that lim c→1 y(c) = Nv for all v; this limit may fail to exist for some v if λ is not semisimple. As a special case of our results, we obtain a complex analog of PageRank for the Web hyperlink matrix G(c) with a complex parameter c. We study regularity, limits, expansions, and conditioning of y(c) and we propose algorithms (e.g., complex extrapolation, power method on a modified matrix etc.) that may provide an efficient way to compute PageRank also with c close or equal to 1. An interpretation of the limit vector Nv and a related critical discussion on the model, on its adherence to reality, and possible ways for its improvement, represent the contribution of the paper on modeling issues.
doi:10.1016/ fatcat:op62lwbnxjcztamc5z4yx2uony

Stabilization and Variations to the Adaptive Local Iterative Filtering Algorithm: the Fast Resampled Iterative Filtering Method [article]

Giovanni Barbarino, Antonio Cicone
2021 arXiv   pre-print
Non-stationary signals are ubiquitous in real life. Many techniques have been proposed in the last decades which allow decomposing multi-component signals into simple oscillatory mono-components, like the groundbreaking Empirical Mode Decomposition technique and the Iterative Filtering method. When a signal contains mono-components that have rapid varying instantaneous frequencies, we can think, for instance, to chirps or whistles, it becomes particularly hard for most techniques to properly
more » ... tor out these components. The Adaptive Local Iterative Filtering technique has recently gained interest in many applied fields of research for being able to deal with non-stationary signals presenting amplitude and frequency modulation. In this work, we address the open question of how to guarantee a priori convergence of this technique, and propose two new algorithms. The first method, called Stable Adaptive Local Iterative Filtering, is a stabilized version of the Adaptive Local Iterative Filtering that we prove to be always convergent. The stability, however, comes at the cost of higher complexity in the calculations. The second technique, called Resampled Iterative Filtering, is a new generalization of the Iterative Filtering method. We prove that Resampled Iterative Filtering is guaranteed to converge a priori for any kind of signal. Furthermore, in the discrete setting, by leveraging on the mathematical properties of the matrices involved, we show that its calculations can be accelerated drastically. Finally, we present some artificial and real-life examples to show the powerfulness and performance of the proposed methods.
arXiv:2111.02764v1 fatcat:wdc6cwgyxzddfhru5jaolbf7vu

Time-frequency representation of nonstationary signals: the IMFogram [article]

Philippe Barbe, Antonio Cicone, Wing Suet Li, Haomin Zhou
2021 arXiv   pre-print
Iterative filtering methods were introduced around 2010 to improve definitions and measurements of structural features in signal processing. Like many applied techniques, they present considerable challenges for mathematicians to theorize their effectiveness and limitations in commercial and scientific usages. In this paper we recast iterative filtering methods in a mathematical abstraction more conducive to their understanding and applications. We also introduce a new visualization of
more » ... ous local frequencies and amplitudes. By combining a theoretical and practical exposition, we hope to stimulate efforts to understand better these methods. Our approach acknowledges the influence of Ciprian Foias, who was passionate about pure, applied, and applications of mathematics.
arXiv:2011.14209v2 fatcat:rotvgmft7veazcd4rizlkdjhoq

Spacetime Hall-MHD turbulence at sub-ion scales: structures or waves? [article]

Emanuele Papini and Antonio Cicone and Luca Franci and Mirko Piersanti and Simone Landi and Petr Hellinger and Andrea Verdini
2021 arXiv   pre-print
Here we employ a Fokker-Plank filter Cicone et al. (2016) . This approach has been recently accelerated in what is known as Fast Iterative Filtering (FIF) Cicone (2020). B.  ...  (Lin et al. 2009; Cicone et al. 2016 ) is a technique for the analysis of nonlinear nonstationary signals.  ... 
arXiv:2107.03843v1 fatcat:4pi4m4w7hvgutmjpn6booeyd2u

Adaptive local iterative filtering for signal decomposition and instantaneous frequency analysis

Antonio Cicone, Jingfang Liu, Haomin Zhou
2016 Applied and Computational Harmonic Analysis  
Antonio Cicone acknowledges support by National Group for Scientific Computation (GNCS -INdAM) 'Progetto giovani ricercatori 2014', and by Istituto Nazionale di Alta Matematica (INdAM) 'INdAM Fellowships  ... 
doi:10.1016/j.acha.2016.03.001 fatcat:7l4eesvthzav3m2f6zgvvovyne

Lifted Polytope Methods for Computing the Joint Spectral Radius

Raphaël M. Jungers, Antonio Cicone, Nicola Guglielmi
2014 SIAM Journal on Matrix Analysis and Applications  
We present new methods for computing the joint spectral radius of finite sets of matrices. The methods build on two ideas that previously appeared in the literature: the polytope norm iterative construction, and the lifting procedure. Moreover, the combination of these two ideas allows us to introduce a pruning algorithm which can importantly reduce the computational burden. We prove several theoretical properties of our methods, such as finiteness computational result which extends a known
more » ... lt for unlifted sets of matrices, and provide numerical examples of their good behavior.
doi:10.1137/130907811 fatcat:wvevq4qz6bbvtliatqxpyz5d5e
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