Cracks in planetary gearbox casings generate additional vibration responses, which may be used for monitoring structural degradations. This paper provides a signal processing framework to effectively track casing crack-related features in planetary gearboxes using the carrier synchronous signal average (C-SSA). The proposed algorithm is based on processing the hunting-tooth synchronous signal average (H-SSA) to extract the C-SSA which contains the cyclic interaction between the gear loadings and the corresponding casing response. The root mean square (RMS) of the C-SSA signal can then serve as a health condition indicator (CI) to track crack propagation. Further enhancement can be achieved by applying the Hilbert transform (HT) on the C-SSA using the full bandwidth to derive squared envelope signal, which enhances the trending capability. To remove cyclic temperature influences observed in the trends, singular spectrum analysis technique (SSAT) has been used to ensure that the trend reflects the changes purely due to the damage progression. Experiments using three casing-mounted sensors show good capability to track crack progression. Tests under 100%, 125%, and 150% load levels show consistent performance across these operating conditions, with better results seen at higher loads. The results demonstrate that C-SSA and its squared envelope signal effectively enhance the sensitivity and reliability of vibration-based casing crack detection, providing a practical tool for long-term structural health monitoring of planetary gearboxes.

Alzheimer's disease (AD) and frontotemporal dementia (FTD) are neurodegenerative disorders where early detection is vital. However, the need for long-term monitoring is incompatible with data-scarce settings, and methods trained on one subject often fail on another due to cross-subject variability. To address these limitations, this study proposes a cross-subject, single-channel electroencephalography (EEG)-based method that uses Multi-Entropy Feature Concatenation (MEFC) to classify AD and FTD. First, single-channel EEG is processed through the Discrete Wavelet Transform (DWT) to extract five rhythms: delta, theta, alpha, beta, and gamma. Subsequently, Permutation Entropy (PE), Singular Spectrum Entropy (SSE), and Sample Entropy (SE) are calculated for each rhythm and concatenated to form a combined MEFC to characterize the non-linear dynamic properties of EEG. Lastly, Dynamic Time Warping (DTW), Pearson Correlation Coefficient (PCC), Wavelet Coherence (WC), and Hilbert Transform Correlation (HTC) are employed to measure the similarity between unknown rhythmic MEFC and those from AD, FTD, and Healthy Control (HC) groups, performing a data-driven classification via similarity measurement. Experimental results on 88 subjects in the AHEPA dataset demonstrate that the beta-rhythm with PCC yields a three-class accuracy of 76.14% using single-channel FP2. In another dataset, the Florida-Based dataset, involving 48 subjects, theta-rhythm with WC achieves a two-class accuracy of 83.33% using FP2. Furthermore, a MATLAB R2023b-based toolbox is developed using the proposed method. Such outcomes are impressive, given the limited data per individual (data-efficient), reliable performance across new subjects (cross-subject), and compatibility with wearable devices (single-channel), providing a novel entropy-based approach for EEG-based applications in biomedical engineering.

Dynamic monitoring and modal identification of super high‐rise buildings using <scp>GNSS</scp> ‐ <scp>RTK</scp> in combination with the <scp>ICEEMDAN</scp> ‐ <scp>ICA</scp> / <scp>HT</scp> ‐ <scp>FFT</scp> method

This paper proposes an improved variational mode decomposition (VMD) framework integrated with the Hilbert transform (HT) for decomposing and reconstructing nonstationary signals in high-noise, multi-frequency environments. Unlike traditional VMD methods, the proposed framework introduces a soft data fidelity constraint and a frequency alignment scheme to mitigate the effects of heavy-tailed noise and reduce mode mixing. Employing adaptive regularization in the transform domain further refines intrinsic mode extraction, capturing finer multi-scale details. An additional amplitude matching stage, driven by an LMS-based mechanism, adjusts gain factors to rebuild each component accurately. Experiments on synthetic signals demonstrate improved noise suppression and mode separation, as evidenced by lower RMSE/MAE and higher SNR and correlation values compared to traditional VMD. Across SNRs of 10, 15, and 20 dB, the proposed method consistently outperforms traditional VMD in RMSE/MAE, SNR, and correlation. Hilbert spectra for the two-tone signal and the real bearing signal exhibit sharper ridges and more concentrated energy, indicating improved mode separation and noise suppression. Furthermore, the HT-based timefrequency representation clearly illustrates energy concentration and instantaneous frequency variations, enabling time-frequency analysis of complex, nonstationary signals. These results underscore the potential of the improved VMD-HT framework for a wide range of applications in engineering, energy, and biomedical contexts, where robust, adaptive, and precise signal processing is critical.

Tunable diode laser absorption spectroscopy (TDLAS) based on wavelength modulation spectroscopy (WMS) is widely used for gas concentration measurement due to its rapid detection, high accuracy, and non-destructive nature. However, traditional WMS produces unreliable results for residual oxygen detection in pharmaceutical vials due to laser attenuation caused by glass walls. Although advanced methods such as ln-WMS and WMS-2<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i>/<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> attempt to overcome this limitation, they suffer from algorithmic inflexibility or high computational cost. This paper introduces ln-Hilbert-WMS, an improved technique that integrates natural logarithm processing with the Hilbert transform. This method effectively isolates gas absorption components from laser intensity variations while simultaneously enabling harmonic extraction, laser intensity elimination, and offset noise suppression. A detection system for oxygen within pharmaceutical vials is established for validation. Experimental results demonstrate that the method can accurately measure the oxygen concentration without being affected by variations in vial transmittance. Furthermore, comparative analysis under different offset-noise conditions, together with FPGA implementation results, shows that the proposed method provides greater algorithmic generality than ln-WMS while requiring lower computational cost than WMS-2<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i>/<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i>. In pharmaceutical vial testing, ln-Hilbert-WMS achieves the best detection performance, with a standard deviation of 0.45% and an RMSE of 0.51%, outperforming traditional WMS, ln-WMS, and WMS-2<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i>/<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> techniques.

Heart rate variability (HRV) comprises several components driven by various internal processes, the least understood of which is the ultra-low frequency (ULF) one. Recently published research has shown that the HRV frequency distribution in this range is bimodal. The main aims of this work were to verify this finding, to determine the basic characteristics of these two components and to analyze their potential physiological couplings. For this purpose, two components within the conventional ULF band (below 4 mHz) were extracted from HRVs of 25 patients with apnea using adaptive variational mode decomposition (AVMD) and continuous wavelet transform (CWT), and then analyzed with the Hilbert transform (HT), Savitzky–Golay filter, and empirical distributions of instantaneous amplitudes and frequencies. These studies have demonstrated the existence of both components in HRVs of all subjects and apnea groups: extremely low frequencies (ELFs) in the range of 0.01–0.4 mHz and narrowed ultra-low frequencies (nULFs) in the range of 0.1–4 mHz. The independence of both components is also shown. Concluding, heart rate variability is separately regulated by circadian rhythms (ELF bound) and ultradian fluctuations (nULF bound), which can be assessed by decomposing HRV, and the obtained components may be helpful to better understand the underlying homeostatic mechanisms, as well as in the long-term monitoring of patients.

This research introduces a hybrid mathematical-deep learning framework for the early ‎prediction of Parkinson’s Disease (PD) using hand-drawn spiral and wave imagery. The ‎grayscale pictures were changed using the Hilbert Transform to get amplitude and phase details ‎that show the severity of the tremor and how it moves in an irregular way. We combined these ‎attributes with the original photos and ran them through three Transformer backbones: Swin-T, ‎ViT-B/16, and BEiT-B/16. The experimental findings showed that Swin-T exhibited superior ‎performance, achieving an AUC of 0.983, sensitivity of 0.951, and accuracy of 94.1%. This ‎was followed by ViT-B/16, which attained an AUC of 0.972. In contrast, BEiT-B/16 ‎underperformed, recording an AUC of 0.613. Combining Hilbert-based mathematical modeling ‎with Transformer designs creates a strong and understandable way to do early PD screening ‎without surgery. Furthermore, the limitations resulting from the tiny clinical dataset are ‎explicitly examined, and a stability–separability formalism is given to assess the resilience and ‎discriminative strength of Hilbert-derived features‎.

Stress is a prevalent and inherent phenomenon in people. It triggers the production of hormones that assist in managing the scenarios; nevertheless, chronic stress adversely impacts physical and mental health, which may result in detrimental effects such as depression, anxiety, digestive and heart diseases. Thus, early stress detection is essential to avoiding such negative effects. Addressing this challenge, this research attempted to create a Machine Learning (ML) based stress identification model utilizing two available datasets, namely K-EmoCon and WESAD, which acquired most discriminative signals for stress identification - Inter Beat Interval (IBI), Electro Dermal Activity (EDA) using the Empatica E4 wrist band. Time-Frequency features are extracted from these signals using Ensemble Empirical Mode Decomposition (EEMD) based on Hilbert Transform (HT). Instantaneous Frequency (IF) from IBI and EDA were fed as input to traditional ML models, showing a reduction of the computational power needed, which is especially relevant for setups with limited resources. Among those models, k-NN provides the highest accuracy of about 99.85% and an F1-score of 99.87%. Furthermore, real-time data acquired using a Fitbit smartwatch is also validated using the proposed approach, thereby improving the model's efficiency.

This study presents an innovative methodology for the detection of faults in electric motors, specifically in single-phase induction motors, using the Hilbert Transform combined with spectral density analysis. The main innovation lies in the integration of field-programmable gate array (FPGA) technology with the Hilbert Transform for real-time data acquisition and accurate signal analysis, allowing early detection of faults such as short circuits in the coils. The system uses an analog-to-digital converter to capture current and voltage signals, and a first in, first out memory buffer to ensure continuous acquisition without data loss. The Hilbert transform allows the decomposition of the signals and extraction of analytical frequencies, which facilitates the identification of fault-generated harmonics. The results show a significant improvement in fault detection, with the identification of high-frequency harmonics indicating internal problems such as short circuits. This approach, by integrating FPGA for fast signal acquisition and processing, optimizes the monitoring of electric motors, enabling more effective predictive maintenance and reducing downtime in industrial applications. The innovation of this system improves the accuracy and efficiency of fault diagnosis, contributing to the advancement of real-time monitoring technology.

Phase sensitive optical time domain reflectometry (φOTDR) systems based on different types of interferometers for phase retrieval typically require two or three photodetectors to record the outputs from the interferometer. A novel signal processing principle is proposed for phase retrieval by taking the difference between two outputs as the quadrature component and reconstructing the in-phase component via Hilbert transformation of the Q component for IQ demodulation. Thus, only one balanced photodetector or two standard photodetectors are need, reducing system complexity and data volume. This principle can also be used to suppress fading effect for the traditional three-detector φOTDR systems by selecting optimal phases across detector pairs. Experiments with a φOTDR systems based on an imbalanced Mach-Zehnder interferometer validate the feasibility of this method and demonstrate a high fading suppression of about 90%.

A Brain-Computer Interface (BCI) enables direct communication between the brain and external devices, such as computers or prosthetic limbs. This allows the brain to send commands while receiving sensory feedback from the device. Despite their potential, the performance limitations of existing BCI systems have motivated researchers to improve their efficiency and reliability. To address this challenge, the present study introduces a novel BCI paradigm centered on a cognitive task involving the reading of scrolling text in four different directions: right, left, up and down. The primary objective was to explore the electroencephalography (EEG) and near-infrared spectroscopy (NIRS) signals within this framework and assess the potential of hybrid BCI systems based on this innovative paradigm. The experimental protocol involved eight participants performing tasks across four classes of scrolling text. To optimize system accuracy and speed, EEG and NIRS data were segmented into discrete temporal windows. Features were extracted using the Hilbert Transform, while classification was performed via the k-nearest neighbor algorithm. The proposed approach achieved a classification accuracy of 96.28% 1.30% for multi-class tasks, demonstrating the effectiveness of hybrid modalities. This study not only introduces a novel paradigm for hybrid BCI systems, but also validates its performance, providing a promising direction for advancing the field.

Abstract Introduction Ischemic stroke disrupts cardiovascular regulation and can induce significant electrocardiogram (ECG) abnormalities, yet its specific effects on the shape of ECG signal remain poorly understood. Common ischemic stroke-associated ECG changes often result from autonomic dysregulation and neurogenic stress. However, distinguishing stroke-induced ECG alterations from pre-existing cardiac conditions remains a challenge. Purpose In this study, we propose a new time-frequency approach to analyze ECG signals more effectively. This approach uncovers novel metrics that provide new insights into stroke-related ECG dynamics. Methods Ischemic stroke was induced in 27 adult male and female Sprague Dawley rats (8–12 weeks old; 11% female) using the standard middle cerebral artery (MCA) occlusion/reperfusion model. A monofilament suture was advanced through the internal carotid artery to occlude the MCA for 1 hour, followed by 3 hours of reperfusion. Cerebral infarction was confirmed post-surgery using triphenyl tetrazolium chloride (TTC) staining. ECG signals were continuously recorded throughout the procedure. To analyze ECG dynamics, the Hilbert-Huang Transform (HHT) was applied, consisting of 1) Empirical mode decomposition to decompose the ECG signal into intrinsic mode functions (IMFs); and 2) the Hilbert Transform to derive analytic signal of IMFs. These analytic signals were then mapped onto the complex plane, where they exhibited a distinct eyeball-shaped pattern for IMF1 (ECG time-frequency eyeball) (Fig1). To quantify ECG time-frequency changes, we evaluated symmetry level of this eyeball via the structural similarity index measurement (SSIM) method, where we incrementally rotated the eyeball over 360 degrees and computed the symmetry value between the original and rotated images (Fig1). The normalized area under the curve across all rotation angles (SSIM-AUC) was used as a global symmetry metric. SSIM-AUC was computed at three time points: baseline, 1 hour post-MCA-occlusion (pre-reperfusion), and 3 hours post-MCA-reperfusion. 2-minute ECG recordings were used at each time point for HHT and symmetry analysis. Results Significant changes (P&amp;lt;0.05) were observed in SSIM-AUC of the first intrinsic mode function (IMF1) during ischemic stroke progression (Fig2). SSIM-AUC increased significantly from baseline to pre-MCA-reperfusion (ischemic stroke timepoint), followed by a significant decrease from pre-MCA-reperfusion to 3 hours post-reperfusion (therapy phase timepoint). Conclusions We introduced a novel concept of ECG time-frequency eyeball for the first time. Here, we demonstrated that the symmetry analysis of our ECG Eyeball can effectively capture ischemic stroke-induced changes in the heart’s electrical system. This novel approach opens new possibilities for using ECG in developing noninvasive, AI-driven tools for ischemic stroke detection and monitoring.ECG Time-Frequency Eyeball and Symmetry SSIM-AUC of Eyeballs in Ischemic Stroke

Introduction: Myocardial infarction (MI) alters the heart’s electrophysiology, often seen as ST-segment deviation, T-wave inversion, or QRS distortion in electrocardiogram (ECG). While these features support diagnosis, they may miss early or subtle waveform changes in single-channel ECGs during ischemic injury. Capturing such changes could enhance MI detection, particularly in non-classical presentations. Here, we propose a new analytical approach that reveals advanced ECG morphology changes, to capture MI-related signatures not easily detectable by standard interpretation. Methods: Acute MI was induced in SD rats (n=13; Male; ~300g) via 30 minutes of proximal left coronary artery occlusion, followed by 3 hours of reperfusion. Necrosis was confirmed post-surgery via triphenyl tetrazolium chloride (TTC) staining. ECG signals were continuously recorded via subcutaneous needle electrodes. The ECG time-frequency eyeball method involves: (1) empirical mode decomposition to extract intrinsic mode functions (IMFs) from ECG signal; (2) the Hilbert Transform to derive analytic signal of each IMF; (3) rotational mapping of the analytic signals onto the complex plane, where they exhibited a distinct eyeball-shaped pattern for IMF1 (ECG eyeball, Fig1). To quantify ECG dynamic changes, we performed symmetry analysis on the ECG eyeballs using the Structural Similarity Index Measurement (SSIM). Specifically, each eyeball was mirrored across incrementally rotated axes, and SSIM was calculated between the original and mirrored images at each angle. The normalized area under the SSIM curve over all rotation angles (SSIM-AUC) was used as a global symmetry metric (Fig1). SSIM-AUC was computed at three time points: baseline, pre-reperfusion (MI with occluded coronary), and 3 hours post-reperfusion (early recovery after MI). 2-minute ECG recordings were used at each time point for computing the eyeballs. Results: SSIM-AUC significantly decreased after MI (P&lt;0.05), from baseline to both pre-reperfusion and post-reperfusion (Fig2). A modest post-reperfusion increase vs. pre-reperfusion was observed but not significant. Conclusion: We introduced a time-frequency-based analytics approach (ECG Eyeball) that maps multi-minute ECG data into a single interpretable pattern. Symmetry analysis of the ECG eyeball effectively captured MI-induced electrical changes. This method offers new directions for leveraging single-channel ECG data in noninvasive and interpretable tools for MI detection.

Cardiovascular disease (CD) is the leading cause of death in the world. Electrocardiogram (ECG) analysis is an effective method to diagnose CD. In this study, we introduced a microcontroller-based embedded system that allows the collection and processing of ECG signals directly on the device. By integrating low-pass filters (LPFs) and high-pass filters (HPFs), the system can effectively eliminate ultra-low frequency noise, power line noise, and unwanted high-frequency components, thereby improving the fidelity of the signal. R peak detection algorithms (Pan-Tompkins, Hilbert Transform, and Englese &amp; Zeelenberg) have been applied to the acquired ECG of 10 volunteers aged 21–28 years. The results show that these algorithms achieved accuracy of over 99.5%. This study not only proves the ability to improve the reliability of direct ECG collection and analysis based on microcontrollers but also lays the foundation for the development of portable cardiovascular diagnostic devices, supporting early detection and more effective and accessible healthcare.

Abstract In this study, the authors propose an adaptive double piecewise interpolation reproducing Hilbert kernel method (ADPIRHKM) for the first time to solve the model of the neutron transporting process in the nuclear reactor core. The theory focuses on the reproducing kernel theory, integrated with the adaptive technique and the double piecewise interpolation means, which can produce a sparse matrix B by selecting the appropriate parameters, avoiding calculating the conjugate operator and practising Gram-Schmidt orthogonalization. The adaptive multi-step technique, which ensures a more reasonable segment count, and the double piecewise interpolation approach, which enhances accuracy, combine together to give a key innovation point of this paper: a simple and efficient numerical method. Three numerical experiments are done to show the accuracy of the new method and the comparisons are based on the known results. The numerical simulation indicates the effect of time t and β on neutron flux behavior of graphite.

Introduction: Accurate short-term photovoltaic (PV) power prediction is crucial for ensuring the safety of the power grid and promoting the consumption of PV. However, due to factors such as Internet access conditions and information security control, some industrial parks are unable to obtain real-time weather forecast information, and there is an urgent need to develop a PV power prediction method that does not rely on weather forecast information. Method: In this paper, we propose an innovative architecture for the Morphological Filtering Empirical Wavelet Transform (MFEWT) and the Frequency Decoupled Multi-Cycle Fusion Network (FDMFNet). Firstly, MFEWT is used to decompose the historical photovoltaic (PV) power generation into a number of frequency sub-sequences, which are then classified into major and minor components based on their frequency energies. For the primary component, amplitude features are extracted using the Hilbert transform and supplemented with feature columns using the Signal Cycle- Based Adaptive Historical Feature Set Construction Method (CAF), which are then predicted by a convolutional neural network. For the secondary component, the FDMFNet is designed to accurately capture the trend of the high-frequency secondary components through frequency-domain decoupling. Finally, the major and minor components are linearly superimposed to obtain the final PV power prediction. Result: Experimental validation based on photovoltaic (PV) datasets from two industrial parks in China, Wuhan and Qingdao, confirms the effectiveness of the proposed method. In terms of overall prediction accuracy, the MAE of the proposed method is 0.2108, the RMSE is 0.3297, and the R2 is 0.8708. Discussion: The MFEWT proposed in this study effectively suppresses mode mixing. Combined with Hilbert Transform and FDMFNet, it achieves multi-scale feature mining of PV power. This fusion mechanism significantly enhances the model's capability to characterize the intrinsic timefrequency properties of PV sequences. Conclusion: The PV prediction method introduced in this paper, which operates without weather forecast information, demonstrates favorable accuracy and stability in actual ultra-short-term PV power prediction scenarios. It provides a novel solution for PV power forecasting under conditions where meteorological information is lacking.

This article is devoted to the study of the physical properties of deterministic, chaotic, and stochastic signals used in modern information systems with the aim of enhancing their spectral efficiency. Special attention is given to chaotic and stochastic signals, which, due to their unique structures, ensure a high level of information security. However, they require further development to achieve optimal utilization of the frequency spectrum. The study addresses a pressing issue in communication systems: the need to balance high spectral efficiency with robust data protection and interference resilience. Deterministic signals, such as harmonic signals, traditionally used in narrowband systems, are characterized by simplicity and predictability but suffer from low spectral efficiency and poor resistance to interference. In contrast, chaotic and stochastic signals exhibit significant advantages in terms of security and interference immunity but require advanced signal processing techniques to overcome challenges associated with their wide spectral bandwidth and energy consumption. The research methodology integrates mathematical modeling and signal analysis. Traditional approaches, such as Fourier transformation, wavelet transformation, and Hilbert transformation, are compared with innovative techniques, including Volterra series and Karhunen–Loève transformation. The comparative analysis is based on evaluating spectral efficiency, interference resilience, and the energy requirements of different signal types. The results demonstrate that chaotic signals outperform deterministic and stochastic signals in terms of spectral efficiency across broader frequency ranges. However, chaotic signals require more sophisticated processing methods to ensure their stability and reliability in modern communication systems. Stochastic signals, while offering superior interference resistance and information security, exhibit lower spectral efficiency due to their broad frequency spectrum and uneven energy distribution. Innovative approaches, such as Volterra series and Karhunen–Loève transformation, significantly improve the spectral efficiency of chaotic and stochastic signals by reducing redundancy and optimizing frequency utilization. These findings highlight the need for integrating advanced signal processing methods into information systems to enhance their performance and reliability. The study's results have practical implications for the development of advanced communication systems, such as cellular networks, the Internet of Things, and satellite communication systems, where high data confidentiality and efficient spectrum usage are critical.

Objective.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 the 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.Approach.We evaluated thein silicoperformance of three phase detection algorithms [Endpoint-corrected Hilbert transform (ecHT), Hilbert transform (HT), and phase mapping (PM)] on three real-world biological signals with distinct spectral properties (theta oscillations from rodent hippocampal local field potential, alpha oscillations from human electroencephalogram (EEG), and hand movement kinematics from essential tremor patients) to identify the optimal model and parameters. We then validated the performance of an algorithm for estimating theta phase in real-time using rats implanted with electrodes in the hippocampus.Results. First, we found that signal amplitude and frequency variations strongly influence algorithm performance. Frequency-specific signal-to-noise ratio was positively correlated with performance (meanR2= 0.42 across metrics), while amplitude and frequency variability were negatively correlated (meanR2= 0.50 across metrics). Second, we showed that the length of the data window used for phase estimation is the key parameter for optimal performance of FFT-based algorithms, where the optimal data window length corresponds to the period of the oscillation (∼150 ms for hippocampal theta oscillations, ∼100 ms for human EEG alpha, and ∼125 ms for essential tremor kinematics). We validated this findingin vivoby estimating the phase of theta oscillations from the hippocampus of freely behaving rats, where a data window length corresponding to one theta cycle yielded the best performance across all metrics compared with shorter or longer window lengths.Significance. Our findings clarify the relationship between signal properties and algorithm performance and provide a convenient method for optimizing FFT-based phase detection algorithms. We show that a data window length corresponding to one cycle of an oscillation can lead to improved performance.

Alzheimer's Disease (AD) is a chronic neurological disorder that impairs the cognitive and behavioral abilities of older people. Early detection and treatment are crucial for minimizing the progression of the disease. Electroencephalogram (EEG) makes it possible to investigate the brain activities linked to various forms of disabilities experienced by individuals with AD. Nevertheless, the EEG signals are non-linear and non-stationary in nature making it difficult to retrieve the concealed information from the EEG signals. Therefore, a Fourier Decomposition Method (FDM) and Hilbert Transform (HT) based EEG signals analysis (FHESA) method is developed in this paper for the automated detection of AD. The FHESA method aims to efficiently analyze the EEG data to identify the important brain regions vulnerable to AD, and to assess the impact of various EEG channels for the timely and early detection of AD. The proposed FHESA method is divided into three primary stages. The first stage deals with the decomposition of the EEG signals into a finite number of Fourier Intrinsic Band Functions (FIBFs). In the second stage, HT is applied to all FIBFs to obtain instantaneous amplitude, frequency, and phase, that are then used to construct feature vectors. In the last stage, various Machine Learning (ML) algorithms are used to classify these feature vectors for efficient AD detection. Two distinct data sets are employed to assess the effectiveness of the proposed FHESA method. The outcome demonstrates that with dataset-I and dataset-II, the proposed methodology can detect AD with 98% and 99% accuracy, respectively. The performance of the proposed FHESA method is compared to other state-of-the-art methods used for AD detection. The promising results show that the proposed FHESA method can assist neurological experts in identifying and utilizing EEG signals for AD detection.

Ultrasonics in the medical field require a safe treatment for patients. The uncontrolled intensities of the ultrasonic waves cause ineffective treatment. So far, the hydrophone probe provides a standard for ultrasonic visualization. However, this method has constraints such as being time-consuming, intrusive, and requiring off-axis measurements. In this paper, an optical method called background-oriented schlieren imaging (BOSI) has been developed as an alternative. The BOSI uses a background of fringe patterns captured by a digital camera. The ultrasonic waves in water displace the patterns relative to the reference. A Hilbert Transform (HT) has been used to estimate the displacement of patterns proportional to the phase difference. The developed BOSI reconstructs these phase differences as an ultrasonic visualization. This paper reports that the developed BOSI is capable of visualizing the ultrasonic waves produced by a 1-MHz frequency medical transducer operated in continuous-wave (CW) mode. The visualization shows an undulation of phase difference that corresponds to the change in water density due to ultrasonic exposure. Meanwhile, the amplitude mode is proportional to the ultrasonic intensity profile. Thus, the developed BOSI is promising to be used as a calibration device to ensure safe ultrasonics in the medical field.