Wavelet Analysis: Mother Wavelet Selection Methods

A Robust Deep Feature Extraction Method for Human Activity Recognition Using a Wavelet Based Spectral Visualisation Technique

Human Activity Recognition (HAR), alongside Ambient Assisted Living (AAL), are integral components of smart homes, sports, surveillance, and investigation activities. To recognize daily activities, researchers are focusing on lightweight, cost-effective, wearable sensor-based technologies as traditional vision-based technologies lack elderly privacy, a fundamental right of every human. However, it is challenging to extract potential features from 1D multi-sensor data. Thus, this research focuses on extracting distinguishable patterns and deep features from spectral images by time-frequency-domain analysis of 1D multi-sensor data. Wearable sensor data, particularly accelerator and gyroscope data, act as input signals of different daily activities, and provide potential information using time-frequency analysis. This potential time series information is mapped into spectral images through a process called use of 'scalograms', derived from the continuous wavelet transform. The deep activity features are extracted from the activity image using deep learning models such as CNN, MobileNetV3, ResNet, and GoogleNet and subsequently classified using a conventional classifier. To validate the proposed model, SisFall and PAMAP2 benchmark datasets are used. Based on the experimental results, this proposed model shows the optimal performance for activity recognition obtaining an accuracy of 98.4% for SisFall and 98.1% for PAMAP2, using Morlet as the mother wavelet with ResNet-101 and a softmax classifier, and outperforms state-of-the-art algorithms.

Wavelet Transforms Significantly Sparsify and Compress Tactile Interactions

As higher spatiotemporal resolution tactile sensing systems are being developed for prosthetics, wearables, and other biomedical applications, they demand faster sampling rates and generate larger data streams. Sparsifying transformations can alleviate these requirements by enabling compressive sampling and efficient data storage through compression. However, research on the best sparsifying transforms for tactile interactions is lagging. In this work we construct a library of orthogonal and biorthogonal wavelet transforms as sparsifying transforms for tactile interactions and compare their tradeoffs in compression and sparsity. We tested the sparsifying transforms on a publicly available high-density tactile object grasping dataset (548 sensor tactile glove, grasping 26 objects). In addition, we investigated which dimension wavelet transform-1D, 2D, or 3D-would best compress these tactile interactions. Our results show that wavelet transforms are highly efficient at compressing tactile data and can lead to very sparse and compact tactile representations. Additionally, our results show that 1D transforms achieve the sparsest representations, followed by 3D, and lastly 2D. Overall, the best wavelet for coarse approximation is Symlets 4 evaluated temporally which can sparsify to 0.5% sparsity and compress 10-bit tactile data to an average of 0.04 bits per pixel. Future studies can leverage the results of this paper to assist in the compressive sampling of large tactile arrays and free up computational resources for real-time processing on computationally constrained mobile platforms like neuroprosthetics.

Weakened hydrological oscillation period increased the frequency of river algal blooms

The evolution of riverine aquatic ecosystems typically exhibits notable characteristic with cumulative, enduring, and hysteresis. Exploring the non-linear response of riverine ecology to long-term hydrological fluctuations become a major challenge in contemporary interdisciplinary research. In response to the critical issue of frequent river algal blooms in the lower Han River, which is impacted by Asian largest inter-basin water diversion project. We identified the non-linear response of eco-hydrology across various time scales through the integration of Continuous Wavelet Transform (CWT) and Inverse Wavelet Transform (IWT). Our study revealed that: 1) Over the past half century, the hydrological regime in the lower Han river showed a significant downward trend, and existed three significant hydrological oscillation periods (HOPs), including the short-scale Intra-AC (180 days), the medium-scale AC (365 days, the first major period), and the long-scale Inter-AC (2500 days), the variation of Inter-AC changed most dramatically. 2) We further found that the Inter-AC variation of hydrology is more closely related to the formation of river algal blooms in the Han River, and when the hydrological Inter-AC shows steady state or downward trend, the frequency of algal blooms in the lower Han River increases significantly. 3) The river algal blooms in the lower Han River is a cumulative consequence to the long-term hydrological influences. Weakened hydrological Inter-AC is more likely to increase the frequency of river algal blooms, and 10-years Inter-AC cumulation increased the frequency by 60%. Therefore, the weaken of long-scale HOP will significantly increase the frequency of river algal blooms in the future. This study received a critical scientific insight and aimed at provide guidance for the optimization of ecological management within the framework of national large-scale water conservation.

Wavelet denoising of fiber optic monitoring signals in permafrost regions

To address the noise issue in fiber optic monitoring signals in frozen soil areas, this study employs wavelet denoising techniques to process the fiber optic signals. Since existing parameter choices for wavelets are typically based on conventional environments, selecting suitable parameters for frozen soil regions becomes crucial. In this work, an index library is constructed based on commonly used wavelet basis functions in civil engineering. An optimal wavelet basis function is objectively selected through specific criteria. Considering the characteristic of small root mean square error in fiber optic signals in frozen soil areas, a multi-index fusion approach is applied to determine the optimal decomposition level. Field observations validate that denoised signals, with parameters set appropriately, can more accurately identify locations where settlement occurs.

A New Denoising Method for Belt Conveyor Roller Fault Signals

In the process of the intelligent inspection of belt conveyor systems, due to problems such as its long duration, the large number of rollers, and the complex working environment, fault diagnosis by acoustic signals is easily affected by signal coupling interference, which poses a great challenge to selecting denoising methods of signal preprocessing. This paper proposes a novel wavelet threshold denoising algorithm by integrating a new biparameter and trisegment threshold function. Firstly, we elaborate on the mutual influence and optimization process of two adjustment parameters and three wavelet coefficient processing intervals in the BT-WTD (the biparameter and trisegment of wavelet threshold denoising, BT-WTD) denoising model. Subsequently, the advantages of the proposed threshold function are theoretically demonstrated. Finally, the BT-WTD algorithm is applied to denoise the simulation signals and the vibration and acoustic signals collected from the belt conveyor experimental platform. The experimental results indicate that this method's denoising effectiveness surpasses that of traditional threshold function denoising algorithms, effectively addressing the denoising preprocessing of idler roller fault signals under strong noise backgrounds while preserving useful signal features and avoiding signal distortion problems. This research lays the theoretical foundation for the non-contact intelligent fault diagnosis of future inspection robots based on acoustic signals.

Automated identification of atrial fibrillation from single-lead ECGs using multi-branching ResNet

Introduction: Atrial fibrillation (AF) is the most common cardiac arrhythmia, which is clinically identified with irregular and rapid heartbeat rhythm. AF puts a patient at risk of forming blood clots, which can eventually lead to heart failure, stroke, or even sudden death. Electrocardiography (ECG), which involves acquiring bioelectrical signals from the body surface to reflect heart activity, is a standard procedure for detecting AF. However, the occurrence of AF is often intermittent, costing a significant amount of time and effort from medical doctors to identify AF episodes. Moreover, human error is inevitable, as even experienced medical professionals can overlook or misinterpret subtle signs of AF. As such, it is of critical importance to develop an advanced analytical model that can automatically interpret ECG signals and provide decision support for AF diagnostics. Methods: In this paper, we propose an innovative deep-learning method for automated AF identification using single-lead ECGs. We first extract time-frequency features from ECG signals using continuous wavelet transform (CWT). Second, the convolutional neural networks enhanced with residual learning (ReNet) are employed as the functional approximator to interpret the time-frequency features extracted by CWT. Third, we propose to incorporate a multi-branching structure into the ResNet to address the issue of class imbalance, where normal ECGs significantly outnumber instances of AF in ECG datasets. Results and Discussion: We evaluate the proposed Multi-branching Resnet with CWT (CWT-MB-Resnet) with two ECG datasets, i.e., PhysioNet/CinC challenge 2017 and ECGs obtained from the University of Oklahoma Health Sciences Center (OUHSC). The proposed CWT-MB-Resnet demonstrates robust prediction performance, achieving an F1 score of 0.8865 for the PhysioNet dataset and 0.7369 for the OUHSC dataset. The experimental results signify the model's superior capability in balancing precision and recall, which is a desired attribute for ensuring reliable medical diagnoses.

Correlation between acoustic characteristics and sensory evaluation of puffed-grain food based on energy analysis

Puffed-grain food is a crispy snack whose consumer satisfaction depends on snack crispness and crunchiness, which can be characterized by the sound and the acoustic signals of food breaking. This study aimed to evaluate whether acoustic characteristics can be used to predict the crispness of various puffed-grain food. Sensory evaluation was performed on puffed-grain products with varying hygroscopic durations and different types. The relation between sensory evaluation and acoustic characteristics of nine different types of food was examined. The Hilbert-Huang transform was used to perform energy segmentation of the acoustic signal of puffed-grain food and observe its energy migration process. The results showed that energy release was more concentrated in the low-frequency range for grain-puffed foods with different hygroscopic durations. No notable correlation was observed between the low-frequency interval and sensory crispness for the different types of puffed-grain foods. However, the acoustic features extracted from their inherent low-frequency intervals showed a significantly improved correlation with sensory crispness. Therefore, it provides a theoretical reference for applying acoustic characteristics to describe food texture.

Quantitative Analysis of Mother Wavelet Function Selection for Wearable Sensors-Based Human Activity Recognition

Recent advancements in the Internet of Things (IoT) wearable devices such as wearable inertial sensors have increased the demand for precise human activity recognition (HAR) with minimal computational resources. The wavelet transform, which offers excellent time-frequency localization characteristics, is well suited for HAR recognition systems. Selecting a mother wavelet function in wavelet analysis is critical, as optimal selection improves the recognition performance. The activity time signals data have different periodic patterns that can discriminate activities from each other. Therefore, selecting a mother wavelet function that closely resembles the shape of the recognized activity's sensor (inertial) signals significantly impacts recognition performance. This study uses an optimal mother wavelet selection method that combines wavelet packet transform with the energy-to-Shannon-entropy ratio and two classification algorithms: decision tree (DT) and support vector machines (SVM). We examined six different mother wavelet families with different numbers of vanishing points. Our experiments were performed on eight publicly available ADL datasets: MHEALTH, WISDM Activity Prediction, HARTH, HARsense, DaLiAc, PAMAP2, REALDISP, and HAR70+. The analysis demonstrated in this paper can be used as a guideline for optimal mother wavelet selection for human activity recognition.

Artificial neural network analysis for classification of defected high voltage ceramic insulators

Partial discharge (PD) could lead to the formation of small arcs or sparks within the insulating material, which can cause damage and degradation to the insulator over time. In ceramic insulators, there are several factors that can cause PD including manufacturing defects, aging, and exposure to environmental conditions such as moisture and temperature extremes. As a result, detecting and monitoring PD in ceramic insulators is important for ensuring the reliability and safety of electrical systems that rely on these insulators. In this study, acoustic emission technique is introduced for PD detection and condition monitoring of defective ceramic insulators. A sequence of data processing techniques is performed on the captured signals to extract and select the most significant signatures for classification of defects in insulator strings. Artificial neural network (ANN) has been used to build an intelligent classifier for easily and accurately classification of defective insulators. The overall recognition rate of the classifier was obtained at 96.03% from discrete wavelet transform analysis and 88.65% from fast Fourier transform analysis. This obtained result indicates high accuracy and performance classification. The outcomes of ANN were verified by SVM and KNN algorithms.

Identification of broken conductor faults in interconnected transmission systems based on discrete wavelet transform

Interconnected transmission systems are increasingly spreading out in HV networks to enhance system efficiency, decrease reserve capacity, and improve service reliability. However, the protection of multi-terminal lines against Broken Conductor Fault (BCF) imposes significant difficulties in such networks as the conventional distance relays cannot detect BCF, as the BCF is not associated with a significant increase in current or reduction in voltage Traditionally, the earth fault relays in transmission lines may detect such fault; Nonetheless, it suffers from a long delay time. Moreover, many of the nearby earth fault relays detect the BCF causing unnecessary trips and badly affecting the system stability. In this article, a novel single-end scheme based on extracting transient features from current signals by discrete wavelet transform (DWT) is proposed for detecting BCFs in interconnected HV transmission systems. The suggested scheme unit (SSU) is capable of accurately detecting all types of BCFs and shunt high impedance faults (SHIFs). It also adaptively calculates the applied threshold values. The accurate selectivity in multi-terminal lines is achieved based on a fault directional element by analyzing transient power polarity. The SSU discriminates between internal/external faults effectively utilizing the time difference observed between the first spikes of aerial and ground modes in the current signals. Different fault scenarios have been simulated on the IEEE 9-Bus, 230 kV interconnected system. The achieved results confirm the effectiveness, robustness, and reliability of SSU in detecting correctly BCFs as well as the SHIFs within only 24.5 ms. The SSU has confirmed its capability to be implemented in interconnected systems without any requirement for communication or synchronization between the SSU installed in multi-terminal lines.

Discrete Wavelet Transformation for the Sensitive Detection of Ultrashort Radiation Pulse with Radiation-induced Acoustics

Radiation-induced acoustics (RIA) shows promise in advancing radiological imaging and radiotherapy dosimetry methods. However, RIA signals often require extensive averaging to achieve reasonable signal-to-noise ratios, which increases patient radiation exposure and limits real-time applications. Therefore, this paper proposes a discrete wavelet transform (DWT) based filtering approach to denoise the RIA signals and avoid extensive averaging. The algorithm was benchmarked against low-pass filters and tested on various types of RIA sources, including low-energy X-rays, high-energy X-rays, and protons. The proposed method significantly reduced the required averages (1000 times less averaging for low-energy X-ray RIA, 32 times less averaging for high-energy X-ray RIA, and 4 times less averaging for proton RIA) and demonstrated robustness in filtering signals from different sources of radiation. The coif5 wavelet in conjunction with the sqtwolog threshold selection algorithm yielded the best results. The proposed DWT filtering method enables high-quality, automated, and robust filtering of RIA signals, with a performance similar to low-pass filtering, aiding in the clinical translation of radiation-based acoustic imaging for radiology and radiation oncology.

Exponential feedback effects in a parametric resonance climate model

The variations in the distribution of solar radiation due to the  ~ 105 years Milankovitch cycle, which is connected to the Earth eccentricity variation, cannot explain the sharp drop in temperature of 6 °C ÷ 10 °C that marks the transition from the interglacial to the glacial age registered in the last ~ 5.5 106 years temperature variation behavior. More specifically, neglecting other effects, only a temperature variation of 0.2 °C ÷ 0.3 °C can be attributed to this cycle and, therefore, positive feedback effects should be taken into account to explain the registered effect. In the present work, a comparative Wavelet-Fourier analysis of the Vostok recontructed temperature record, for which different sampling steps are taken into account, is performed. Then, a study of exponential feedback effects within a climate parametric resonance model is dealt and discussed. The obtained findings put into evidence an exponential amplification of the temperature variation from the interglacial to the glacial age supporting the hypothesis that the system energization be connected to periodic variations in the internal solar system parameters. More in details, it is shown that, following the parametric resonance climate model, even small oscillations increase over time proportionally to the system energy itself, i.e. exponentially, and hence, a series of connected resonances is able to energize the climate system.

Deep Wavelet Convolutional Neural Networks for Multimodal Human Activity Recognition Using Wearable Inertial Sensors

Recent advances in wearable systems have made inertial sensors, such as accelerometers and gyroscopes, compact, lightweight, multimodal, low-cost, and highly accurate. Wearable inertial sensor-based multimodal human activity recognition (HAR) methods utilize the rich sensing data from embedded multimodal sensors to infer human activities. However, existing HAR approaches either rely on domain knowledge or fail to address the time-frequency dependencies of multimodal sensor signals. In this paper, we propose a novel method called deep wavelet convolutional neural networks (DWCNN) designed to learn features from the time-frequency domain and improve accuracy for multimodal HAR. DWCNN introduces a framework that combines continuous wavelet transforms (CWT) with enhanced deep convolutional neural networks (DCNN) to capture the dependencies of sensing signals in the time-frequency domain, thereby enhancing the feature representation ability for multiple wearable inertial sensor-based HAR tasks. Within the CWT, we further propose an algorithm to estimate the wavelet scale parameter. This helps enhance the performance of CWT when computing the time-frequency representation of the input signals. The output of the CWT then serves as input for the proposed DCNN, which consists of residual blocks for extracting features from different modalities and attention blocks for fusing these features of multimodal signals. We conducted extensive experiments on five benchmark HAR datasets: WISDM, UCI-HAR, Heterogeneous, PAMAP2, and UniMiB SHAR. The experimental results demonstrate the superior performance of the proposed model over existing competitors.

Forecasting CO2 emissions from road fuel combustion using grey prediction models: A novel approach

This paper proposes an optimized wavelet transform Hausdorff multivariate grey model (OWTHGM(1,N)) that addresses some of the weaknesses of the conventional GM(1,N) model such as inaccurate prediction and poor stability. Three improvements have been made: First, all inputs are filtered using a wavelet transform; second, a new time response function is established using the Hausdorff derivative; and finally, the use of Rao's algorithm to optimise the model's parameters as well as the ξ-order accumulated value of the observation data described by the Hausdorff derivative. In order to demonstrate the effectiveness of OWTHGM(1,N), it is applied to predict CO₂ emissions from road fuel combustion. The new model scores 1.27% MAPE and 79.983 RMSE, and is therefore more accurate than competing models. OWTHGM(1,N) could therefore serve a reliable forecasting tool and used to monitor the evolution of CO₂ emissions in Cameroon. The forecast results also serve as a sound foundation for the formulation of energy consumption strategies and environmental policies. • Modification, extension and optimization of grey multivariate model is done. • The model is very generic can be applied to a wide variety of energy sectors. • OWTHGM(1,N) is a valid forecasting tool that can be used to track CO₂ emissions.

Radiation-induced acoustic signal denoising using a supervised deep learning framework for imaging and therapy monitoring

Radiation-induced acoustic (RA) imaging is a promising technique for visualizing the invisible radiation energy deposition in tissues, enabling new imaging modalities and real-time therapy monitoring. However, RA imaging signal often suffers from poor signal-to-noise ratios (SNRs), thus requiring measuring hundreds or even thousands of frames for averaging to achieve satisfactory quality. This repetitive measurement increases ionizing radiation dose and degrades the temporal resolution of RA imaging, limiting its clinical utility. In this study, we developed a general deep inception convolutional neural network (GDI-CNN) to denoise RA signals to substantially reduce the number of frames needed for averaging. The network employs convolutions with multiple dilations in each inception block, allowing it to encode and decode signal features with varying temporal characteristics. This design generalizes GDI-CNN to denoise acoustic signals resulting from different radiation sources. The performance of the proposed method was evaluated using experimental data of x-ray-induced acoustic, protoacoustic, and electroacoustic signals both qualitatively and quantitatively. Results demonstrated the effectiveness of GDI-CNN: it achieved x-ray-induced acoustic image quality comparable to 750-frame-averaged results using only 10-frame-averaged measurements, reducing the imaging dose of x-ray-acoustic computed tomography (XACT) by 98.7%; it realized proton range accuracy parallel to 1500-frame-averaged results using only 20-frame-averaged measurements, improving the range verification frequency in proton therapy from 0.5 to 37.5 Hz; it reached electroacoustic image quality comparable to 750-frame-averaged results using only a single frame signal, increasing the electric field monitoring frequency from 1 fps to 1k fps. Compared to lowpass filter-based denoising, the proposed method demonstrated considerably lower mean-squared-errors, higher peak-SNR, and higher structural similarities with respect to the corresponding high-frame-averaged measurements. The proposed deep learning-based denoising framework is a generalized method for few-frame-averaged acoustic signal denoising, which significantly improves the RA imaging's clinical utilities for low-dose imaging and real-time therapy monitoring.

Assessment of a 16-Channel Ambulatory Dry Electrode EEG for Remote Monitoring

Ambulatory EEGs began emerging in the healthcare industry over the years, setting a new norm for long-term monitoring services. The present devices in the market are neither meant for remote monitoring due to their technical complexity nor for meeting clinical setting needs in epilepsy patient monitoring. In this paper, we propose an ambulatory EEG device, OptiEEG, that has low setup complexity, for the remote EEG monitoring of epilepsy patients. OptiEEG's signal quality was compared with a gold standard clinical device, Natus. The experiment between OptiEEG and Natus included three different tests: eye open/close (EOC); hyperventilation (HV); and photic stimulation (PS). Statistical and wavelet analysis of retrieved data were presented when evaluating the performance of OptiEEG. The SNR and PSNR of OptiEEG were slightly lower than Natus, but within an acceptable bound. The standard deviations of MSE for both devices were almost in a similar range for the three tests. The frequency band energy analysis is consistent between the two devices. A rhythmic slowdown of theta and delta was observed in HV, whereas photic driving was observed during PS in both devices. The results validated the performance of OptiEEG as an acceptable EEG device for remote monitoring away from clinical environments.

A Novel Wavelet Selection Method for Seismic Signal Intelligent Processing

Wavelet transform is a widespread and effective method in seismic waveform analysis and processing. Choosing a suitable wavelet has also aroused many scholars’ research interest and produced many effective strategies. However, with the convenience of seismic data acquisition, the existing wavelet selection methods are unsuitable for the big dataset. Therefore, we proposed a novel wavelet selection method considering the big dataset for seismic signal intelligent processing. The relevance r is calculated using the seismic waveform’s correlation coefficient and variance contribution rate. Then values of r are calculated from all seismic signals in the dataset to form a set. Furthermore, with a mean value μ and variance value σ2 of that set, we define the decomposition stability w as μ/σ2. Then, the wavelet that maximizes w for this dataset is considered to be the optimal wavelet. We applied this method in automatic mining-induced seismic signal classification and automatic seismic P arrival picking. In classification experiments, the mean accuracy is 93.13% using the selected wavelet, 2.22% more accurate than other wavelets generated. Additionally, in the picking experiments, the mean picking error is 0.59 s using the selected wavelet, but is 0.71 s using others. Moreover, the wavelet packet decomposition level does not affect the selection of wavelets. These results indicate that our method can really enhance the intelligent processing of seismic signals.

IoT System for Detecting the Condition of Rotating Machines Based on Acoustic Signals

Modern predictive maintenance techniques have been significantly improved with the development of Industrial Internet of Things solutions which have enabled easier collection and analysis of various data. Artificial intelligence-based algorithms in combination with modular interconnected architecture of sensors, devices and servers, have resulted in the development of intelligent maintenance systems which outperform most traditional machine maintenance approaches. In this paper, a novel acoustic-based IoT system for condition detection of rotating machines is proposed. The IoT device designed for this purpose is mobile and inexpensive and the algorithm developed for condition detection consists of a combination of discrete wavelet transform and neural networks, while a genetic algorithm is used to tune the necessary hyperparameters. The performance of this system has been tested in a real industrial setting, on different rotating machines, in an environment with strong acoustic pollution. The results show high accuracy of the algorithm, with an average F1 score of around 0.99 with tuned hyperparameters.

Photoplethysmography-Based Respiratory Rate Estimation Algorithm for Health Monitoring Applications

Purpose

Respiratory rate can provide auxiliary information on the physiological changes within the human body, such as physical and emotional stress. In a clinical setup, the abnormal respiratory rate can be indicative of the deterioration of the patient's condition. Most of the existing algorithms for the estimation of respiratory rate using photoplethysmography (PPG) are sensitive to external noise and may require the selection of certain algorithm-specific parameters, through the trial-and-error method.

Methods

This paper proposes a new algorithm to estimate the respiratory rate using a photoplethysmography sensor signal for health monitoring. The algorithm is resistant to signal loss and can handle low-quality signals from the sensor. It combines selective windowing, preprocessing and signal conditioning, modified Welch filtering and postprocessing to achieve high accuracy and robustness to noise.

Results

The Mean Absolute Error and the Root Mean Square Error of the proposed algorithm, with the optimal signal window size, are determined to be 2.05 breaths count per minute and 2.47 breaths count per minute, respectively, when tested on a publicly available dataset. These results present a significant improvement in accuracy over previously reported methods. The proposed algorithm achieved comparable results to the existing algorithms in the literature on the BIDMC dataset (containing data of 53 subjects, each recorded for 8 min) for other signal window sizes.

Conclusion

The results endorse that integration of the proposed algorithm to a commercially available pulse oximetry device would expand its functionality from the measurement of oxygen saturation level and heart rate to the continuous measurement of the respiratory rate with good efficiency at home and in a clinical setting.

Supplementary Information

The online version contains supplementary material available at 10.1007/s40846-022-00700-z.

The Evolution of Preseismic Patterns Related to the Central Crete (Mw6.0) Strong Earthquake on 27 September 2021 Revealed by Multiresolution Wavelets and Natural Time Analysis

On 27 September 2021, a shallow earthquake with focal depth of 10 km and moment magnitude Mw6.0 occurred onshore in central Crete (Greece). The evolution of possible preseismic patterns in the area of central Crete before the Mw6.0 event was investigated by applying the method of multiresolution wavelet analysis (MRWA), along with that of natural time (NT). The monitoring of preseismic patterns by critical parameters defined by NT analysis, integrated with the results of MRWA as the initiation point for the NT analysis, forms a promising framework that may lead to new universal principles that describe the evolution patterns before strong earthquakes. Initially, we apply MRWA to the interevent time series of the successive regional earthquakes in order to investigate the approach of the regional seismicity towards critical stages and to define the starting point of the natural time domain. Then, using the results of MRWA, we apply the NT analysis, showing that the regional seismicity approached criticality for a prolonged period of ~40 days before the occurrence of the Mw6.0 earthquake, when the κ1 natural time parameter reached the critical value of κ1 = 0.070, as suggested by the NT method.

Robustness of ventilation systems in the control of walking-induced indoor fluctuations: Method development and case study

Walking-induced fluctuations have a significant influence on indoor airflow and pollutant dispersion. This study developed a method to quantify the robustness of ventilation systems in the control of walking-induced fluctuation control. Experiments were conducted in a full-scale chamber with four different kinds of ventilation systems: ceiling supply and side return (CS), ceiling supply and ceiling return (CC), side supply and ceiling return (SC), and side supply and side return (SS). The measured temperature, flow and pollutant field data was (1) denoised by FFT filtering or wavelet transform; (2) fitted by a Gaussian function; (3) feature-extracted for the range and time scale disturbance; and then (4) used to calculate the range scale and time scale robustness for different ventilation systems with dimensionless equations developed in this study. The selection processes for FFT filtering and wavelet transform, FFT filter cut-off frequency, wavelet function, and decomposition layers are also discussed, as well as the threshold for wavelet denoising, which can be adjusted accordingly if the walking frequency or sampling frequency differs from that in other studies. The results show that for the flow and pollutant fields, the use of a ventilation system can increase the range scale robustness by 19.7%-39.4% and 10.0%-38.8%, respectively; and the SS system was 7.0%-25.7% more robust than the other three ventilation systems. However, all four kinds of ventilation systems had a very limited effect in controlling the time scale disturbance.

Correlation Analysis of Ultrasonic Stress Wave Characteristics and the Destructive Strength Measurements in Cylindrical Wooden Structure

The utility sector has been employing ultrasonic-based nondestructive evaluation (NDE) to determine the cross-sectional groundline integrity of wooden utility poles. While it is far less invasive than other methods, its efficacy has not been thoroughly studied. This study aims to fill this technical gap by analyzing the correlation between the propagational characteristics of the ultrasonic stress wave using a novel embedded waveguide technique and the existing destructive testing methods. The proposed embedded waveguide technique excites diffusive Rayleigh mode (AW2) propagating in the shell region of the cross-sectional plane. This discovery allows a direct examination of the shell region condition through stress wave analysis. By employing the Gabor wavelet transformation and the model-based arrival region identification, this proposed technique extracts the propagation velocity and the associated spectral response of AW2. This study uses the static break assessment per ASTM 1036 Standard Test Methods And The longitudinal compression test per ASTM D143-14 "secondary method" to quantify the cross-sectional strength of the test specimen. This work performs a comprehensive correlation analysis between the extracted AW2 features and the associated destructive test. An overall correlation R² from 0.2 to 0.5 is achieved between the AW2 features and the static break test results. An overall correlation of R² of 0.4 is achieved for 30-35 ft poles in the longitudinal compression test.

Motion robust ICG measurements using a two-step spectrum denoising method

Objective. Impedance cardiography (ICG) is a noninvasive and continuous method for evaluating stroke volume and cardiac output. However, the ICG measurement is easily interfered due to respiration and body movements. Taking into consideration about the spectral correlations between the simultaneously collected ICG, electrocardiogram (ECG), and acceleration signals, this paper introduces a two-step spectrum denoising method to remove motion artifacts of ICG measurements in both resting and exercising scenarios.Approach. First, the major motion artifacts of ECG and ICG are separately suppressed by the spectral subtraction with respect to acceleration signals. The obtained ECG and ICG are further decomposed into two sets of intrinsic mode functions (IMFs) through the ensemble empirical mode decomposition. We then extract the shared spectral information between the two sets of IMFs using the canonical correlation analysis in a spectral domain. Finally, the ICG signal is reconstructed using those canonical variates with largest spectral correlations with ECG IMFs.Main results. The denoising method was evaluated for 30 subjects under both resting and cycling scenarios. Experimental results show that the beat contribution factor of ICG signals increases from its original 80.1%-97.4% after removing the motion artifacts.Significance. The proposed denoising scheme effectively improves the reliability of diagnosis and analysis on cardiovascular diseases relying on ICG signals.

Examining feedback mechanisms of postural control in Chiari Malformation by average wavelet coefficient decomposition and the Hurst exponent

BACKGROUND

Chiari Malformation (CM) is a congenital disorder occurring when the cerebellar tonsils descend into the foramen magnum, inhibiting cerebrospinal fluid (CSF) flow, causing headaches, dizziness, difficulty swallowing, muscle weakness, and loss of neuromuscular coordination. While there is no cure, surgical decompression of the hindbrain is used to alleviate symptoms. Loss of postural control is a main symptom reported by these patients; however, no study has examined postural stability in this cohort of patients.

RESEARCH QUESTION

Do patients with CM exhibit impaired postural stability compared to healthy controls?.

METHODS

Twelve female participants diagnosed with CM performed a postural stability test where six participants had undergone decompression (CM-D) surgery while six had not (CM-ND). Participants stood in Romberg fashion on an AMTI force plate according to an IRB-approved protocol. Postural stability measures were quantified by computing Hurst exponents. These values were determined from the Average Wavelet Coefficient method using a level 12 Symlet-2 wavelet to analyze anterior-posterior (AP) center-ofpressure (COP) trajectories in MATLAB. Identical procedures and analyses were performed on healthy control participants with no known neuromuscular disorders.

RESULTS

CM participants displayed significantly impaired postural stability compared to healthy controls (p = 0.0002). CM-D participants displayed significantly impaired postural stability compared to CM-ND (p = 0.002). CM-D and CM-ND both displayed significantly impaired postural stability compared to controls (p < 0.0001 and p < 0.003, respectively).

SIGNIFICANCE

Loss of postural stability is considered a main symptom of CM, however no study has previously quantified human postural control in this cohort of patients. Quantifying this relationship can provide further insight to neurologists studying the disorder and to therapists planning rehabilitation and pain relief methods.

On the Breaking of the Milankovitch Cycles Triggered by Temperature Increase: The Stochastic Resonance Response

Recent decades have registered the hottest temperature variation in instrumentally recorded data history. The registered temperature rise is particularly significant in the so-called hot spot or sentinel regions, characterized by higher temperature increases in respect to the planet average value and by more marked connected effects. In this framework, in the present work, following the climate stochastic resonance model, the effects, due to a temperature increase independently from a specific trend, connected to the 105 year Milankovitch cycle were tested. As a result, a breaking scenario induced by global warming is forecasted. More specifically, a wavelet analysis, innovatively performed with different sampling times, allowed us, besides to fully characterize the cycles periodicities, to quantitatively determine the stochastic resonance conditions by optimizing the noise level. Starting from these system resonance conditions, numerical simulations for increasing planet temperatures have been performed. The obtained results show that an increase of the Earth temperature boosts a transition towards a chaotic regime where the Milankovitch cycle effects disappear. These results put into evidence the so-called threshold effect, namely the fact that also a small temperature increase can give rise to great effects above a given threshold, furnish a perspective point of view of a possible future climate scenario, and provide an account of the ongoing registered intensity increase of extreme meteorological events.

The Optimal Selection of Mother Wavelet Function and Decomposition Level for Denoising of DCG Signal

The aim of this paper is to find the optimal mother wavelet function and wavelet decomposition level when denoising the Doppler cardiogram (DCG), the heart signal obtained by the Doppler radar sensor system. To select the best suited mother wavelet function and wavelet decomposition level, this paper presents the quantitative analysis results. Both the optimal mother wavelet and decomposition level are selected by evaluating signal-to-noise-ratio (SNR) efficiency of the denoised signals obtained by using the wavelet thresholding method. A total of 115 potential functions from six wavelet families were examined for the selection of the optimal mother wavelet function and 10 levels (1 to 10) were evaluated for the choice of the best decomposition level. According to the experimental results, the most efficient selections of the mother wavelet function are "db9" and "sym9" from Daubechies and Symlets families, and the most suitable decomposition level for the used signal is seven. As the evaluation criterion in this study rates the efficiency of the denoising process, it was found that a mother wavelet function longer than 22 is excessive. The experiment also revealed that the decomposition level can be predictable based on the frequency features of the DCG signal. The proposed selection of the mother wavelet function and the decomposition level could reduce noise effectively so as to improve the quality of the DCG signal in information field.

Understanding the surface condition of gamma irradiated epoxy alumina nanocomposites adopting wavelets and fractal technique

The influence of alumina nanofiller and gamma irradiation on the surface potential variation of epoxy-alumina nanocomposites was investigated. The surface potential decay rate of nanocomposites has increased and the trap depth decreased with alumina nanoparticles addition to the matrix as well as upon exposure to gamma irradiation, Surface roughness was estimated using the wavelets and fractal technique. Daubechies wavelet of order 4 (db4) wavelet was chosen as the most suitable mother wavelet for surface roughness measurement. Multi resolution signal decomposition (MRSD) analysis of surface profile has revealed that with increasing wt% of alumina nanofiller in the nanocomposites, reduction in surface roughness of nanocomposites was observed. Upon gamma irradiation, the surface roughness factor at each level of MRSD has increased marginally. Fractal dimension and lacunarity were calculated for unaged and gamma ray irradiated samples and it exhibits inverse correlation.

Transform-Based Multiresolution Decomposition for Degradation Detection in Cellular Networks

Anomaly detection in the performance of the huge number of elements that are part of cellular networks (base stations, core entities, and user equipment) is one of the most time consuming and key activities for supporting failure management procedures and ensuring the required performance of the telecommunication services. This activity originally relied on direct human inspection of cellular metrics (counters, key performance indicators, etc.). Currently, degradation detection procedures have experienced an evolution towards the use of automatic mechanisms of statistical analysis and machine learning. However, pre-existent solutions typically rely on the manual definition of the values to be considered abnormal or on large sets of labeled data, highly reducing their performance in the presence of long-term trends in the metrics or previously unknown patterns of degradation. In this field, the present work proposes a novel application of transform-based analysis, using wavelet transform, for the detection and study of network degradations. The proposed system is tested using cell-level metrics obtained from a real-world LTE cellular network, showing its capabilities to detect and characterize anomalies of different patterns and in the presence of varied temporal trends. This is performed without the need for manually establishing normality thresholds and taking advantage of wavelet transform capabilities to separate the metrics in multiple time-frequency components. Our results show how direct statistical analysis of these components allows for a successful detection of anomalies beyond the capabilities of detection of previous methods.

A Study of Personal Recognition Method Based on EMG Signal

With the increasing development of internet, the security of personal information becomes more and more important. Thus, variety of personal recognition methods have been introduced to ensure persons' information security. Traditional recognition methods such as Personal Identification Number (PIN), or Identification tag (ID) are vulnerable to hackers. Then the biometric technology, which uses the unique physiological characteristics of human body to identify user information has been proposed. But the biometrics widely used at present such as human face, fingerprint, iris, and voice can also be forged and falsified. The biometric with living body features such as electromyography (EMG) signal is a good method to achieve aliveness detection and prevent the spoofing attacks. However, there are few studies on personal recognition based on EMG signal. According to the application context, personal recognition system may operate either in identification mode or verification mode. In the personal identification mode, the system recognizes an individual by searching the templates of all the users in the database for a match. While in the personal verification mode, the system validates a person's identity by comparing the captured features with her or his own template(s) stored in the system database. In this paper, both EMG-based personal identification method and EMG-based personal verification method are investigated. First, the Myo armband is placed on the right forearm (specifically, the height of the radiohumeral joint) of 21 subjects to collect the surface EMG signal under hand-open gesture. Then, two different methods are proposed for EMG-based personal identification, i.e., personal identification method based on Discrete Wavelet Transform (DWT) and ExtraTreesClassifier, and personal identification method based on Continuous Wavelet Transform (CWT) and Convolutional Neural Networks (CNN). Experiments with 21 subjects show that the identification accuracy of this two methods can achieve 99.206% and 99.203% respectively. Then based on the identification method using CWT and CNN, transfer learning algorithm is adopted to solve the model update problem when new data is added. Finally, an EMG-based personal verification method using CWT and siamese networks is proposed. Experiments show that the verification accuracy of this method can achieve 99.285%.

Model-Based Data Driven Approach for Fault Identification in Proton Exchange Membrane Fuel Cell

This paper develops a model-based data driven algorithm for fault classification in proton exchange membrane fuel cells (PEMFCs). The proposed approach overcomes the drawbacks of voltage and current density assumptions in conventional model-based fault identification methods and data limitations in existing data driven approaches. This is achieved by developing a 3D model of fuel cells (FC) based on semi empirical model, analytical representation of electrochemical model, thermal model, and impedance model. The developed model is simulated for membrane drying and flooding faults in PEMFC and their effects are identified for the action of varying temperature, pressure, and relative humidity. The ohmic, concentration, activation and cell voltage losses for the simulated faults are observed and processed with wavelet transforms for feature extraction. Furthermore, the support vector machine learning algorithm is adapted to develop the proposed fault classification approach. The performance of the developed classifier is tested for an unknown data and calibrated through classification accuracy. The results showed 95.5% training efficiency and 98.6% testing efficiency.

Higher Sensitivity and Reproducibility of Wavelet-Based Amplitude of Resting-State fMRI

The fast Fourier transform (FFT) is a widely used algorithm used to depict the amplitude of low-frequency fluctuation (ALFF) of resting-state functional magnetic resonance imaging (RS-fMRI). Wavelet transform (WT) is more effective in representing the complex waveform due to its adaptivity to non-stationary or local features of data and many varieties of wavelet functions with different shapes being available. However, there is a paucity of RS-fMRI studies that systematically compare between the results of FFT versus WT. The present study employed five cohorts of datasets and compared the sensitivity and reproducibility of FFT-ALFF with those of Wavelet-ALFF based on five mother wavelets (namely, db2, bior4.4, morl, meyr, and sym3). In addition to the conventional frequency band of 0.0117-0.0781 Hz, a comparison was performed in sub-bands, namely, Slow-6 (0-0.0117 Hz), Slow-5 (0.0117-0.0273 Hz), Slow-4 (0.0273-0.0742 Hz), Slow-3 (0.0742-0.1992 Hz), and Slow-2 (0.1992-0.25 Hz). The results indicated that the Wavelet-ALFF of all five mother wavelets was generally more sensitive and reproducible than FFT-ALFF in all frequency bands. Specifically, in the higher frequency band Slow-2 (0.1992-0.25 Hz), the mean sensitivity of db2-ALFF results was 1.54 times that of FFT-ALFF, and the reproducibility of db2-ALFF results was 2.95 times that of FFT-ALFF. The findings suggest that wavelet-ALFF can replace FFT-ALFF, especially in the higher frequency band. Future studies should test more mother wavelets on other RS-fMRI metrics and multiple datasets.

Doppler Radar System for In-Home Gait Characterization using Wavelet Transform Analysis

The evaluation of walking speed plays an important role in gerontology as it reflects the health and functional status of older people. In this paper, we propose the use of a Doppler radar system with continuous wavelet transform (CWT) analysis for in-home gait characterization. A methodology based on an accurate 3D motion-capture camera system (Vicon) has been developed in order to validate the suitable mother wavelet. The CWT analysis with several mother wavelets has been applied to our experimental Doppler radar signals. The Pearson Correlation coefficient (ρ) has been computed between the gait speed signals obtained from the radar and those obtained from the Vicon system. Our outcomes suggest the use of Daubechies5 and Symlets7 wavelets giving a ρ values of 0.86 and 0.85 respectively with a mean square error value less than 0.05 m/s in comparison with the correct gait speed value.

High-contrast photoacoustic imaging through scattering media using correlation detection of adaptive time window

Photoacoustic imaging has the advantages of high contrast and deep imaging depth. However, with the increasing of imaging depth, the signal-to-noise ratio (SNR) of the detected signal decreases, due to the light scattering that seriously affects the recovery image quality. In this paper, we experimentally demonstrated that higher contrast photoacoustic imaging was achieved using photoacoustic wavefront shaping technology in the presence of light scattering and low SNR signals. The imaging contrast is improved from 1.51 to 5.30. More importantly, we propose a dynamic time window method for the photoacoustic signal extraction algorithm, named correlation detection of adaptive time window, which further improves the contrast of photoacoustic imaging to 9.57. Our method effectively improves the contrast of photoacoustic imaging through scattering media.

Wavelet Packet Singular Entropy-Based Method for Damage Identification in Curved Continuous Girder Bridges under Seismic Excitations

Curved continuous girder bridges (CCGBs) have been widely adopted in the civil engineering field in recent decades for complex interchanges and city viaducts. Unfortunately, compared to straight bridges, this type of bridge with horizontal curvature is relatively vulnerable to earthquakes characterized by large energy and short duration. Seismic damage can degrade the performance of CCGBs, threatening their normal operation and even resulting in collapse. Detection of seismic damage in CCGBs is thus significantly important but is still not well resolved. To this end, a new method based on wavelet packet singular entropy (WPSE) is proposed to identify seismic damage by analyzing the dynamic responses of CCGBs to seismic excitation. This WPSE-based approach features characterizing damage using synergistic advantage of the wavelet packet transform, singular value decomposition, and information entropy. To testify the algorithm, a finite element model of a typical CCGB with two types of seismic damage is built, in which the seismic damage is individually modeled by stiffness reductions at the bottom of piers and at pier-girder connections. The displacement responses of the model to El Centro seismic excitation is used to identify the damage. The results show that damage indices in the WPSE-based approach can correctly locate the seismic damage in CCGBs. Furthermore, the WPSE-based method is competent to identify damage with higher accuracy in comparison with the wavelet packet energy based method, and has a strong immunity to noise revealed by robustness analysis. An array of responses used in this approach paves the way of developing practical technologies for detecting seismic damage using advanced distributed sensing techniques, typically the optical sensors.

Appropriate Mother Wavelets for Continuous Gait Event Detection Based on Time-Frequency Analysis for Hemiplegic and Healthy Individuals

Gait event detection is a crucial step towards the effective assessment and rehabilitation of motor dysfunctions. Recently, the continuous wavelet transform (CWT) based methods have been increasingly proposed for gait event detection due to their robustness. However, few investigations on determining the appropriate mother wavelet with proper selection criteria have been performed, especially for hemiplegic patients. In this study, the performances of commonly used mother wavelets in detecting gait events were systematically investigated. The acceleration signals from the tibialis anterior muscle of both healthy and hemiplegic subjects were recorded during ground walking and the two core gait events of heel strike (HS) and toe off (TO) were detected from the signal recordings by a CWT algorithm with different mother wavelets. Our results showed that the overall performance of the CWT algorithm in detecting the two gait events was significantly different when using various mother wavelets. By using different wavelet selection criteria, we also found that the accuracy criteria based on time-error minimization and F1-score maximization could provide the appropriate mother wavelet for gait event detection. The findings from this study will provide an insight on the selection of an appropriate mother wavelet for gait event detection and facilitate the development of adequate rehabilitation aids.

Application of wavelet analysis on transient reflectivity in ultra-thin films

Applications of wavelet analysis in ultra-thin film transient reflectivity (TR) measurements have been investigated. Advantages of utilizing different localized wavelet bases, in position and time, have been addressed on the residual TR signals. Morse wavelets have been used to obtain information from the abrupt oscillatory modes in the signal, which are not distinguishable with conventional methods such as Fourier transforms. These abrupt oscillatory modes are caused by the surface, interface, or any short-lived oscillatory modes which are suppressed in the TR signal in ultra-thin films. It is demonstrated that by choosing different Morse wavelets, information regarding different oscillatory modes in the TR signal of a heterostructure thin film is achievable. Moreover, by performing wavelet analysis on multiferroic heterostructures, oscillatory modes with very close energy ranges are easily distinguishable. For illustration, residuals of the TR signals have been obtained by a pump-probe setup in reflectivity mode on La_0.7Sr_0.3MnO₃/SrTiO₃ and BaTiO₃/La_0.7Sr_0.3MnO₃/SrTiO₃ samples, where sufficient signal to noise ratios have been achieved by taking multiple scans. The residual signals have been analyzed with Morse wavelets, and multiple oscillatory modes with close energy ranges have been observed and distinguished. This approach can isolate the location of various oscillatory modes at the surface, interface and in the bulk of the heterostructure sample.

Photoacoustic Wavefront Shaping with High Signal to Noise Ratio for Light Focusing Through Scattering Media

Noninvasive light focusing and imaging through a scattering medium can be achieved by wavefront shaping using the photoacoustic signal as feedback. Unfortunately, the signal to noise ratio (SNR) of the traditional photoacoustic method is very low, which limits the wavefront shaping focusing speed and intensity. In this paper, we propose a completely new photoacoustic-signal-extraction method which combines wavelet denoising and correlation detection. With this method, the SNR of the photoacoustic signal reaches 25.2, 6.5 times higher than that of the unprocessed photoacoustic signal. Moreover, we achieve the simultaneous multipoint focusing, which is crucial for improving the speed of scanning imaging. The superior performance of the proposed method was experimentally demonstrated in extracting and denoising the photoacoustic signals deeply buried in noise, one critical step in in vivo photoacoustic imaging.

Identification and Representation of Multi-Pulse Near-Fault Strong Ground Motion Using Adaptive Wavelet Transform

In order to identify the horizontal seismic motion owning the largest pulse energy, and represent the dominant pulse-like component embedded in this seismic motion, we used the adaptive wavelet transform algorithm in this paper. Fifteen candidate mother wavelets were evaluated to select the optimum wavelet based on the similarities between the candidate mother wavelet and the target seismic motion, evaluated by the minimum cross variance. This adaptive choosing algorithm for the optimum mother wavelet was invoked before identifying both the horizontal direction owning the largest pulse energy and every dominant pulse, which provides the optimum mother wavelet for the continuous wavelet transform. Each dominant pulse can be represented by its adaptively selected optimum mother wavelet. The results indicate that the identified multi-pulse component fits well with the seismic motion. In most cases, mother wavelets in one multi-pulse seismic motion were different from each other. For the Chi-Chi event (1999-Sep-20 17:47:16 UTC, Mw = 7.6), 62.26% of the qualified pulse-like earthquake motions lay in the horizontal direction ranging from ±15° to ±75°. The Daubechies 6 (db6) mother wavelet was the most frequently used type for both the first and second pulse components.

Analysis of the tennis racket vibrations during forehand drives: Selection of the mother wavelet

The time-frequency analysis of the tennis racket and hand vibrations is of great interest for discomfort and pathology prevention. This study aimed to (i) to assess the stationarity of the vibratory signal of the racket and hand and (ii) to identify the best mother wavelet to perform future time-frequency analysis, (iii) to determine if the stroke spin, racket characteristics and impact zone can influence the selection of the best mother wavelet. A total of 2364 topspin and flat forehand drives were performed by fourteen male competitive tennis players with six different rackets. One tri-axial and one mono-axial accelerometer were taped on the racket throat and dominant hand respectively. The signal stationarity was tested through the wavelet spectrum test. Eighty-nine mother wavelet were tested to select the best mother wavelet based on continuous and discrete transforms. On average only 25±17%, 2±5%, 5±7% and 27±27% of the signal tested respected the hypothesis of stationarity for the three axes of the racket and the hand respectively. Regarding the two methods for the detection of the best mother wavelet, the Daubechy 45 wavelet presented the highest average ranking. No effect of the stroke spin, racket characteristics and impact zone was observed for the selection of the best mother wavelet. It was concluded that alternative approach to Fast Fourier Transform should be used to interpret tennis vibration signals. In the case where wavelet transform is chosen, the Daubechy 45 mother wavelet appeared to be the most suitable.

Towards Real-Time Detection of Freezing of Gait Using Wavelet Transform on Wireless Accelerometer Data

Injuries associated with fall incidences continue to pose a significant burden to persons with Parkinson’s disease (PD) both in terms of human suffering and economic loss. Freezing of gait (FOG), which is one of the symptoms of PD, is a common cause of falls in this population. Although a significant amount of work has been performed to characterize/detect FOG using both qualitative and quantitative methods, there remains paucity of data regarding real-time detection of FOG, such as the requirements for minimum sensor nodes, sensor placement locations, and appropriate sampling period and update time. Here, the continuous wavelet transform (CWT) is employed to define an index for correctly identifying FOG. Since the CWT method uses both time and frequency components of a waveform in comparison to other methods utilizing only the frequency component, we hypothesized that using this method could lead to a significant improvement in the accuracy of FOG detection. We tested the proposed index on the data of 10 PD patients who experience FOG. Two hundred and thirty seven (237) FOG events were identified by the physiotherapists. The results show that the index could discriminate FOG in the anterior–posterior axis better than other two axes, and is robust to the update time variability. These results suggest that real time detection of FOG may be realized by using CWT of a single shank sensor with window size of 2 s and update time of 1 s (82.1% and 77.1% for the sensitivity and specificity, respectively). Although implicated, future studies should examine the utility of this method in real-time detection of FOG.