Fig 21 - uploaded by Xianyao Chen
Content may be subject to copyright.
Comparison among the spectrograms (a) narrow band and (b) wide band; (c) continuous Morlet wavelet and (d) Hilbert spectral representations for the speech signal given in Fig. 20.
Source publication
As the original definition on Hilbert spectrum was given in terms of total energy and amplitude, there is a mismatch between the Hilbert spectrum and the traditional Fourier spectrum, which is defined in terms of energy density. Rigorous definitions of Hilbert energy and amplitude spectra are given in terms of energy and amplitude density in the ti...
Similar publications
Recent work suggests that dissociable activity in theta and delta frequency bands underlies several common ERP components, including the no-go N2/P3 complex, which can better index separable functional processes than traditional time-domain measures. Reports have also demonstrated that neural activity can be affected by stimulus sequence context in...
Citations
... In this case, a kernel estimates of not the density itself (as done previously), but its Hilbert transform, is introduced. The authors of article [3] note that the definition of the Hilbert spectrum is described in terms of total energy and amplitude. However, there is a mismatch between the Hilbert spectrum and the traditional Fourier spectrum, which is defined through energy density. ...
Modern heterogeneous packet networks generate network traffic with a complex structure. In this article, the object of study is a time series. The total number of User Datagram Protocol (UDP) packets has reached 250242. According to analysts, the growth trend of traffic , including real-time applications, will continue and the volume of data will grow, which may lead to the formation of packet queues when processed by network devices. In this case, there may be losses in case of long queues. To solve this problem, a power spectrum assessment was carried out. The AR maximum entropy estimator has been shown to be more sensitive than the auxiliary Fourier estimator. Accounting for non-stationarity by spectral methods is possible only through estimation in a sliding time window. Nine diagrams of spectral temporal analysis of the original series, its increments, and the mixed series of increments were obtained: with default parameters, with small and large windows. Diagrams related to the original series reflect the dynamics of changes in data transmission intensity in the network; they show higher temporal resolution, indicating the presence of high-frequency components (noise) and the presence of low-frequency components (trend). Diagrams with increments describe signals of periodic components ; changing the length of the window did not reflect the presence of noise or trend signs. Diagrams with mixed increments show that frequency components are uniformly distributed. The uniqueness of this work lies in the real measured data, and a distinctive feature of the obtained results is the visual examination of the complex traffic structure, allowing for the resolution of the investigated problem. Practical application of the results obtained can be applied in Quality of Service (QoS) management , resource planning, and network performance optimization Keywords: UDP, AR-estimation, moving window , packet intensity, long-term trend, high-frequency component UDC 004.434
... Residuals use a monotonic function, and reflect data trends [21]. The decomposed IMF has one vibration mode, the lowerorder IMF shows high-frequency components of an input signal, and the high-order IMF shows lowfrequency components [22]. The decomposed IMF satisfies the following two conditions, and IMF 1-4 contains information from the sEMG [23]. ...
As Internet of Things (IoT) technology develops, integrating network functions into diverse equipment introduces new challenges, particularly in dealing with counterfeit issues. Over the past few decades, research efforts have focused on leveraging electromyogram (EMG) for personal recognition, aiming to address security concerns. However, obtaining consistent EMG signals from the same individual is inherently challenging, resulting in data irregularity issues and consequently decreasing the accuracy of personal recognition. Notably, conventional studies in EMG-based personal recognition have overlooked the issue of data irregularities. This paper proposes an innovative approach to personal recognition that combines a siamese fusion network with an auxiliary classifier, effectively mitigating the impact of data irregularities in EMG-based recognition. The proposed method employs empirical mode decomposition (EMD) to extract distinctive features. The model comprises two sub-networks designed to follow the siamese network architecture and a decision network integrated with the novel auxiliary classifier, specifically designed to address data irregularities. The two sub-networks sharing a weight calculate the compatibility function. The auxiliary classifier collaborates with a neural network to implement an attention mechanism. The attention mechanism using the auxiliary classifier solves the data irregularity problem by improving the importance of the EMG gesture section. Experimental results validated the efficacy of the proposed personal recognition method, achieving a remarkable 94.35% accuracy involving 100 subjects from the multi-session CU_sEMG database (DB). This performance outperforms the existing approaches by 3%, employing auxiliary classifiers. Furthermore, an additional experiment yielded an improvement of over 0.85% of Ninapro DB, 3% of CU_sEMG DB compared to the existing EMG-based recognition methods. Consequently, the proposed personal recognition using EMG proves to secure IoT devices, offering robustness against data irregularities.
... The HHT method shows a sharp TF resolution that can only be affected by the sampling rate of data. Notably, the instantaneous frequency (IF) computed in the HHT method can conquer the restriction of uncertainty principle and eliminate the spurious harmonics in the Fourier analysis [25]. ...
The Holo-Hilbert spectral analysis (HHSA) is an emerging analysis tool for rotating machinery fault diagnosis. It has an excellent performance in reflecting the cross-scale coupling relationship in the nonlinear and non-stationary vibration signals, by combining the two-layer empirical mode decomposition structure. However, the random phase shift involved in the envelope signal analysis limits the wide application of HHSA and may lead to an inaccurate instantaneous frequency estimation. To solve the aforementioned problem and acquire an accurate modulation relationship between amplitude-modulated (AM) and frequency-modulated (FM) characteristics, a novel non-stationary signal analysis method, namely Holo-Hilbert square spectral analysis (HHSSA), is put forward in this paper by combing the square envelope analysis. The proposed HHSSA is integrated to compute a new quantity called the AM-marginal spectrum to reveal the separation efficiency of fault characteristics. Moreover, the relationships between HHSSA with the commonly used second-order cyclostationary methods (Cyclic Modulation Spectrum and Fast Spectral Correlation) are further investigated. Furthermore, the analysis of simulation, experimental data, and industrial data are conducted to demonstrate the high resolution and superior modulation relationship recognition capability of HHSSA. The analysis results further prove that the proposed HHSSA-based AM-marginal spectrum has the best fault identification performance and robustness compared with traditional methods.
... The standard deviation value, which is calculated from the two consecutive results of the iteration process, was used as a criterion for completing the partial calculation of each component for the purposes of this paper. E. Huang determined a typical value of the standard deviation for the end of the iteration in the interval 0.2 and 0.3 [13][14]. Note that the first modal component represents the highest frequency component of the signal s(t). ...
... In the case of calculating the Hilbert-Huang transformation, this limit does not apply. Furthermore, the calculation procedure of the empirical modal decomposition, according to the author of the method of scientist E. Huang, is described [13][14]. The calculation procedure takes place in several steps. ...
The paper presents an analysis and comparison of selected dynamic parameters in the common crossing and switch unit of a railway turnout. The paper includes a description of the measurement methodology, the report of mathematical methods used to evaluate the measured data and comparison of selected parameters describing dynamic processes in individual parts of the structure. The paper also includes a mathematical analysis of the lesser-known Hilbert Huang transformation, including its practical application. From the presented case study, practical experience and recommendations for the railway line managers, research organizations and possibly for the wider technical public are derived.
... The original definition of the Hilbert spectrum presented by Huang et al. [14] is only a qualitative definition in terms of total energy. It was refined by Huang et al., in 2011 [15]. The new definition of Hilbert energy spectrum is the energy density distribution in a time-frequency space which is divided into equal-sized bins of Δt × Δω: ...
... resolution must be determined according to the total data length and sampling rate, which are unrelated to the physical properties, because of the integration operation in time-frequency conversion. This integration operation is eschewed in the HSA, where frequency is computed through differentiation rather than integration [15]. The HSA is not restricted by the "uncertainty principle", and it is a physically meaningful time-frequency analysis tool. ...
A new automatic baseline correction method based on the Hilbert spectral analysis (HSA) is proposed to recover a relatively reasonable time history of baseline offset, permanent displacement, and stable peak ground motion displacement (PGD) from a raw near-fault ground motion record. This method can get rid of the selection of the start time of strong motion (corresponding to t1 in traditional methods) by an adaptive extraction procedure, then a stable PGD as well as an accurate permanent displacement can be obtained. For baseline offsets, there is no two-stage-segment assumption in this procedure, and the extracted time histories of these offsets include complex frequency changes, which is more consistent with the explanations of causes for baseline offsets. All causes of baseline offsets are treated as contaminants that exist in all frequency ranges in a record. Uncontaminated components can be extracted from the original record by the HSA, then information about strong motions can be retained as much as possible. The residual part is regarded as a heavily contaminated component of which the energy of the noise rivals that of the real ground motion. It is corrected based on only one time point. Finally, the corrected record is contributed by both of the uncontaminated and adjusted contaminated components. The HSA method, which depends on the energy distribution of original record in different frequency component, can obtain the baseline offset, PGD, and permanent displacement reasonably, stably, and automatically.
... In addition, a common drawback of these TFA methods is the lack of decomposition adaptability. Hilbert-Huang transform (HHT) [9][10][11][12] is a novel and adaptive for nonstationary signal processing tool, which includes empirical mode decomposition (EMD) and Hilbert transform (HT). EMD is a data-driven signal separation approach that decomposes a given signal into numbers of intrinsic mode functions (IMFs) regardless of any preset basis functions adaptively. ...
... However, the mechanical vibration signals have relatively more complex components and the frequency band obtained by EWT contains many interference components, which is difficult for spectrum segmentation. 11 12 13 f f f f , where 11 appended to 1 f . The spectrum segmentation methods are employed by AEFD and EWT to process noisy signals, respectively, and the outputs are displayed in Fig. 1(a). ...
Adaptive empirical Fourier decomposition (AEFD) is a recently developed approach of nonstationary signal mode separation. However, it requires to set the spectrum segmentation boundary relying on the users’ professional experience ahead of time. In this paper, a novel spectral envelope-based adaptive empirical Fourier decomposition (SEAEFD) method is proposed to improve the performance of AEFD for rolling bearing vibration signal analysis. In the proposed SEAEFD approach, fast Fourier transform (FFT) of the raw signal is calculated to obtain the frequency spectrum at first. Then, the spectral envelope processing is implemented on the spectrum signal obtained by FFT to achieve an adaptive segmentation. In the traditional segmentation method, generally, the minima and midpoints between adjacent extreme points are taken as the spectrum segmentation boundary, in which the obtained frequency band contains more interference components. To achieve the effect of denoising and restrain the noise that existed in the collected vibration signal, SEAEFD is proposed to optimize the spectrum segmentation boundary so that the obtained frequency band contains the least noise components. Lastly, the inverse FFT is used to reconstruct the component signal within each frequency band and the gained signals are termed as Fourier intrinsic mode functions (FIMFs). Therefore, SEAEFD enables a nonstationary signal to be decomposed into several single-component signals with instantaneous frequencies of physical significance. The proposed SEAEFD method is compared with recently developed methods, including EAEFD, AEFD, EWT, VMD and EMD methods, by analyzing the simulation signals and the measured data of rolling bearing. The results indicate that SEAEFD is valid in diagnosing rolling bearing faults and gets a better diagnosis performance than the compared methods.
... In this sense, the interpretations of MHS and Fourier spectra are quite different. While in the latter, the existence of energy at the frequency index k means the persistence of a sinusoidal component in the whole period [0,T] of the data, in the MHS, it means that there is a higher likelihood of this component having appeared locally [4,72]. Fig. 7 shows the results of HHT analysis of the passive SONAR signal from Fig. 5a. ...
Empirical mode decomposition (EMD) is a signal processing method that produces a data-driven multiresolution representation in time-domain suited to characterize time-varying and nonlinear phenomena. In EMD, intrinsic mode functions (IMF) are sequentially estimated from the signal of interest to represent different intrinsic oscillation modes and produce an orthogonal representation of the original information. Different algorithms have been proposed for IMF estimation to deal with limitations such as mode-mixing and noise sensitivity. EMD is usually associated with the Hilbert transform to obtain a frequency-domain representation. In this case, the method is referred to as the Hilbert-Huang transform (HHT). This paper presents a theoretical review of the fundamental aspects of both EMD and HHT, such as the IMF estimation procedure. Variations of the original EMD algorithm are also presented. Both simulated and experimental underwater acoustic signals are used to illustrate the efficiency of EMD/HHT in revealing relevant characteristics from time-varying and nonlinear phenomena.
... The HMS offers a measure of total amplitude (or energy) contribution from each frequency value and its graphical representation is very similar to the spectrum calculated by other traditionally used methods including the FFT: The X-axis includes the spectral discrete frequencies, and the Y -axis the corresponding amplitude values (power). 5,31 The HMS has been used by different authors after applying the Hilbert-Huang method to the EEG signal [32][33][34][35][36][37][38] but to our knowledge, the possible differences between the results obtained using the HMS and the conventional FFT spectra in resting conditions of healthy humans have not been studied in detail and it results imperative, because the universally used method for the spectral analysis of the EEG has been the FFT spectra and because of that, its profits and limitations had shaped our understanding of the spectral properties of EEG signal for many years. ...
... This lack of agreement could be occasioned by the higher ability of the HMS for the detection of instantaneous frequencies previous to the marginalization of the HMS. 31 This could be evidence of the capabilities of the HMS method to allow us explore this zone of the EEG spectrum with major precision, in order to capture its frequency variations in a way essentially different to the FFT-based method. ...
The fast Fourier transform (FFT) has been the main tool for electroencephalo-graphic (EEG) Spectral Analysis (SPA). However, as the EEG dynamics show nonlinear and non-stationary behavior, results using the FFT approach may result meaningless. A novel method has been developed for the analysis of nonlinear and non-stationary signals known as the Hilbert-Huang transform method. In this study we analyze the differences for the broadband (SPA) of the EEG using the traditional FFT approach with those calculated with the Hilbert Marginal Spectra (HMS) after decomposition of the EEG with a multi-variate empirical mode decomposition algorithm. EEG segments recorded from 19 leads of 47 healthy volunteers were studied. Statistically significant differences between methods were found for almost all leads by variance analyses. The agreement assessment shows that mean weighted frequencies have a good agreement for almost all bands, with the exception of beta-2 and gamma bands where values for the HMS were higher than 3 Hz. Also, the HMS method received lower than 5% energy values for alpha activity with an increment in the adjacent bands. The HMS may be considered a good alternative for the SPA of the EEG when nonlinearity or non-stationarity may be present.
... It should be pointed out that the definition of frequency in h(ω) is different from the definition in the Fourier framework. The interpretation of the Hilbert marginal spectrum should thus be given with more caution [30,35,50]. Figure 3 (left panel) shows an example of the second order moment L 2 (ω) obtained for the different components B i of the magnetic field of sample 2005/01/03. ...
The statistical properties of fast Alfvénic solar wind turbulence have been analyzed by means of empirical mode decomposition and the associated Hilbert spectral analysis. The stringent criteria employed for the data selection in the Wind spacecraft database, has made possible to sample multiple k‖ field-aligned intervals of the three magnetic field components. The results suggest that the spectral anisotropy predicted by the critical balance theory is not observed in the selected database, whereas a Kolmogorov-like scaling (E(k‖)∼k−5/3) and a weak or absent level of intermittency are robust characteristics of the Alfvénic slab component of solar wind turbulence.
... The HMS offers a measure of total amplitude (or energy) contribution from each frequency value and its graphical representation is very similar to the spectrum calculated by other traditionally used methods including the FFT: The X-axis includes the spectral discrete frequencies, and the Y -axis the corresponding amplitude values (power). 5,31 The HMS has been used by different authors after applying the Hilbert-Huang method to the EEG signal [32][33][34][35][36][37][38] but to our knowledge, the possible differences between the results obtained using the HMS and the conventional FFT spectra in resting conditions of healthy humans have not been studied in detail and it results imperative, because the universally used method for the spectral analysis of the EEG has been the FFT spectra and because of that, its profits and limitations had shaped our understanding of the spectral properties of EEG signal for many years. ...
... This lack of agreement could be occasioned by the higher ability of the HMS for the detection of instantaneous frequencies previous to the marginalization of the HMS. 31 This could be evidence of the capabilities of the HMS method to allow us explore this zone of the EEG spectrum with major precision, in order to capture its frequency variations in a way essentially different to the FFT-based method. ...
The fast Fourier transform (FFT), has been the main tool for the EEG spectral analysis (SPA). However, as the EEG dynamics shows nonlinear and non-stationary behavior, results using the FFT approach may result meaningless. A novel method has been developed for the analysis of nonlinear and non-stationary signals known as the Hilbert-Huang transform method. In this study we describe and compare the spectral analyses of the EEG using the traditional FFT approach with those calculated with the Hilbert marginal spectra (HMS) after decomposition of the EEG with a multivariate empirical mode decomposition algorithm. Segments of continuous 60-seconds EEG recorded from 19 leads of 47 healthy volunteers were studied. Although the spectral indices calculated for the explored EEG bands showed significant statistical differences for different leads and bands, a detailed analysis showed that for practical purposes both methods performed substantially similar. The HMS showed a reduction of the alpha activity (-5.64%), with increment in the beta-1 (+1.67%), and gamma (+1.38%) fast activity bands, and also an increment in the theta band (+2.14%), and in the delta (+0.45%) band, and vice versa for the FFT method. For the weighted mean frequencies insignificant mean differences (lower than 1Hz) were observed between both methods for the delta, theta, alpha, beta-1 and beta-2 bands, and only for the gamma band values for the HMS were 3 Hz higher than with the FFT method. The HMS may be considered a good alternative for the SPA of the EEG when nonlinearity or non-stationarity may be present.
