Discrete Energy Separation Algorithm Research Articles

AFM signal model for dysarthric speech classification using speech biomarkers.

Neurological disorders include various conditions affecting the brain, spinal cord, and nervous system which results in reduced performance in different organs and muscles throughout the human body. Dysarthia is a neurological disorder that significantly impairs an individual's ability to effectively communicate through speech. Individuals with dysarthria are characterized by muscle weakness that results in slow, slurred, and less intelligible speech production. An efficient identification of speech disorders at the beginning stages helps doctors suggest proper medications. The classification of dysarthric speech assumes a pivotal role as a diagnostic tool, enabling accurate differentiation between healthy speech patterns and those affected by dysarthria. Achieving a clear distinction between dysarthric speech and the speech of healthy individuals is made possible through the application of advanced machine learning techniques. In this work, we conducted feature extraction by utilizing the Amplitude and frequency modulated (AFM) signal model, resulting in the generation of a comprehensive array of unique features. A method involving Fourier-Bessel series expansion is employed to separate various components within a complex speech signal into distinct elements. Subsequently, the Discrete Energy Separation Algorithm is utilized to extract essential parameters, namely the Amplitude envelope and Instantaneous frequency, from each component within the speech signal. To ensure the robustness and applicability of our findings, we harnessed data from various sources, including TORGO, UA Speech, and Parkinson datasets. Furthermore, the classifier's performance was evaluated based on multiple measures such as the area under the curve, F1-Score, sensitivity, and accuracy, encompassing KNN, SVM, LDA, NB, and Boosted Tree. Our analyses resulted in classification accuracies ranging from 85 to 97.8% and the F1-score ranging between 0.90 and 0.97.

A new method based on the discrete time energy separation algorithm for high and low impedance faults detection in distribution systems

A new method based on the discrete time energy separation algorithm for high and low impedance faults detection in distribution systems

Electromechanical Modes Identification Based on an Iterative Eigenvalue Decomposition of the Hankel Matrix

This paper proposes a novel strategy to precisely extract modal patterns from non-stationary multi-component signals associated with electromechanical oscillations in large-scale power systems. The strategy is composed of two stages: ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</i> ) a time-frequency representation (TFR) method; and ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ii</i> ) an energy-based operator. The former is equipped with a multivariate and iterative eigenvalue decomposition of the Hankel matrix (IEVDHM) that captures the swing dynamics as a mono-component signal criterion is fulfilled, meanwhile the latter instantaneously estimates the modal information (damping and frequency) through the discrete energy separation algorithm (DESA) that implements the discrete-time energy operators derived from the Teager-Kaiser energy operators (TKEO). The attained results and their comparisons with state-of-the-art techniques confirm the effectiveness and performance of the proposed strategy to demodulate synthetic, simulated and real oscillating signals, even under high noisy conditions, and to be a useful tool for off-line contingency analysis thanks to the capability of differentiating concurrent modes with close frequencies.

Empirical Mode Decomposition-Based Feature Extraction for Environmental Sound Classification

In environment sound classification, log Mel band energies (MBEs) are considered as the most successful and commonly used features for classification. The underlying algorithm, fast Fourier transform (FFT), is valid under certain restrictions. In this study, we address these limitations of Fourier transform and propose a new method to extract log Mel band energies using amplitude modulation and frequency modulation. We present a comparative study between traditionally used log Mel band energy features extracted by Fourier transform and log Mel band energy features extracted by our new approach. This approach is based on extracting log Mel band energies from estimation of instantaneous frequency (IF) and instantaneous amplitude (IA), which are used to construct a spectrogram. The estimation of IA and IF is made by associating empirical mode decomposition (EMD) with the Teager–Kaiser energy operator (TKEO) and the discrete energy separation algorithm. Later, Mel filter bank is applied to the estimated spectrogram to generate EMD-TKEO-based MBEs, or simply, EMD-MBEs. In addition, we employ the EMD method to remove signal trends from the original signal and generate another type of MBE, called S-MBEs, using FFT and a Mel filter bank. Four different datasets were utilised and convolutional neural networks (CNN) were trained using features extracted from Fourier transform-based MBEs (FFT-MBEs), EMD-MBEs, and S-MBEs. In addition, CNNs were trained with an aggregation of all three feature extraction techniques and a combination of FFT-MBEs and EMD-MBEs. Individually, FFT-MBEs achieved higher accuracy compared to EMD-MBEs and S-MBEs. In general, the system trained with the combination of all three features performed slightly better compared to the system trained with the three features separately.

A new fast method for improvement of power transformer differential protection based on discrete energy separation algorithm

Differential protection is one of the most widely used protections in power transformers. The challenges associated with this protection are distinguishing the inrush current, overexcitation, and external fault conditions from internal and winding faults. So far, various methods have been proposed to prevent differential protection from mal-operation, which are not necessarily simple to implement and do not guarantee the proper performance in all scenarios. This paper proposes a new method based on the discrete energy separation algorithm to improve differential protection. The proposed method consists of two sections. The first section detects internal disturbances from external faults, and the other distinguishes the inrush current and overexcitation from internal and winding faults. One of the advantages of the proposed method is the parallel employment of these two sections in the logic of the method, which reduces the detection time. Moreover, other advantages such as the fast detection speed (1.5 ms), simple implementation, and low computational burden make it possible to implement the method in real-time. The simulation results show the appropriate efficiency of the proposed method in detecting all disturbances even in noisy conditions and saturation of current transformers.

A Nonparametric Approach for Multicomponent AM–FM Signal Analysis

In this paper, a novel method is presented to analyze the amplitude modulated and frequency modulated (AM–FM) multicomponent signals using a combination of the variational mode decomposition (VMD) and the discrete energy separation algorithm (DESA). In the presented method, firstly, a multicomponent signal is decomposed using VMD method applied in an iterative way. In order to separate the monocomponent signals from multicomponent signal, a suitable convergence criterion is developed based on the values of estimated center frequencies ( $$\overline{\text {CF}}$$ ) and standard deviations ( $$\sigma _{\text {CF}}$$ ) of the decomposed components. Further, the estimation of amplitude envelope and the instantaneous frequency functions of monocomponent AM–FM signals has been carried out by employing DESA. Moreover, the proposed method is also applied on the synthetic AM–FM signal and speech signals to evaluate its performance. Furthermore, its performance is also compared with the Fourier–Bessel series expansion-based DESA, empirical wavelet transform-based DESA, and iterative eigenvalue decomposition-based DESA methods. The performance of the proposed method is compared with the other methods in terms of mean square error between actual and estimated amplitude envelopes ( $${\text {MSE}_{\text {AE}}}$$ ), mean square error between actual and estimated instantaneous frequencies ( $${\text {MSE}_{\text {IF}}}$$ ) for synthetic signal. The COSH distance measure is used as a performance measure for speech signals. It is found that the proposed method gives better results in terms of performance measures in several cases.

A Novel AFM Signal Model for Parametric Representation of Speech Phonemes

A new multicomponent multitone amplitude and frequency-modulated signal model for parametric modelling of speech phoneme (voiced and unvoiced) is presented in this paper. As the speech signal is a multicomponent non-stationary signal, the Fourier–Bessel expansion is used to separate all individual components from the multicomponent speech signal. The parameter estimation is done by analysing the amplitude envelope (AE) and instantaneous frequency (IF) of the signal component separately. The AE and IF functions for separated components are extracted by using the discrete energy separation algorithm. The amplitude-modulated signal parameters and the amplitude of the signal are estimated by analysing the AE function, whereas the frequency-modulated signal parameters and the carrier frequency of the signal are estimated by analysing the IF function. This technique is found to be quite efficient for accurate parameter estimation of the speech phoneme. As an illustration of model-based speech processing, the proposed model is used for various speech signal processing applications.

Low bit-rate speech coding based on multicomponent AFM signal model

In this paper, we propose a novel multicomponent amplitude and frequency modulated (AFM) signal model for parametric representation of speech phonemes. An efficient technique is developed for parameter estimation of the proposed model. The Fourier–Bessel series expansion is used to separate a multicomponent speech signal into a set of individual components. The discrete energy separation algorithm is used to extract the amplitude envelope (AE) and the instantaneous frequency (IF) of each component of the speech signal. Then, the parameter estimation of the proposed AFM signal model is carried out by analysing the AE and IF parts of the signal component. The developed model is found to be suitable for representation of an entire speech phoneme (voiced or unvoiced) irrespective of its time duration, and the model is shown to be applicable for low bit-rate speech coding. The symmetric Itakura–Saito and the root-mean-square log-spectral distance measures are used for comparison of the original and reconstructed speech signals.

Automatic sleep stages classification based on iterative filtering of electroencephalogram signals

Computer-aided sleep monitoring system can effectively reduce the burden of experts in analyzing the large volume of electroencephalogram (EEG) recordings corresponding to sleep stages. In this paper, a new technique for automated classification of sleep stages based on iterative filtering of EEG signals is presented. In order to perform sleep stages classification, the EEG signals are decomposed using iterative filtering method. The modes obtained from iterative filtering of EEG signal can be considered as amplitude-modulated and frequency-modulated (AM-FM) components. The discrete energy separation algorithm (DESA) is applied to the modes to determine amplitude envelope and instantaneous frequency functions. The extracted amplitude envelope and instantaneous frequency functions have been used to compute Poincare plot descriptors and statistical measures. The Poincare plot descriptors and statistical measures are applied as input features for different classifiers in order to classify sleep stages. The classifiers namely, naive Bayes, k-nearest neighbor, multilayer perceptron, C4.5 decision tree, and random forest are applied in order to classify the EEG epochs corresponding to various sleep stages. The experimental study has been performed on online available Sleep-EDF database for two-class to six-class classification of sleep stages based on EEG signals. The two-class to six-class classification problems are formulated by taking different combinations of EEG signals corresponding to various sleep stages. The comparison of the results is presented for different multi-class classification problems with the other recently proposed methods. The results show that the proposed method has provided better tenfold cross-validation classification accuracy than other existing methods.

An AM-FM Based Image Segmentation: Detection of Clouds in MSG Images of Algeria

In this paper, amplitude and frequency modulation (AM-FM) data are extracted from satellite images and processed to facilitate meteorological observations. The approach used is mainly based on 2D-DESA (Discrete Energy Separation Algorithm) where the Teager Kaiser Energy Operator (TKEO) acts as data discriminator. Dominant energy parameters selected by this operator, are employed to get the AM-FM components and segment the images under study via K-means classifier. The AM-FM method so described has been tested on a set of multispectral satellite images collected by Meteosat 9 (MSG-2) over North Africa in November 2011. Applied to both visible and infrared Meteosat Second Generation (MSG) images, it yields a compact and coherent segmentation map of Northern Algeria, Mediterranean Sea and South Western Europe, where the object contours are satisfactorily reproduced and typical clouds, detected.

Time Varying Autoregressive Model Parameters Estimation using Discrete Energy Separation Algorithm

Time Varying Autoregressive (TVAR) model for the Amplitude and Frequency modulated (AM-FM) signal is presented In this paper. TVAR parameters of AM-FM signal are estimated using Discrete Energy Separation (DESA) Algorithm. The performance of DESA method is shown to be comparable to the existing basis function method for AM, FM, AM-FM signal models. The proposed method is simpler to execute in hardware and consumes considerably less computational resources compared to the method using Adaptive and the Basis function methods. .It is demonstrated that the proposed technique based on DESA has certain distinct advantages over the conventional method employing basis functions. Another advantage is that the present method works well with quickly varying signals

Estimation of phase derivatives using discrete energy separation algorithm in digital holographic interferometry.

This Letter proposes a new method for the estimation of the first- and second-order phase derivatives corresponding to strain and curvature from a single fringe pattern in digital holographic interferometry. The method is based on a discrete energy separation algorithm, which provides a biased phase derivative estimate in a noisy environment. Subsequently, the least-squares spline approximation with optimal number of knots selection technique is used to obtain the accurate estimation of phase derivatives. The accuracy and computational efficiency of the proposed method is validated with simulation and experimental results.

Analysis of Acoustic Events in Speech Signals Using Bessel Series Expansion

In this paper, we propose an approach for the analysis and detection of acoustic events in speech signals using the Bessel series expansion. The acoustic events analyzed are the voice onset time (VOT) and the glottal closure instants (GCIs). The hypothesis is that the Bessel functions with their damped sinusoid-like basis functions are better suited for representing the speech signals than the sinusoidal basis functions used in the conventional Fourier representation. The speech signal is band-pass filtered by choosing the appropriate range of Bessel coefficients to obtain a narrow-band signal, which is decomposed further into amplitude modulated (AM) and frequency modulated (FM) components. The discrete energy separation algorithm (DESA) is used to compute the amplitude envelope (AE) of the narrow-band AM-FM signal. Events such as the consonant and vowel beginnings in an unvoiced stop consonant vowel (SCV) and the GCIs are derived by processing the AE of the signal. The proposed approach for the detection of the VOT using the Bessel expansion is shown to perform better than the conventional Fourier representation. The performance of the proposed GCI detection method using the Bessel series expansion is compared against some of the existing methods for various noise environments and signal-to-noise ratios.

A parametric approach for the estimation of the instantaneous speed of rotating machinery

A parametric method is proposed for the estimation of the instantaneous speed of rotating machines. The method belongs typically to the class of eigenvalue based parametric signal processing methods. The major advantage of parametric methods over frequency domain or time-frequency domain based methods, is their increased resolution and their reduced computational cost. Moreover, advantages of eigenvalue based methods over other parametric methods include their robustness to noise. Sensitivity analysis for the key parameters of the proposed method is performed, including the sampling frequency, the signal length and the robustness to noise. The effectiveness of the method is demonstrated in vibration measurements from a test rig during start-up and run-down, as well as during variations of the speed of a motorcycle engine. Compared to the Hilbert Transform and to the Discrete Energy Separation Algorithm (DESA), the proposed approach exhibits a better behavior, while it simultaneously presents computational simplicity, being able to be implemented analytically, even online.

Video viewing: do auditory salient events capture visual attention?

We assess whether salient auditory events contained in soundtracks modify eye movements when exploring videos. In a previous study, we found that, on average, nonspatial sound contained in video soundtracks impacts on eye movements. This result indicates that sound could play a leading part in visual attention models to predict eye movements. In this research, we go further and test whether the effect of sound on eye movements is stronger just after salient auditory events. To automatically spot salient auditory events, we used two auditory saliency models: the discrete energy separation algorithm and the energy model. Both models provide a saliency time curve, based on the fusion of several elementary audio features. The most salient auditory events were extracted by thresholding these curves. We examined some eye movement parameters just after these events rather than on all the video frames. We showed that the effect of sound on eye movements (variability between eye positions, saccade amplitude, and fixation duration) was not stronger after salient auditory events than on average over entire videos. Thus, we suggest that sound could impact on visual exploration not only after salient events but in a more global way.

Multicomponent AM–FM signals analysis based on EMD–B-splines ESA

In this paper a signal analysis framework for estimating time-varying amplitude and frequency functions of multicomponent amplitude and frequency modulated (AM–FM) signals is introduced. This framework is based on local and non-linear approaches, namely Energy Separation Algorithm (ESA) and Empirical Mode Decomposition (EMD). Conjunction of Discrete ESA (DESA) and EMD is called EMD–DESA. A new modified version of EMD where smoothing instead of an interpolation to construct the upper and lower envelopes of the signal is introduced. Since extracted IMFs are represented in terms of B-spline (BS) expansions, a closed formula of ESA robust against noise is used. Instantaneous Frequency (IF) and Instantaneous Amplitude (IA) estimates of a multicomponent AM–FM signal, corrupted with additive white Gaussian noise of varying SNRs, are analyzed and results compared to ESA, DESA and Hilbert transform-based algorithms. SNR and MSE are used as figures of merit. Regularized BS version of EMD–ESA performs reasonably better in separating IA and IF components compared to the other methods from low to high SNR. Overall, obtained results illustrate the effectiveness of the proposed approach in terms of accuracy and robustness against noise to track IF and IA features of a multicomponent AM–FM signal.

Monaural speech/music source separation using discrete energy separation algorithm

In this paper, we address the problem of monaural source separation of a mixed signal containing speech and music components. We use Discrete Energy Separation Algorithm (DESA) to estimate frequency-modulating (FM) signal energy. The FM signal energy is used to design a time-varying filter in the time–frequency domain for rejecting the interfering signal. The FM signal energy was chosen due to its good ability to differentiate between speech and music signals using localized information both in time and frequency. We present experimental results which demonstrate the advantages and limitations of the proposed method using synthetic data and real audio signals.

A joint 2D AM–FM estimation based on higher order Teager–Kaiser energy operators

In this work, an image demodulation algorithm based on two-dimensional higher order Teager–Kaiser (TK) operators is presented. We show quantitatively and qualitatively that the introduction of higher orders in TK operator improves amplitude modulation (AM) and frequency modulation (FM) estimation results, compared to classical approaches such as the Discrete Energy Separation Algorithm (DESA) or the Analytic Signal (AS) method. Indeed, for a wide class of images, obtained demodulation errors for both the amplitude and frequency are numerically lower than the obtained ones with the DESA and AS method. The proposed method is illustrated on both synthetic and real images. Moreover, it turns out for some real images that the algorithm is very efficient in the sense that it tracks the most significant part in images and segments regions of interests, particularly, the AM counterpart. Finally, an application of our approach to the segmentation of mines’ shadows in Sonar images is presented. This is very important for both civil and military applications.

Analysis of multicomponent AM-FM signals using FB-DESA method

The discrete energy separation algorithm (DESA) together with the Gabor's filtering provides a standard approach to estimate the amplitude envelope (AE) and the instantaneous frequency (IF) functions of a multicomponent amplitude and frequency modulated (AM-FM) signal. The filtering operation introduces amplitude and phase modulations in the separated monocomponent signals, which may lead to an error in the final estimation of the modulation functions. In this paper, we have proposed a method called the Fourier-Bessel expansion-based discrete energy separation algorithm (FB-DESA) for component separation and estimation of the AE and IF functions of a multicomponent AM-FM signal. The FB-DESA method does not introduce any amplitude or phase modulation in the separated monocomponent signal leading to accurate estimations of the AE and IF functions. Simulation results with synthetic and natural signals are included to illustrate the effectiveness of the proposed method.

Extraction of FM components from speech signals using all-pole model

Frequency modulation has recently emerged as a promising model for characterising the phase of a speech signal. Proposed is a novel technique for extracting the frequency modulation (FM) components from the subband speech signal, using a second-order all-pole model. Evaluation of a speaker recognition system employing FM features, extracted using the proposed technique, on the NIST 2001 database reveals improvement over MFCC baseline and significant improvements over the discrete energy separation algorithm and a Hilbert transform based approach in terms of equal error rate.