Multiple-view time–frequency distribution based on the empirical mode decomposition

Stevenson, Nathan J.; Mesbah, Mostefa; Boashash, Boualem

doi:10.1049/iet-spr.2009.0084

Cited by 14 publications

(7 citation statements)

References 16 publications

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“…The presented results indicate that the MBD, being an example of Separable kernel TFDs, is a good choice of a TFD when the proposed method is applied in practical situations [4]. These results show that the proposed algorithm can be useful in many applications that require component count and component separation; and, it can be a preferred alternative to other methods such as the Empirical Mode Decomposition [15]. …”

Section: Resultsmentioning

confidence: 82%

Estimating the number of components of a multicomponent nonstationary signal using the short-term time-frequency Rényi entropy

Sucic

Saulig

Boashash

2011

EURASIP J. Adv. Signal Process.

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The time-frequency Rényi entropy provides a measure of complexity of a nonstationary multicomponent signal in the time-frequency plane. When the complexity of a signal corresponds to the number of its components, then this information is measured as the Rényi entropy of the time-frequency distribution (TFD) of the signal. This article presents a solution to the problem of detecting the number of components that are present in short-time interval of the signal TFD, using the short-term Rényi entropy. The method is automatic and it does not require a prior information about the signal. The algorithm is applied on both synthetic and real data, using a quadratic separable kernel TFD. The results confirm that the short-term Rényi entropy can be an effective tool for estimating the local number of components present in the signal. The key aspect of selecting a suitable TFD is also discussed.1 Time-frequency distributions and instantaneous frequency estimation When dealing with highly complex signals, such as multicomponent nonstationary signals, several pieces of information are required for their characterization. Classical approaches of the time signal representation, x(t), and the frequency representation, X(f), are not best tools for obtaining those information when dealing with multicomponent signals. These representations define the signal duration, the changes of amplitude in time, as well as the entire signal frequency content. Timefrequency representations (TFRs), or TFDs, are two variable functions, C s (t, f), defined over the two-dimensional (t, f) space [4]. Such a joint TFR shows how the frequency content of a signal changes in time.One of the most popular TFDs, introduced by Wigner and extended by Ville to analytic signals [4], has been treated as a pseudo probability density function in [2,3,5] to which the Rényi entropy has been applied as a measure of signal complexity. The intuitive idea of the Wigner-Ville distribution (WVD) was to obtain a kind of instantaneous signal spectrum by performing the Fourier transform of a function related to the signal, called the kernel function K s (t, τ). The WVD of a signal s(t), denoted as W s (t, f), represents a monocomponent frequency modulated (FM) signal as a knife-edge ridge in the (t, f) plane, whose crest is the IF of the signal [4].Let s(t) be an analytic FM signal of the form [4] s(t) = a(t)e jφ(t) ,where a(t) is the instantaneous signal amplitude (assumed to be equal to one in the rest of the article), and the signal IF is defined as the time derivative of its instantaneous phase j(t) [4] f i (t) = φ (t) 2π .

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Section: Resultsmentioning

confidence: 82%

Estimating the number of components of a multicomponent nonstationary signal using the short-term time-frequency Rényi entropy

Sucic

Saulig

Boashash

2011

EURASIP J. Adv. Signal Process.

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“…The Johansen test is a procedure for testing the cointegrating relationships of several integrated processes of order zero or one [44]. Since the test evaluates more than one cointegrating relationship within the time series, it is applicable for multivariate signals such as multi-channel EEG.…”

Section: Appendix a Empirical Mode Decomposition (Emd)mentioning

confidence: 99%

“…The technique is an adaptive method which breaks down a nonstationary and nonlinear signal into its intrinsic mode functions (IMFs) [43]. Each IMF is a monocomponent signal which generates no interference in a QTFD [44]. In other words, the IMFs represent simple oscillatory modes with time-varying amplitude and frequency:…”

Section: Monocomponent Signals Vs Multicomponent Signals: Necessity mentioning

confidence: 99%

A time–frequency based approach for generalized phase synchrony assessment in nonstationary multivariate signals

Omidvarnia

Azemi

Colditz

et al. 2013

Digital Signal Processing

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This paper proposes a new approach to estimate the phase synchrony among nonstationary multivariate signals using the linear relationships between their instantaneous frequency (IF) laws. For cases where nonstationary signals are multi-component, a decomposition method like multi-channel empirical mode decomposition (MEMD) is used to simultaneously decompose the multi-channel signals into their intrinsic mode functions (IMFs). We then apply the Johansen method on the IF laws to assess the phase synchrony within multivariate nonstationary signals. The proposed approach is validated first using multichannel synthetic signals. The method is then used for quantifying the inter-hemispheric EEG asynchrony during ictal and inter-ictal periods using a newborn EEG seizure/non-seizure database of five subjects. For this application, pair-wise phase synchrony measures may not be able to account for phase interactions between multiple channels. Furthermore, the classical definition of phase synchrony, which is based on the rational relationships between phases, may not reveal the hidden phase interdependencies caused by irrational long-run relationships. We evaluate the performance of the proposed method using the differentiation of unwrapped phase as well as other IF estimation techniques. The results obtained on newborn EEG signals confirm that the generalized phase synchrony within EEG channels increases significantly during ictal periods. A statistically consistent phase coupling is also observed within the non-seizure segments supporting the concept of constant inter-hemispheric connectivity in the newborn brain during inter-ictal periods.

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“…It is superior to the traditional methods based on fast Fourier transform (FFT) in terms of non-stationary signals and has achieved successful application in a variety of areas as fault diagnosis, information detection, biomedical industry and etc. [2][3][4]. WP analysis can solve the contradiction between time and frequency resolution well and provides an ever finer way of non-stationary signal analysis.…”

Section: Introductionmentioning

confidence: 99%

Time-Frequency Characteristics Analysis on Vibration Signals of a Three-Supported Rotor System with Misalignment

Wang

Lin

et al. 2011

AEF

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Abstract. In light of the complex and non-stationary characteristics of misalignment vibration signal, this paper proposed a novel method to analyze in time-frequency domain under different working conditions. Firstly, decompose raw misalignment signal into different frequency bands by wavelet packet (WP) and reconstruct it in accordance with the band energy to remove noises. Secondly, employ empirical mode decomposition (EMD) to the reconstructed signal to obtain a certain number of stationary intrinsic mode functions (IMF). Finally, apply further spectrum analysis on the interested IMFs. In this way, weak signal is caught and dominant frequency is picked up for the diagnosis of misalignment fault. Experimental results show that the proposed method is able to detect misalignment fault characteristic frequency effectively.

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Multiple-view time–frequency distribution based on the empirical mode decomposition

Abstract: Original citationStevenson It was also shown to have performance comparable to the WVD when estimating the instantaneous frequency (IF) of multiple signal components in the presence of noise.

Cited by 14 publications

References 16 publications

Estimating the number of components of a multicomponent nonstationary signal using the short-term time-frequency Rényi entropy

Estimating the number of components of a multicomponent nonstationary signal using the short-term time-frequency Rényi entropy

A time–frequency based approach for generalized phase synchrony assessment in nonstationary multivariate signals

Time-Frequency Characteristics Analysis on Vibration Signals of a Three-Supported Rotor System with Misalignment

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