High-concentration time–frequency analysis for multi-component nonstationary signals based on combined multi-window Gabor transform

PurposeThis study aims to reveal the essential characteristics of nonstationary signals and explore the high-concentration representation in the joint time–frequency (TF) plane.Design/methodology/approachIn this paper, the authors consider the effective TF analysis for nonstationary signals consisting of multiple components.FindingsTo make it, the authors propose the combined multi-window Gabor transform (CMGT) under the scheme of multi-window Gabor transform by introducing the combination operator. The authors establish the completeness utilizing the discrete piecewise Zak transform and provide the perfect-reconstruction conditions with respect to combined TF coefficients. The high-concentration is achieved by optimization. The authors establish the optimization function with considerations of TF concentration and computational complexity. Based on Bergman formulation, the iteration process is further analyzed to obtain the optimal solution.Originality/valueWith numerical experiments, it is verified that the proposed CMGT performs better in TF analysis for multi-component nonstationary signals.

A combined generalized Warblet transform and second order synchroextracting transform for analyzing nonstationary signals of rotating machinery

In recent years, considerable attention has been paid in time–frequency analysis (TFA) methods, which is an effective technology in processing the vibration signal of rotating machinery. However, TFA techniques are not sufficient to handle signals having a strong non-stationary characteristic. To overcome this drawback, taking short-time Fourier transform as a link, a TFA methods that using the generalized Warblet transform (GWT) in combination with the second order synchroextracting transform (SSET) is proposed in this study. Firstly, based on the GWT and SSET theories, this paper proposes a method combining the two TFA methods to improve the TFA concentration, named GWT–SSET. Secondly, the method is verified numerically with single-component and multi-component signals, respectively. Quantized indicators, Rényi entropy and mean relative error (MRE) are used to analyze the concentration of TFA and accuracy of instantly frequency (IF) estimation, respectively. Finally, the proposed method is applied to analyze nonstationary signals in variable speed. The numerical and experimental results illustrate the effectiveness of the GWT–SSET method.

New insights and best practices for the successful use of Empirical Mode Decomposition, Iterative Filtering and derived algorithms

Algorithms 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.

Empirical Wavelet Transform; Stationary and Nonstationary Signals

Signal decomposition into the frequency components is one of the oldest challenges in the digital signal processing. In early nineteenth century, Fourier transform (FT) showed that any applicable signal can be decomposed by unlimited sinusoids. However, the relationship between time and frequency is lost under using FT. According to many researches for appropriate time-frequency representation, in early twentieth century, wavelet transform (WT) was proposed Wavelet transform (WT) is a well-known method which developed in order to decompose a signal into frequency components. In contrast with original WT which is not adaptive according to the input signal, empirical wavelet transform (EWT) was proposed to overcome this problem. In this paper, the performance of WT and EWT in terms of signal decomposing into basic components are compared. For this purpose, a stationary signal include five sinusoids and ECG as biomedical and nonstationary signal are used. Due to being non-adaptive, WT may remove signal components but EWT because of being adaptive is appropriate. EWT can also extract the baseline of ECG signal easier than WT.

New insights and best practices for the succesful use of Empirical Mode Decomposition, Iterative Filtering and derived algorithms in the decomposition of nonlinear and nonstationary signals

<p>Nonlinear and nonstationary signals are ubiquitous in real life. Their time–frequency analysis and features extraction can help in solving open problems in many fields of research. Two decades ago, the Empirical Mode Decomposition (EMD) algorithm was introduced to tackle highly nonlinear and nonstationary signals. It consists of a local and adaptive data–driven method which relaxes several limitations of the standard Fourier transform and the wavelet Transform techniques, yielding an accurate time-frequency representation of a signal. Over the years, several variants of the EMD algorithm have been proposed to improve the original technique, such as the Ensemble Empirical Mode Decomposition (EEMD) and the Iterative Filtering (IF).<br><br></p><p>The versatility of these techniques has opened the door to their application in many applied fields, like geophysics, physics, medicine, and finance. Although the EMD– and IF–based techniques are more suitable than traditional methods for the analysis of nonlinear and nonstationary data, they could easily be misused if their known limitations, together with the assumptions they rely on, are not carefully considered. Here we call attention to some of the pitfalls encountered when implementing these techniques. Specifically, there are three critical factors that are often neglected: boundary effects; presence of spikes in the original signal; signals containing a high degree of stochasticity. We show how an inappropriate implementation of the EMD and IF methods could return an artefact–prone decomposition of the original signal. We conclude with best practice guidelines for researchers who intend to use these techniques for their signal analysis.</p>