1,721,007 research outputs found
Stabilization and variations to the adaptive local iterative filtering algorithm: the fast resampled iterative filtering method
No full textNon-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 like chirps or whistles, it becomes particularly hard for most techniques to properly factor 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, we show that in the discrete setting its calculations can be drastically accelerated by leveraging on the mathematical properties of the matrices involved. Finally, we present some artificial and real-life examples to show the power and performance of the proposed methods.Kindly check and confirm that the Article note is correctly identified
Study of boundary conditions in the Iterative Filtering method for the decomposition of nonstationary signals
No full textNonstationary and non-linear signals are ubiquitous in real life. Their decomposition and analysis is an important research topic of signal processing. Recently a new technique, called Iterative Filtering, has been developed with the goal of decomposing such signals into simple oscillatory components. Several papers have been devoted to the investigation of this technique from a mathematical point of view. All these works start with the assumption that each compactly supported signal is extended periodically outside the boundaries. In this work, we tackle the problem of studying the influence of different boundary conditions on the decompositions produced by the Iterative Filtering method. In particular, the choice of boundary conditions gives rise to different types of structured matrices. Thus, we describe their spectral properties and the convergence properties of Iterative Filtering algorithm when such matrices are involved. Numerical results on artificial and real life signals provide interesting insight on important aspects such as accuracy and error propagation of the proposed technique and pave the way for further promising developments
Numerical analysis for iterative filtering with new efficient implementations based on FFT
No full textThe development of methods able to extract hidden features from non-stationary and non-linear signals in a fast and reliable way is of high importance in many research fields. In this work we tackle the problem of further analyzing the convergence of the Iterative Filtering method both in a continuous and a discrete setting in order to provide a comprehensive analysis of its behavior. Based on these results we provide a new efficient implementation of Iterative Filtering algorithm, called Fast Iterative Filtering, which reduces the original iterative algorithm computational complexity by utilizing, in a nontrivial way, Fast Fourier Transform in the computations
Lifted Polytope Methods for Computing the Joint Spectral Radius.
No full textWe 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 like a finiteness computational result which extends a known result for unlifted sets of matrices, and provide numerical examples of their good behaviour
One or two frequencies? The Iterative Filtering answers
Full text linkThe Iterative Filtering method is a technique aimed at the decomposition of non-stationary and non-linear signals into simple oscillatory components. This method, proposed a decade ago as an alternative technique to the Empirical Mode Decomposition, has been used extensively in many applied fields of research and studied, from a mathematical point of view, in several papers published in the last few years. However, even if its convergence and stability are now established both in the continuous and discrete setting, it is still an open problem to understand up to what extent this approach can separate two close-by frequencies contained in a signal. In this paper, first we recall previously discovered theoretical results about Iterative Filtering. Afterward, we prove a few new theorems regarding the ability of this method in separating two nearby frequencies both in the case of continuously and discrete sampled signals. Among them, we prove a theorem which allows to construct filters which captures, up to machine precision, a specific frequency. We run numerical tests to confirm our findings and to compare the performance of Iterative Filtering with the one of Empirical Mode Decomposition and Synchrosqueezing methods. All the results presented confirm the ability of the technique under investigation in addressing the fundamental “one or two frequencies” question
Hyperspectral chemical plume detection algorithms based on multidimensional iterative fltering decomposition
No full textChemicals released in the air can be extremely dangerous for human beings and the environment. Hyperspectral images can be used to identify chemical plumes, however the task can be extremely challenging. Assuming we know a priori that some chemical plume, with a known frequency spectrum, has been photographed using a hyperspectral sensor, we can use standard techniques such as the so-called matched filter or adaptive cosine estimator, plus a properly chosen threshold value, to identify the position of the chemical plume. However, due to noise and inadequate sensing, the accurate identification of chemical pixels is not easy even in this apparently simple situation. In this paper, we present a post-processing tool that, in a completely adaptive and data-driven fashion, allows us to improve the performance of any classification methods in identifying the boundaries of a plume. This is done using the multidimensional iterative filtering (MIF) algorithm (Cicone et al. 2014 (http://arxiv.org/abs/1411.6051); Cicone & Zhou 2015 (http://arxiv.org/abs/1507.07173)), which is a non-stationary signal decomposition method like the pioneering empirical mode decomposition method (Huang et al. 1998 Proc. R. Soc. Lond. A 454, 903. (doi:10.1098/rspa.1998.0193)). Moreover, based on the MIF technique, we propose also a pre-processing method that allows us to decorrelate and mean-centre a hyperspectral dataset. The cosine similarity measure, which often fails in practice, appears to become a successful and outperforming classifier when equipped with such a pre-processing method. We show some examples of the proposed methods when applied to real-life problems
Multidimensional Iterative Filtering Method for the Decomposition of High–Dimensional Non–Stationary Signals
No full textAbstractIterative Filtering (IF) is an alternative technique to the Empirical Mode Decomposition (EMD) algorithm for the decomposition of non–stationary and non–linear signals. Recently in [3] IF has been proved to be convergent for anyL2signal and its stability has been also demonstrated through examples. Furthermore in [3] the so called Fokker–Planck (FP) filters have been introduced. They are smooth at every point and have compact supports. Based on those results, in this paper we introduce the Multidimensional Iterative Filtering (MIF) technique for the decomposition and time–frequency analysis of non–stationary high–dimensional signals. We present the extension of FP filters to higher dimensions. We prove convergence results under general sufficient conditions on the filter shape. Finally we illustrate the promising performance of MIF algorithm, equipped with high–dimensional FP filters, when applied to the decomposition of two dimensional signals.</jats:p
New insights and best practices for the successful use of Empirical Mode Decomposition, Iterative Filtering and derived algorithms
Full text linkAlgorithms based on Empirical Mode Decomposition (EMD) and Iterative Filtering (IF) are largely implemented for representing a signal as superposition of simpler well-behaved components called Intrinsic Mode Functions (IMFs). Although they are more suitable than traditional methods for the analysis of nonlinear and nonstationary signals, they could be easily misused if their known limitations, together with the assumptions they rely on, are not carefully considered. In this work, we examine the main pitfalls and provide caveats for the proper use of the EMD- and IF-based algorithms. Specifically, we address the problems related to boundary errors, to the presence of spikes or jumps in the signal and to the decomposition of highly-stochastic signals. The consequences of an improper usage of these techniques are discussed and clarified also by analysing real data and performing numerical simulations. Finally, we provide the reader with the best practices to maximize the quality and meaningfulness of the decomposition produced by these techniques. In particular, a technique for the extension of signal to reduce the boundary effects is proposed; a careful handling of spikes and jumps in the signal is suggested; the concept of multi-scale statistical analysis is presented to treat highly stochastic signals
New theoretical insights in the decomposition and time-frequency representation of nonstationary signals: The IMFogram algorithm
No full textThe analysis of the time–frequency content of a signal is a classical problem in signal processing, with a broad number of applications in real life. Many different approaches have been developed over the decades, which provide alternative time–frequency representations of a signal each with its advantages and limitations. In this work, following the success of nonlinear methods for the decomposition of signals into intrinsic mode functions (IMFs), we first provide more theoretical insights into the so–called Iterative Filtering decomposition algorithm, proving an energy conservation result for the derived decompositions. Furthermore, we present a new time–frequency representation method based on the IMF decomposition of a signal, which is called IMFogram. We prove theoretical results regarding this method, including its convergence to the spectrogram representation for a certain class of signals, and we present a few examples of applications, comparing results with some of the most well-known approaches available in the literature
Adaptive local iterative filtering for signal decomposition and instantaneous frequency analysis
No full textTime–frequency analysis for non-linear and non-stationary signals is extraordinarily challenging. To capture features in these signals, it is necessary for the analysis methods to be local, adaptive and stable. In recent years, decomposition based analysis methods, such as the empirical mode decomposition (EMD) technique pioneered by Huang et al., were developed by different research groups. These methods decompose a signal into a finite number of components on which the time–frequency analysis can be applied more effectively. In this paper we consider the Iterative Filtering (IF) approach as an alternative to EMD. We provide sufficient conditions on the filters that ensure the convergence of IF applied to any L2 signal. Then we propose a new technique, the Adaptive Local Iterative Filtering (ALIF) method, which uses the IF strategy together with an adaptive and data driven filter length selection to achieve the decomposition. Furthermore we design smooth filters with compact support from solutions of Fokker–Planck equations (FP filters) that can be used within both IF and ALIF methods. These filters fulfill the derived sufficient conditions for the convergence of the IF algorithm. Numerical examples are given to demonstrate the performance and stability of IF and ALIF techniques with FP filters. In addition, in order to have a complete and truly local analysis toolbox for non-linear and non-stationary signals, we propose new definitions for the instantaneous frequency and phase which depend exclusively on local properties of a signal
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