Hilbert Transform Research Articles

Synthesis of Kantil Tone Using The Frequency Modulation Method

Music is a creative form of expression that utilizes sound arranged in specific patterns to create artistic works that are enjoyable to the listener. However, in music, excessive or continuous exposure to loud sounds can damage the hair cells in the ear, potentially leading to hearing loss or even deafness. One challenge in musical instrument craftsmanship is the variation in sound produced by different kantil artisans. These differences in sound output lead to inconsistencies in the rhythm of the angklung gamelan in Bali. This research addresses the issue by focusing on the process of synthesizing kantil sounds to achieve a more consistent output. The research begins by inputting audio files for each sound bar in format. The recorded audio data undergoes preprocessing using the Fast Fourier Transform (FFT) method, which extracts key features from the dataset, such as the fundamental frequency. Additionally, the Hilbert Transform is applied to obtain the optimal sound each blade, which will later be used in the Frequency Modulation process. Once preprocessing is completed on the dataset for each blade, the fundamental frequency and signal are acquired. To evaluate the accuracy of the synthesis, the Root Mean Square Error (RMSE) is calculated to compare the original signal with the synthesized signal. This step helps determine the degree of difference between the two signals. Ultimately, the result is a synthesized kantil sound that closely resembles the original, helping to standardize sound output among different craftsmen and ensuring consistency in musical performances

A Highly Accurate Double-Ended Traveling Wave Fault Location Method Using GWO-VMD and the Hilbert Transform for Offshore MMC-MTDC Grids

Accurate and reliable DC fault location methods can significantly enhance the resilience and reliability of offshore MMC-based multi-terminal direct current (MTDC) grids. This research proposes a novel double-ended DC fault location method using the GWO-VMD and the Hilbert transform. First, the propagation of traveling waves (TWs) in the faulty line-mode network is described, leading to the theoretical expressions for the Backward Line-mode Voltage TWs (BLVTWs). Next, the Grey Wolf Optimizer-Variational Mode Decomposition (GWO-VMD) algorithm is employed to extract the high-frequency components contained in the measured BLVTWs, and the Hilbert transform is used to obtain the Instantaneous Energy Spectrum (IES) of the specific IMFs, allowing for the determination of the arrival times of the TWs. Numerous simulations in the PSCAD/EMTDC and RTDS environments confirm that the fault location method is accurate under various sampling frequencies and for close-in faults. Comparison studies also demonstrate that the proposed method is more accurate than existing classical TW-based methods. Additionally, the RTDS tests show that the method can withstand noise disturbances of at least 30 dB and has the potential to be applied in real projects.

Enhancing Radar Tracking Accuracy Using Combined Hilbert Transform and Proximal Gradient Methods

Accurate radar tracking is crucial in defense, navigation, and surveillance applications, where high precision and resilience to noise are essential. Traditional radar tracking techniques, such as Kalman Filters and Particle Filters, often struggle with performance limitations in noisy and non-linear environments, leading to inaccuracies in target tracking. To address these challenges, we propose a hybrid radar tracking approach combining the Hilbert Transform with the Proximal Gradient Method within a convex optimization framework. This combination leverages the Hilbert Transform's signal enhancement capabilities with the Proximal Gradient Method's optimization strength, improving accuracy and robustness under challenging conditions. Experimental results demonstrate that the proposed method achieves a 23% reduction in Mean Squared Error (MSE) and a 20% increase in tracking accuracy compared to conventional methods, alongside a Signal-to-Noise Ratio (SNR) of approximately 18.3 dB, indicating superior noise resilience. While the hybrid method offers significant improvements, it does involve increased computational complexity and may be sensitive to initial parameter settings, requiring careful tuning for optimal performance. Nevertheless, this method represents a promising advancement over traditional techniques, providing a more accurate and resilient solution for modern radar tracking applications.

Fourier Hilbert: The Input Transformation to Enhance CNN Models for Speech Emotion Recognition

Signal processing in general, and speech emotion recognition in particular, have long been familiar Artificial Intelligence (AI) tasks. With the explosion of deep learning, CNN models are used more frequently, accompanied by the emergence of many signal transformations. However, these methods often require significant hardware and runtime. In an effort to address these issues, we analyze and learn from existing transformations, leading us to propose a new method: Fourier Hilbert Transformation (FHT). In general, this method applies the Hilbert curve to Fourier images. The resulting images are small and dense, which is a shape well-suited to the CNN architecture. Additionally, the better distribution of information on the image allows the filters to fully utilize their power. These points support the argument that FHT provides an optimal input for CNN. Experiments conducted on popular datasets yielded promising results. FHT saves a large amount of hardware usage and runtime while maintaining high performance, even offers greater stability compared to existing methods. This opens up opportunities for deploying signal processing tasks on real-time systems with limited hardware.

Detecting damage on engine mounts using hilbert-huang transform vibration analysis

Engine mounts, which are usually composed of elastomeric materials like rubber that can absorb excessive vibrations, are built to withstand vibration sources from engines. Engine mounts may eventually degrade from extended use. When rubber products age or sustain damage, they may grow harder and crack. Engine mounts need to be maintained regularly to ensure optimal performance. Visual examinations and the detection of excessive vibrations can be used to accomplish this. Vibration sensors are mounted on the engine mount in axial, vertical, and horizontal orientations using a vibration detection technique utilizing the Hilbert-Huang Transform (HHT) methodology. Matlab is used to examine the data that is gathered at three distinct rotational speeds: 750 rpm, 2000 rpm, and 3000 rpm. The HHT approach combines two key components: the Hilbert Transform, which analyzes the time-frequency signal of the first decomposition until only residuals remain, and Empirical Mode Decomposition (EMD), which breaks down the signal into Intrinsic Mode Functions (IMFs). According to test data, a damaged mount had an amplitude of 0.00005212 m/s² and a frequency of 8 Hz. On the other hand, in typical circumstances, the highest frequency was 7 Hz with the same amplitude. Five frequency increases were made in the damaged mount throughout this operation. In the damaged mount, the Hilbert Transform showed a frequency of 2124 Hz with an amplitude of 0.007594 m/s², indicating a significant resonance. This illustrates how the Hilbert-Huang Transform's capacity to handle non-stationary and nonlinear signal forms allows it to detect damage in components efficiently

Ambiguity-Free, Multiparametric, and Multipoint Fiber Refractometer Based on the Hilbert Transform

Ambiguity-Free, Multiparametric, and Multipoint Fiber Refractometer Based on the Hilbert Transform

Bridge modal identification method based on adaptive VMD-HT algorithm

ABSTRACT Bridge engineering structures play a crucial role in transportation. Traditional methods of road and bridge closures for inspection and evaluation, while effective, increase bridge inspection costs and disrupt normal traffic flow. Therefore, a rapid detection and evaluation method for bridge structural modal parameters in the operational state is more suitable for practical engineering applications. However, under real operating conditions, bridge vibration signals typically contain a large amount of noise and interference, and modal identification must overcome issues of non-stationarity and non-linearity in the vibration signals caused by vehicle loads and environmental changes to ensure the accuracy of the identification. This study replaces the traditional Empirical Mode Decomposition algorithm in the Hilbert-Huang Transform with the Variational Mode Decomposition algorithm. It proposes a new method that combines the VMD algorithm with the Hilbert Transform, referred to as the Variational Mode Decomposition-Hilbert Transform method. Compared to the EMD algorithm, it offers significant improvements in suppressing mode mixing and endpoint effects. A vehicle-bridge coupling model was constructed, and the bridge’s natural modal information was successfully extracted from the vibration response signals. The research results indicate that the improved algorithm offers higher accuracy and faster computational speed compared to traditional identification algorithms.

A complex neural network model by Hilbert Transform

The phase information of the optical wave plays a vital role in processing wave-related signals. In deep learning fields, complex-valued neural networks are put forward on the concept of complex amplitudes for full utilization of phase information. To build a complex-valued neural network, the common way is to exploit Fourier Transform of the observed signal to extract amplitude and phase information. However, this will lead to spectrum waste for a real-valued signal by introducing negative frequencies that have no physical meaning. To this end, we attempt to use Hilbert Transform as an alternative to yield a single sideband spectrum and avoid negative frequencies from interacting with positive ones. On the other hand, Fourier transform is a global analysis thus it tells nothing about the time domain. As our key insight, we further explore the usage of instantaneous frequency calculated by Hilbert Transform and propose a new method of constructing complex input from a time–frequency angle. Simple pixel-wise classification experiments are carried out on two hyperspectral datasets and MNIST dataset. Experimental results have demonstrated that Hilbert Transform with instantaneous frequency performs better by a large margin than Fourier Transform owing to the additional time information.

Emphasizing on the envelope spectra of hydraulic turbomachinery vibration response towards cavitation diagnosis

Cavitation attracts the interest of engineers who target the better understanding of its complex physics and the development of efficient detection tools. This research explores the effectiveness of vibration-based indicators in the prompt and effective diagnosis of cavitation initiating in the rotating flow fields of turbomachinery. The indicators are derived from the envelope spectra estimated with the use of Hilbert Transform, Spectral Kurtosis and Cyclic Spectral Correlation algorithms and data acquired from two semi-open impellers. By utilizing a transparent casing, the onset of cavitation can be observed, enabling the establishment of reliable criteria for evaluating the new indicators. Also, their applicability is assessed across a wide range of flow-rate and suction pressure conditions and in two different geometries. The results demonstrate the consistent ability of the indicators to exploit the high frequency carrier information related with the resonances excited from bubble implosions, to promptly and efficiently detect the phenomenon.

Hilbert Transform Applications to Asynchronous Demodulation Methods for RZ SSB, Multichannel ISB and ISB-Based AM Stereo Modulated Signals Propagating through Fading Path

Hilbert Transform Applications to Asynchronous Demodulation Methods for RZ SSB, Multichannel ISB and ISB-Based AM Stereo Modulated Signals Propagating through Fading Path

Optimizing real-time phase detection in diverse rhythmic biological signals for phase-specific neuromodulation.

Closed-loop, phase-specific neurostimulation is a powerful method to modulate ongoing brain activity for clinical and research applications. Phase-specific stimulation relies on estimating the phase of an ongoing oscillation in real time and issuing a control command at a target phase. Phase detection algorithms based on Fast Fourier transform (FFT) are widely used due to their computational efficiency and robustness. However, it is unclear how algorithm performance depends on the spectral properties of the input signal and how algorithm parameters can be optimized. We used offline simulation to evaluate the performance of three algorithms (endpoint-corrected Hilbert Transform, Hilbert Transform and phase mapping) on three rhythmic biological signals with distinct spectral properties (rodent hippocampal theta potential, human EEG alpha and human essential tremor). First, we found that algorithm performance was more strongly influenced by signal amplitude and frequency variation compared with signal to noise ratio. Second, our simulations showed that the size of the data window for phase estimation was critical for the performance of FFT-based algorithms, where the optimal data window corresponds to the period of the oscillation. We validated this prediction with real time phase detection of hippocampal theta oscillations in freely behaving rats performing spatial navigation. Our findings define the relationship between signal properties and algorithm performance and provide a convenient method for optimizing FFT-based phase detection algorithms.

A Ground-Penetrating Radar-Based Study of the Structure and Moisture Content of Complex Reconfigured Soils

To increase the detection accuracy of soil structure and moisture content in reconstituted soils under complex conditions, this study utilizes a 400 MHz ground-penetrating radar (GPR) to examine a study area consisting of loess, sandy loam, red clay, and mixed soil. The research involves analyzing the single-channel waveforms and two-dimensional images of GPR, preprocessing the data, obtaining envelope information via amplitude envelope detection, and performing a Hilbert transformation. This study employs a least squares fitting approach to the instantaneous phase envelope to ascertain the thickness of various soil layers. By utilizing the average envelope amplitude (AEA) method, a correlation between the radar’s early signal amplitude envelope and the soil’s shallow dielectric constant is established to invert the moisture content of the soil. The analysis integrates soil structure and moisture distribution data to investigate soil structure characteristics and moisture content performance under diverse soil properties and depths. The findings indicate that the envelope detection method effectively identifies stratification boundaries across different soil types; the AEA method is particularly efficacious in inverting the moisture content of reconstituted soils up to 3 m deep, with an average relative error ranging from 2.81% to 7.41%. Notably, moisture content variations in stratified reconstituted soils are more pronounced than those in mixed soil areas, displaying a marked stepwise increase with depth. The moisture content trends in the vertical direction of the same soil profile are generally consistent. This research offers a novel approach to studying reconstituted soils under complex conditions, confirming the viability of the envelope detection and AEA methods for intricate soil investigations and broadening the application spectrum of GPR in soil studies.

Bearing Faults Diagnosis by Current Envelope Analysis under Direct Torque Control Based on Neural Networks and Fuzzy Logic—A Comparative Study

Diagnosing bearing defects (BFs) in squirrel cage induction machines (SCIMs) is essential to ensure their proper functioning and avoid costly breakdowns. This paper presents an innovative approach that combines intelligent direct torque control (DTC) with the use of Hilbert transform (HT) to detect and classify these BFs. The intelligent DTC allows precise control of the electromagnetic torque of the asynchronous machine, thus providing a quick response to BFs. Using HT, stator current is analyzed to extract important features related to BFs. The HT provides the analytical signal of the current, thus facilitating the detection of anomalies associated with BFs. The approach presented incorporates an intelligent DTC that adapts to stator current variations and characteristics extracted via the HT. This intelligent control uses advanced algorithms such as neural networks (ANN-DTCs) and fuzzy logic (FL-DTCs). In this paper, a comparison between these two algorithms was performed in the MATLAB/Simulink environment for a three-phase asynchronous machine to evaluate their effectiveness under the proposed approach. The results obtained demonstrated a high ability to detect and classify BFs, confirming the effectiveness of each algorithm. In addition, this comparison highlighted the specific advantages and disadvantages of each approach. This information is valuable in choosing the most suitable algorithm according to the constraints and specific needs of the application.

Performance enhancement of classifiers through Bio inspired feature selection methods for early detection of lung cancer from microarray genes

Gene expression in the microarray is assimilated with redundant and high-dimensional information. Moreover, the information in the microarray genes mostly correlates with background noise. This paper uses dimensionality reduction and feature selection methods to employ a classification methodology for high-dimensional lung cancer microarray data. The approach is enforced in two phases; initially, the genes are dimensionally reduced through Hilbert Transform, Detrend Fluctuation Analysis and Least Square Linear Regression methods. The dimensionally reduced data is further optimized in the next phase using Elephant Herd optimization (EHO) and Cuckoo Search Feature selection methods. The classifiers used here are Bayesian Linear Discriminant, Naive Bayes, Random Forest, Decision Tree, SVM (Linear), SVM (Polynomial), and SVM (RBF). The classifier's performances are analysed with and without feature selection methods. The SVM (Linear) classifier with the DFA Dimensionality Reduction method and EHO feature selection achieved the highest accuracy of 92.26 % compared to other classifiers.

Online Stator Interturn Fault Detection Using Hilbert Transform and Neural Network for Traction Motors of Urban Rail Vehicles

Online Stator Interturn Fault Detection Using Hilbert Transform and Neural Network for Traction Motors of Urban Rail Vehicles

Hilbert Transformation and Properties of Solar Cycles in Envelope−Instantaneous Frequency Variables

Hilbert Transformation and Properties of Solar Cycles in Envelope−Instantaneous Frequency Variables

A Stable Forward Modeling Approach in Heterogeneous Attenuating Media Using Reapplied Hilbert Transform

In the field of geological exploration and wave propagation theory, particularly in heterogeneous attenuating media, the stability of numerical simulations is a significant challenge for implementing effective attenuation compensation strategies. Consequently, the development and optimization of algorithms and techniques that can mitigate these numerical instabilities are critical for ensuring the accuracy and practicality of attenuation compensation methods. This is essential to reveal subsurface structure information accurately and enhance the reliability of geological interpretation. We present a method for stable forward modeling in strongly attenuating media by reapplying the Hilbert transform to eliminate increasing negative frequency components. We derived and validated new constant-Q wave equation (CWE) formulations and a stable solving method. Our study reveals that the original CWE equations, when utilizing the analytic signal, regenerate and amplify negative frequencies, leading to instability. Implementing our method maintains high accuracy between analytical and numerical solutions. The application of our approach to the Chimney Model, compared with results from the acoustic wave equation, confirms the reliability and effectiveness of the proposed equations and method.

Study of the results of Hilbert transformation for some fractional derivatives

ABSTRACT Caputo Fractional Derivative is a base for the Riemann-Liouville Derivative, Katugampola fractional derivative, and other fractional derivatives. In this paper, we have illustrated several critical features of the Caputo Derivative via Hilbert Transformation that have not yet been discussed. We have also investigated the behavior of the Riemann-Liouville integral and studied the results of the k-Riemann-Liouville fractional integral with the applications of Hilbert transformation.

Theoretical analysis of the scattering characteristics of blasting stress waves at an arc-shaped interface crack in a deep rock mass with high in-situ stress

A mathematical model of blasting stress wave scattering at an arc-shaped interface crack is established to theoretically analyze and verify the scattering characteristics of blasting stress waves at an arc-shaped interface crack in a deep rock mass with high in-situ stress. Based on the continuum mechanics, finite deformation, and incremental stress theories and the geometric and physical characteristics of the arc-shaped interface crack, the mathematical model includes a set of the first class of singular integral equations with Hilbert kernels. The opening and dislocating displacements of the arc-shaped interface crack and the effective stress components of scattered stress waves are numerically calculated and discussed with the variation of the type, frequency, and incident angle of the blasting stress wave; the curvature radius and opening angle of the arc-shaped interface crack. The condition that the dynamic stress intensity factors and energy release rates at the upper and lower tips of the arc-shaped interface crack reach peak are also provided. It is found that when the frequency of the blasting stress wave and the curvature radius of the arc-shaped interface crack increase, the peaks of the above dynamic stress intensity factors will increase further, and the arc-shaped interface crack is more likely to expand or destabilize. Although the order of in-situ stress is much smaller than that of Young’s modulus of the deep rock mass, it increases the effective stress concentration of scattered stress waves and the opening and dislocating displacements of the arc-shaped interface crack. These findings will provide theoretical guidance for analyzing the cracking characteristics of blasting stress waves in deep rock masses with high in-situ stress.

Ultrasonic wave characteristics in multiscale cementitious materials at different stages of hydration

Monitoring the microstructural change in cementitious materials during hydration is an essential but challenging task. Therefore, a non-invasive and sophisticated technique is warranted to understand the microscopic behaviour of the multiphase cementitious materials (where the length scale of the constituents varies from centimeters to micrometers) in different stages of hydration. Due to exothermic hydration reactions, different hydration products start to evolve with individual mechanical properties. In concrete, an interface transition zone (ITZ) appears between the aggregate surface and paste matrix, which influences the overall properties of concrete material. In the present research, 1) several wave characteristics, such as wave velocity, energy distribution, and signal phase are found out using Ultrasonic Pulse Velocity (UPV), Wavelet Packet Energy (WPE) and Hilbert Transform (HT) methods, to monitor the hydration mechanism (1d-28d) in cement-based materials with two levels of heterogeneities (cement paste and concrete, representing microscale and mesoscale, respectively). Also, the unique nonlinear behaviour is studied in the frequency domain using the promising Sideband Energy Ratio (SER) and Sideband Peak Count Index (SPC-I) methods. 2) Numerical simulations are carried out to understand the wave interaction in the developing microstructure. A discretized microstructure of cement shows microscopic details of each phase at any instant of hydration (e.g., formation stage and after complete maturity level). The experimental and numerical investigations on the characteristics of the nonlinear ultrasonic wave propagation show the impact of microstructural development of multi-scale cementitious materials during hydration.