Hilbert Transform Research Articles

On Characterization of Hilbert Transform of Riemannian Surface with Boundary

On Characterization of Hilbert Transform of Riemannian Surface with Boundary

Generalized amplitude-phase demodulation for isotropic image decomposition and analysis

It is well known that the amplitude-phase demodulation based on Hilbert transform (HT) plays a fundamental role in signal processing. Also, the Bedrosian principle (BP), the key to HT, determines the exponential form of the complex signals out of real ones. In this paper, the novel BP on 2D HT was proposed in details. At first, a few 2D BPs would be revisited with some new interpretation for 2D time-frequency analysis. Then the new generalized BP (GBP) with new spirit of Riesz transform (RT) were derived with novel features. On one hand, various BPs would be employed jointly for image pattern analysis via our particular design. On the other hand, various π/2 phase shifting operations for the multiplicative signal would be systematically performed in 2D images through BPs so that we could obtain more rational image features. Furthermore, the amplitude-phase demodulation method based on GBP for the isotropic image decomposition would be presented as well. The theoretical analysis and comparison experiments on composite and natural images have been presented to demonstrate the efficiency of our contributions in time-frequency analysis and pattern recognition along with feature extraction.

Experimental investigation in induction motors using signal processing techniques for early detection of inter-turn short circuit faults

ABSTRACT This paper presents a method based on advanced signal processing techniques for the detection of inte-rturn short circuit faults in an induction machine. The techniques presented can be classified into power spectral density estimation techniques and time-frequency techniques. The theoretical principles of these methods are presented and their performances are compared from the stator current analysis (MCSA). This article proposes a comparative study of these signal processing techniques. One is based on the power spectral density estimation techniques, such as Periodogram and Welch periodogram. The second method is based on the Hilbert transform (HT) to extract the envelope for the stator current. Then, this signal is processed via discrete wavelet transform (DWT) for determining the faulty components in the spectrum of the stator current envelope and identifying the eigenvalues of energy levels (HDWT). This technique is powerful for the non stationary signal processing. Moreover, the combination HT-DWT has assured its ability to evaluate the severity in detecting faults of the shorted turns and it is effective for nonstationary and stationary signals to extract useful information for the detection of ITSC fault. The techniques have usd experimentally data issued from the induction motor.

Highly Versatile Broadband RF Photonic Fractional Hilbert Transformer Based on a Kerr Soliton Crystal Microcomb

We demonstrate an RF photonic fractional Hilbert transformer based on an integrated Kerr micro-comb source featuring a record low free spectral range of 48.9 GHz, yielding 75 microcomb lines across the C-band. By programming and shaping the comb lines according to calculated tap weights, we demonstrate that the Hilbert transformer can achieve tunable bandwidths ranging from 1.2 to 15.3 GHz, switchable centre frequencies from baseband to 9.5 GHz, and arbitrary fractional orders. We experimentally characterize the RF amplitude and phase response of the tunable bandpass and lowpass Hilbert transformers with 90 and 45-degree phase shift. The experimental results show good agreement with theory, confirming the effectiveness of our approach as a powerful way to implement the standard as well as fractional Hilbert transformers with broad and switchable processing bandwidths and centre frequencies, together with high reconfigurability and greatly reduced size and complexity.

Closed-Loop Drive Detection and Diagnosis of Multiple Combined Faults in Induction Motor Through Model-Based and Neuro-Fuzzy Network Techniques

In this paper, a fault detection and diagnosis approach adopted for an input-output feedback linearization (IOFL) control of induction motor (IM) drive is proposed. This approach has been employed to detect and identify the simple and mixed broken rotor bars and static air-gap eccentricity faults right from the start its operation by utilizing advanced techniques. Therefore, two techniques are applied: the model-based strategy, which is an online method used to generate residual stator current signal in order to indicate the presence of possible failures by means of the sliding mode observer (SMO) in the closed-loop drive. However, this strategy is not able to recognise the fault types and it can be affected by the other disturbances. Therefore, the offline method using the multi-adaptive neuro-fuzzy inference system (MANAFIS) technique is proposed to identify the faults and distinguish them. However, the MANAFIS required a relevant database to achieve satisfactory results. Hence, the stator current analysis based on the HFFT combination of the Hilbert transform (HT) and Fast Fourier transform (FFT) is applied to extract the amplitude of harmonics due to defects occur and used them as an input data set for the MANFIS under different loads and fault severities. The simulation results show the efficiency of the proposed techniques and its ability to detect and diagnose any minor faults in a closed-loop drive of IM.

Multivariable passive method for detection of islanding events in renewable energy based power grids

Penetration of distributed generation resources (DGR) in power grid is rapidly increasing to meet future energy demand efficiently. It helps in mitigating the problems of high carbon emission, green house effect, and increased cost of oil and natural gases. Island formation of a part of the renewable energy based power grid (REPG) creates hazards to operating personnel and equipments. Hence, efficient identification of islanding condition and disconnection of DGR immediately become essential for avoiding damage to equipment, personnel safety hazards and grid protection. This paper investigated a signal processing based passive islanding detection method (IDM) which is effective with the availability of multi-DGR. A islanding detection factor (MIDF) using multi-variables is proposed which is computed using features extracted by processing the voltage signal, negative sequence current (NSC) and negative sequence voltage (NSV) using Stockwell transform (ST) and Hilbert transform (HT). Total harmonic distortions of voltage ( T H D v $THD_{v}$ ) and current ( T H D i $THD_{i}$ ) are also considered to compute MIDF. Islanding event is recognized and differentiated from non-islanding conditions by comparing the MIDF with two threshold values. This method effectively detects the islanding event and discriminates it from the operational and faulty events. IDM has small non-detection zone (NDZ) and low computational time. Performance of IDM is not affected by noisy environment. Effectiveness of the IDM is established by testing for different event incidence angles, various fault impedances, different values of loads and capacitors, and different penetration levels of RE. Efficacy of IDM is established by testing the IDM through an elaborated study on IEEE-13 bus distribution grid interfaced with wind power plant (WPP) and solar power plant (SPP). Further, IDM is effectively implemented to detect the islanding event created on a practical distribution network. Effectiveness of IDM is better in comparison to IDMs designed by applications of discrete wavelet transform (DWT), empirical mode decomposition (EMD), Slantlet Transform and Ridgelet probabilistic neural network (RPNN), artificial neural network (ANN), change in rate of active and reactive power, rate of change of frequency, and rate of change of voltage angle.

Study of Resonance Helical Magnetic Field (RHF) Effect In IR-T1 Tokamak Plasma Using Hilbert-Huang Transform

In the IR-T1 Tokamak the effect of a resonance helical magnetic field (RHF) on plasma confienment are presented using Hilbert-Huang Transform method.Mirnov coil data analyzed by Hilbert-Huang Transform (HHT) and decomposed to the main intrinsic mode functions(imfs) and their instantanous frequencies (IFs). We find that, HHT method can extract MHD activities with different amplitudes in the different times. Then, the IFs of these modes can be calculated by Hilbert Transform (HT). As a comparison of WT and HHT analysis the Hilbert spectrum has much better frequency definition. Amplitude modulation of Mironov oscillations in IR-T1 tokamak plasma generate intra-wave frequency modulation, In the Hilbert spectrum analysis this effect is small compared to the STFT and WT spectrums. In our study, Magnetic islands with frequency around 40 kHz can be seen in wavlet Transform(WT) and HHT results in ohmic and RHF discharges. The HHT results after application of l=2/n=1 resonant field show that, the amplitude of m=2 poloidal MHD mode are amplified and then suppressed for a few milliseconds after amplification. Similarly, the amplitude of the m=3 MHD mode are amplified and then strongly suppressed by the start of the l=3/n=1 resonant field.

Independent Amplitude and Phase Control of Two Orthogonal Linearly Polarised Light and Its Applications

A technique to provide independent control on the amplitude and phase of two orthogonal linearly polarised light is presented. It is based on operating a commercial dual-polarisation dual-drive Mach Zehnder modulator (DPol-DDMZM) in reverse direction that routes the input light in slow and fast axis into two different DDMZMs. The technique has the advantage of controlling the phase of the slow-axis light and the amplitude of the fast-axis light has no effect on the light travelling in the orthogonal polarisation state. It has applications in linearised microwave photonic links, frequency multipliers and microwave phase shifters. A new microwave photonic Hilbert transformer based on using the reverse operating DPol-DDMZM to alter the phase of an RF modulation sideband without affecting the orthogonally polarised optical carrier is developed. Experimental results demonstrate 24.3 dB attenuation in the fast-axis light with no change in the slow-axis light, and 0°–360° RF phase shift for only 3.3 V change in DC voltage. The new Hilbert transformer with less than 2.5° phase imbalance and 0.4 dB amplitude ripples over 4–18 GHz frequency range is also demonstrated.

Spatiotemporal evolution of a self-excited dust density wave in a nanodusty plasma under strong Havnes effect

A broad-spectrum self-excited dust density wave is experimentally studied in a vertically extended nanodusty plasma consisting of in situ grown carbonaceous nanometer sized particles. The nanodusty plasma having high particle density (of the order of 1012–1013 m−3) is created with vertical extension up to (40±0.1) cm and radial extension up to (5±0.1) cm. The propagation of the self-excited dust density wave under strong Havnes effect is examined over a large axial distance (19±0.1) cm. Time-resolved Hilbert transformation and Fast Fourier transformation techniques are used to study the spatiotemporal evolution of frequency and wavenumbers along three directions from the dust void, viz., axial, radial, and oblique. The propagation is found to be inhomogeneous throughout the dust cloud. The phase velocity of the wave is estimated to be quite low and decreasing along the direction of propagation. This effect is attributed to the strong reduction of particle charge due to a high Havnes parameter along the propagation direction. By the estimation of average particle charge, ion density, and the finite electric field throughout the nanodust cloud, a quantitative analysis of the void formation in nanodusty plasma is presented. New insights are also made regarding wave merging phenomena using time-resolved Hilbert transformation.

Optical diagnostics of hydrogen-air diffusion flame

Work motivation – adaptation of optical Hilbert diagnostic methods for visualization and study of optical density and phase temperature fields in the structure of an axisymmetric diffusion hydrogen-air flame. The diagnostic complex is implemented on the basis of the IAB-451 device with modified blocks of optical filtering, information source and processing. A laminar jet flame H2/N2 in still air is considered. The investigated torch is oriented vertically. Visualization of phase disturbances induced by the medium under study in a multi-wavelength probing (λ1 = 636 nm, λ2 = 537 nm and λ3 = 466 nm) light field is performed using polychromatic Hilbert and Foucault-Hilbert transformations in combination with registration and pixel-by-pixel processing of the dynamic RGB image structure. The dynamic phase structure of the diffusion flame is visualized. The initial temperature approximation, based on the assumption of an air mixture, is corrected so that the calculated hilbertogram matches the measured one as closely as possible. The data obtained are in good agreement with the results of thermocouple measurements. The temperature was recorded by thermocouples at reference points. The phase function is reconstructed in axisymmetric sections from RGB-hilbertograms. The reliability of the results is confirmed by comparing the experimentally obtained hilbertograms and hilbertograms reconstructed from phase structures using the Abel transform.

Reply to “Response to ‘Limitations in the Hilbert Transform Approach to Locating Solar Cycle Terminators’ by R.J. Booth”

Reply to “Response to ‘Limitations in the Hilbert Transform Approach to Locating Solar Cycle Terminators’ by R.J. Booth”

A pipeline for phase-based analysis of in vitro micro-electrode array recordings of gastrointestinal slow waves.

Motility of the gastrointestinal tract (GI) is governed by an bioelectrical event termed slow waves. Accurately measuring the characteristics of GI slow waves is critical to understanding its role in clinical applications. High-resolution (HR) bioelectrical mapping involves placing a spatially dense array of electrodes directly over the surface of the GI wall to record the spatiotemporal changes in slow waves. A micro-electrode array (MEA) with spatial resolution of 200 μm in an 8x8 configuration was employed to record intestinal slow waves using isolated tissues from small animals including rodents, shrews and ferrets. A filtering, processing, and analytic pipeline was developed to extract useful metrics from the recordings. The pipeline relied on CWT and Hilbert Transform to identify the frequency and phase of the signals, from which the individual activation times of slow waves were identified and clustered using k-means. A structural similarity index was applied to group the major activation patterns. Overall, the pipeline identified 91 cycles of slow waves from 300 s of recordings in mice, with an average frequency of 20.68 ± 0.71 cpm, amplitude of 7.94 ± 2.15 µV, and velocity of 3.64 ± 1.75 mm s-1. Three major propagation patterns were identified during this period. The findings of this study will inform the development of a high throughput software platform for future in vitro pharmacological studies using the MEA.

Spectrum Aggregation Dual-Band Real-Time RF/Microwave Analog Signal Processing From Microstrip Line High-Frequency Hilbert Transformer

A uniplanar microstrip line RF/microwave real-time analog signal processing (RAP) units are proposed in this article to operate concurrently at two frequencies for spectrum aggregation applications. First, a fundamental building block novel microstrip line dual-band Hilbert transformer (DBHT) is developed by integrating a dual-band 180° coupler and a dual-band delay line (DBD). The theoretical analysis is carried out to determine the relation of coupler and delay line forming closed loop resonance in the proposed circuit topology. Then, a dual-band edge detector from DBHT and a dual-band single-sideband (DBSSB) modulator composed of dual-band power divider/combiner (DBPD/DBPC), DBHT, and DBD are developed for dual-band real-time RF/microwave signal processing. To verify the proposed concept, a prototype of microstrip line DBHT working at 0.9 and 1.98 GHz is designed, and the measurement and simulation agree well with theoretical analysis. To demonstrate the real-time RF/microwave analog signal processing, a dual-band edge detector composed of DBHT is verified in the experiment. Furthermore, a prototype of microstrip line DBSSB modulator is fabricated and validated in the experiment to demonstrate the real-time single-sideband modulation at two concurrent RF/microwave frequencies.

Integral order photonic RF signal processors based on a soliton crystal micro-comb source

Soliton crystal micro-combs are powerful tools as sources of multiple wavelength channels for radio frequency (RF) signal processing. They offer a compact device footprint, a large number of wavelengths, very high versatility, and wide Nyquist bandwidths. Here, we demonstrate integral order RF signal processing functions based on a soliton crystal micro-comb, including a Hilbert transformer and first, second and third-order differentiators. We compare and contrast the results and the trade-offs involved with varying the comb spacing, and tap design and shaping methods.

A Comprehensive Evaluation for the Tunnel Conditions with Ground Penetrating Radar Measurements

We aim to develop a comprehensive tunnel lining detection method and clustering technique for semi-automatic rebar identification in order to investigate the ten tunnels along the South-link Line Railway of Taiwan (SLRT). We used the Ground Penetrating Radar (GPR) instrument with a 1000 MHz antenna frequency, which was placed on a versatile antenna holder that is flexible to the tunnel’s condition. We called it a Vehicle-mounted Ground Penetrating Radar (VMGPR) system. We detected the tunnel lining boundary according to the Fresnel Reflection Coefficient (FRC) in both A-scan and B-scan data, then estimated the thinning lining of the tunnels. By applying the Hilbert Transform (HT), we extracted the envelope to see the overview of the energy distribution in our data. Once we obtained the filtered radargram, we used it to estimate the Two-dimensional Forward Modeling (TDFM) simulation parameters. Specifically, we produced the TDFM model with different random noise (0–30%) for the rebar model. The rebar model and the field data were identified with the Hierarchical Agglomerative Clustering (HAC) in machine learning and evaluated using the Silhouette Index (SI). Taken together, these results suggest three boundaries of the tunnel lining i.e., the air–second lining boundary, the second–first lining boundary, and the first–wall rock boundary. Among the tunnels that we scanned, the Fangye 1 tunnel is the only one in category B, with the highest percentage of the thinning lining, i.e., 13.39%, whereas the other tunnels are in category A, with a percentage of the thinning lining of 0–1.71%. Based on the clustered radargram, the TDFM model for rebar identification is consistent with the field data, where k = 2 is the best choice to represent our data set. It is interesting to observe in the clustered radargram that the TDFM model can mimic the field data. The most striking result is that the TDFM model with 30% random noise seems to describe our data well, where the rebar response is rough due to the high noise level on the radargram.

Multi-peak detection algorithm based on wavelength feature recognition in FBG sensor networks

We propose an improved Gaussian curve fitting method based on the Hilbert transformation (HTG) to tackle the ineffectiveness of the traditional peak-seeking algorithm in detecting the multi-peak Fiber Bragg grating (FBG) reflection spectra. A five-point sliding filter is used to process the FBG reflection spectral signal, de-noise and smooth the noise, and select the optimal threshold point by the Hilbert transformation (HT). The sub-spectra of the multiple FBG reflection spectral signals were derived and the initial positioning of the spectral peaks were achieved. The Levenberg–Marquardt (LM) algorithm is used to extract the Bragg wavelength from the segmented sub-spectral signals as well as optimize the Gaussian curve fitting coefficients. The HTG-LM algorithm is then proposed, and is optimized and utilized to achieve precise positioning of the spectral peaks. The theoretical analysis and experimental results showed that the proposed HTG-LM algorithm could dynamically detect the multiple reflection spectra of the FBG sensing system with good stability, and at the same time, reduce the amount of peak-seeking data, which is highly beneficial to improve the signal demodulation rate. The peak detection accuracy of the proposed algorithm is better than 1 pm and the precision is better than 4 × 10 − 7 pm, which indicates that this HTG-LM algorithm provides an accurate demodulation algorithm for the FBG sensor networks. As a result, it is a promising multi-peak detection algorithm proposed by this paper to be applied to the FBG sensing systems.

Arrhythmia Detection using Pan-Tompkins Algorithm and Hilbert Transform with Real-Time ECG Signals

Electrocardiography (ECG) is a form of examination based on printing on millimetric paper the contraction and relaxation phases of the atria and ventricles of the heart, the electrical activity that occurs during the stimulation of the heart and the transmission of the stimulus. For the first diagnosis of diseases such as heart attacks, it is very important to make this preliminary impression and inform the doctor and patient as soon as possible.In this study, any arrhythmia risk can be determined by examining the heart rate and QRS width values calculated by graphing the signal value coming from the electrodes of the Electrocardiography monitor taken for heart rhythm monitoring in hospitals and by detecting the QRS points from the signal data with the Pan Tompkins algorithm and Hilbert Transform method. The image of the ECG graph and the signal analysis results, which are the result of the graphing of the data, can be sent via e-mail. In line with the values obtained in this study, it has been determined that the Pan Tompkins algorithm's signal detection accuracy, sensitivity and accurate prediction ratio gives better results than Hilbert Transform method during the detection of peaks from ECG signals.

Enhanced BOTDA Sensors Based on Brillouin Phase Recovery Using Kramers-Kronig Relation

We have proposed and demonstrated an enhanced Brillouin optical time-domain analysis (BOTDA) sensing system with fast measurement speed based on the Brillouin phase recovery using Kramers-Kronig (KK) relation. The non-Lorentz Brillouin gain spectrum (BGS) and Brillouin phase spectrum (BPS) measured by BOTDA are theoretically validated to satisfy KK relation and hence the BPS is digitally recovered by performing Hilbert Transform (HT) to the measured BGS. The recovery of the whole BPS along the 45km fiber only consumes 0.3s. Both simulation and experiment have been carried out to analyze the quality of the recovered BPS under various conditions. By making use of the excellent linearity of the recovered BPS, we accelerate the data processing speed by three times through Linear Fitting (LF) of BPS, without compromise of the sensing accuracy. With implementation of simple HT and LF, this scheme does not need modification of the BOTDA setup and complicated data processing algorithm, which would be a practical way for applications where fast measurement speed is needed, especially in long-distance and high-spatial resolution sensing.

Ranging system based on optical carrier-based microwave interferometry.

To compensate for the refractive index errors in optical carrier-based microwave interferometry (OCMI), a ranging system is designed to measure the single-arm optical path of OCMI. A high-speed photodetector and a downconversion method are used to acquire the microwave envelope of the interference signal. A Hilbert transformation is used to realize phase detection. Simulation shows the linear relationship between the phase and optical length in a period. Adjusting the microwave frequency can resolve the phase ambiguity. The experimental results show that when the maximum microwave modulation frequency is set to 1.5 GHz, the standard deviation of the measured data can be limited to the level of 10-5.

Identification of Linear Time-Variant Systems Based on Ensemble Empirical Mode Decomposition and Hilbert Transform

This paper proposes an identification method based on ensemble empirical mode decomposition (EEMD) and Hilbert transform. The main procedures are: First, the system responses of an n degrees of freedom (DOFs) system are decomposed into intrinsic mode functions (IMFs) and residues by EEMD. The obtained ensemble mean IMFs and residues are then analysed by the Hilbert Transform to form the corresponding analytical signals. Second, the analytical signals of the n IMFs and the residue of each system response of each DOF are added to form a new analytical response. Third, the system equation of motion is rewritten into complex matrix equations for parameter identification. Numerical simulations are carried out on multi-DOFs systems with varying system parameters to demonstrate good robustness, effectiveness and accuracy of the proposed method, which attempts to offer a new means to study identification for linear time variant systems.