ISAR imaging Based on the Empirical Mode Decomposition Time-Frequency Representation

International audienceThis work proposes an adaptation of the Empirical Mode Decomposition Time-Frequency Distribution (EMD-TFD) to non-analytic complex-valued signals. Then, the modified version of EMD-TFD is used in the formation of Inverse Synthetic Aperture Radar (ISAR) image. This new method, referred to as NSBEMD-TFD, is obtained by extending the Non uniformly Sampled Bivariate Empirical Mode Decomposition (NSBEMD) to design a filter in the ambiguity domain and to clean the Time-Frequency Distribution (TFD) of signal. The effectiveness of the proposed scheme of ISAR formation is illustrated on synthetic and real signals. The results of our proposed methods are compared to other Time-Frequency Representation (TFR) such as Spectrogram, Wigner-Ville Distribution (WVD), Smoothed Pseudo Wigner-Ville Distribution (SPWVD) or others methods based on EMD

Fault diagnosis for rotating machinery based on multi-differential empirical mode decomposition

The fault diagnosis of rotating machinery has crucial significance for the safety of modern industry, and the fault feature extraction is the key link of the diagnosis process. As an effective time-frequency method, Empirical Mode Decomposition (EMD) has been widely used in signal processing and feature extraction. However, the mode mixing phenomenon may lead to confusion in the identification of multi frequency signals and restricts the applications of EMD. In this paper, a novel method based on Multi-Differential Empirical Mode Decomposition (MDEMD) was proposed to extract the energy distribution characteristics of fault signals. Firstly, multi-order differential signals were deduced and decomposed by EMD. Then, their energy distribution characteristics were extracted and utilized to construct the feature matrix. Finally, taking the feature matrix as input, the classifiers were applied to diagnosis the existence and severity of rotating machinery faults. Simulative and practical experiments were implemented respectively, and the results demonstrated that the proposed method, i.e. MDEMD, is able to eliminate the mode mixing effectively, and the feature matrix extracted by MDEMD has high separability and universality, furthermore, the fault diagnosis based on MDEMD can be accomplished more effectively and efficiently with satisfactory accuracy

Computer implemented empirical mode decomposition method apparatus, and article of manufacture utilizing curvature extrema

A computer implemented physical signal analysis method is includes two essential steps and the associated presentation techniques of the results. All the steps exist only in a computer: there are no analytic expressions resulting from the method. The first step is a computer implemented Empirical Mode Decomposition to extract a collection of Intrinsic Mode Functions (IMF) from nonlinear, nonstationary physical signals based on local extrema and curvature extrema. The decomposition is based on the direct extraction of the energy associated with various intrinsic time scales in the physical signal. Expressed in the IMF's, they have well-behaved Hilbert Transforms from which instantaneous frequencies can be calculated. The second step is the Hilbert Transform. The final result is the Hilbert Spectrum. Thus, the invention can localize any event on the time as well as the frequency axis. The decomposition can also be viewed as an expansion of the data in terms of the IMF's. Then, these IMF's, based on and derived from the data, can serve as the basis of that expansion. The local energy and the instantaneous frequency derived from the IMF's through the Hilbert transform give a full energy-frequency-time distribution of the data which is designated as the Hilbert Spectrum

A method for estimating the instantaneous frequency of non-stationary heart sound signals

Practical signals such as speech, biomedical measurement and communications turn out to be extremely non-stationary and nonlinear time series. Traditional FFT-based power spectral analysis fails to deal with these transient signals. To provide more efficient way for investigating non-stationary and nonlinear signals with high time-frequency resolution and extract more information regarding the transient frequency features involved in the signals, a novel method based on the instantaneous frequency distribution is developed in this paper to provide the time-frequency distribution of the practical signals. The aim of this contribution is to explore the role that both empirical mode decomposition and Hilbert transform can be used to play in such practical signals. Both simulation and experimental results were presented and analyzed to demonstrate the power and effectiveness of the proposed new time-frequency distribution.published_or_final_versio

Update on EMD and Hilbert-Spectra Analysis of Time Series

This method is especially well suited for analyzing time-series data that represent nonstationary and nonlinear physical phenomena. The method is based principally on the concept of empirical mode decomposition (EMD), according to which any complicated signal (as represented by digital samples) can be decomposed into a finite number of functions, called "intrinsic mode functions" (IMFs), that admit well-behaved Hilbert transforms. The local energies and the instantaneous frequencies derived from the IMFs through Hilbert transforms can be used to construct an energy-frequency-time distribution, denoted a Hilbert spectrum

Computer implemented empirical mode decomposition method, apparatus and article of manufacture

A computer implemented physical signal analysis method is invented. This method includes two essential steps and the associated presentation techniques of the results. All the steps exist only in a computer: there are no analytic expressions resulting from the method. The first step is a computer implemented Empirical Mode Decomposition to extract a collection of Intrinsic Mode Functions (IMF) from nonlinear, nonstationary physical signals. The decomposition is based on the direct extraction of the energy associated with various intrinsic time scales in the physical signal. Expressed in the IMF's, they have well-behaved Hilbert Transforms from which instantaneous frequencies can be calculated. The second step is the Hilbert Transform. The final result is the Hilbert Spectrum. Thus, the invention can localize any event on the time as well as the frequency axis. The decomposition can also be viewed as an expansion of the data in terms of the IMF's. Then, these IMF's, based on and derived from the data, can serve as the basis of that expansion. The local energy and the instantaneous frequency derived from the IMF's through the Hilbert transform give a full energy-frequency-time distribution of the data which is designated as the Hilbert Spectrum

Empirical mode decomposition apparatus, method and article of manufacture for analyzing biological signals and performing curve fitting

A computer implemented physical signal analysis method includes four basic steps and the associated presentation techniques of the results. The first step is a computer implemented Empirical Mode Decomposition that extracts a collection of Intrinsic Mode Functions (IMF) from nonlinear, nonstationary physical signals. The decomposition is based on the direct extraction of the energy associated with various intrinsic time scales in the physical signal. Expressed in the IMF's, they have well-behaved Hilbert Transforms from which instantaneous frequencies can be calculated. The second step is the Hilbert Transform which produces a Hilbert Spectrum. Thus, the invention can localize any event on the time as well as the frequency axis. The decomposition can also be viewed as an expansion of the data in terms of the IMF's. Then, these IMF's, based on and derived from the data, can serve as the basis of that expansion. The local energy and the instantaneous frequency derived from the IMF's through the Hilbert transform give a full energy-frequency-time distribution of the data which is designated as the Hilbert Spectrum. The third step filters the physical signal by combining a subset of the IMFs. In the fourth step, a curve may be fitted to the filtered signal which may not have been possible with the original, unfiltered signal

A Quantitative Measure of Mono-Componentness for Time-Frequency Analysis

Joint time-frequency (TF) analysis is an ideal method for analyzing non-stationary signals, but is challenging to use leading to it often being neglected. The exceptions being the short-time Fourier transform (STFT) and spectrogram. Even then, the inability to have simultaneously high time and frequency resolution is a frustrating issue with the STFT and spectrogram. However, there is a family of joint TF analysis techniques that do have simultaneously high time and frequency resolution – the quadratic TF distribution (QTFD) family. Unfortunately, QTFDs are often more troublesome than beneficial. The issue is interference/cross-terms that causes these methods to become so difficult to use. They require that the “proper” joint distribution be selected based on information that is typically unavailable for real-world signals. However, QTFDs do not produce cross-terms when applied to a mono-component signal. Clearly, determining the mono-componentness of a signal provides a key piece of information. However, until now, the means for determining if a signal is a monocomponent or a multi-component has been to choose a QTFD, generate the TF representation (TFR), and visually examine it. The work presented here provides a method for quantitatively determining if a signal is a mono-component. This new capability provides an important step towards finally allowing QTFDs to be used on multi-component signals, while producing few to no interference terms through enabling the use of the quadratic superposition property. The focus of this work is on establishing the legitimacy for “measuring” mono-componentness along with its algorithmic implementation. Several applications are presented, such as quantifying the quality of the decomposition results produced by the blind decomposition algorithm, Empirical Mode Decomposition (EMD). The mono-componentness measure not only provides an objective means to validate the outcome of a decomposition algorithm, it also provides a practical, quantitative metric for their comparison. More importantly, this quantitative measurement encapsulates mono-componentness in a form which can actually be incorporated in the design of decomposition algorithms as a viable condition/constraint so that true mono-components could be extracted. Incorporating the mono-component measure into a decomposition algorithm will eventually allow interference free TFRs to be calculated from multi-component signals without requiring prior knowledge

Statistical Properties and Applications of Empirical Mode Decomposition

Signal analysis is key to extracting information buried in noise. The decomposition of signal is a data analysis tool for determining the underlying physical components of a processed data set. However, conventional signal decomposition approaches such as wavelet analysis, Wagner-Ville, and various short-time Fourier spectrograms are inadequate to process real world signals. Moreover, most of the given techniques require \emph{a prior} knowledge of the processed signal, to select the proper decomposition basis, which makes them improper for a wide range of practical applications. Empirical Mode Decomposition (EMD) is a non-parametric and adaptive basis driver that is capable of breaking-down non-linear, non-stationary signals into an intrinsic and finite components called Intrinsic Mode Functions (IMF). In addition, EMD approximates a dyadic filter that isolates high frequency components, e.g. noise, in higher index IMFs. Despite of being widely used in different applications, EMD is an ad hoc solution. The adaptive performance of EMD comes at the expense of formulating a theoretical base. Therefore, numerical analysis is usually adopted in literature to interpret the behavior. This dissertation involves investigating statistical properties of EMD and utilizing the outcome to enhance the performance of signal de-noising and spectrum sensing systems. The novel contributions can be broadly summarized in three categories: a statistical analysis of the probability distributions of the IMFs and a suggestion of Generalized Gaussian distribution (GGD) as a best fit distribution; a de-noising scheme based on a null-hypothesis of IMFs utilizing the unique filter behavior of EMD; and a novel noise estimation approach that is used to shift semi-blind spectrum sensing techniques into fully-blind ones based on the first IMF. These contributions are justified statistically and analytically and include comparison with other state of art techniques

Near-field acoustic holography for high-frequency weak sound sources under low signal-to-noise ratio

The mechanical noise in the cabin of the ship is so large that the leakage of high-pressure fluid is not easily noticed. In view of this situation, a near-field acoustic holography for high-frequency weak sound source under low signal-to-noise ratio is proposed. The method uses the empirical mode decomposition method to add weights to the time-domain sampling signals of each array element, and then uses the plane equivalent source near-field acoustic holography combined with compressive sensing to find the holographic surface acoustic pressure distribution. The simulation and experiment show that this method has certain feasibility under low signal-to-noise ratio, and the results are better than the method based on Fourier transform and the traditional boundary element method. It is of positive significance to apply it to engineering practice