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Taking the megacity of Beijing as an example, a short‐time Fourier transform (STFT) method was employed to extract the multi‐timescale evolution pattern of the canopy urban heat island intensity (CUHII) during 2000–2020. The STFT of CUHII showed a close relationship between the evolution of the CUHII in Beijing and the background meteorological forcing at intra‐annual, weather and intra‐daily scales. The intra‐annual‐scale spectrum of CUHII exhibited an increasing trend with obvious seasonal variation of the canopy urban heat island (CUHI). The intra‐daily‐scale spectrum of CUHII showed an increasing trend with the nighttime CUHI developing faster. Increasing Western Pacific Subtropical High intensity can enhance the seasonal and diurnal fluctuations of CUHII. The weather‐scale spectrum of CUHII is controlled by weather system evolution, showing that the frequency of cold/heat waves (CWs/HWs) in Beijing was significantly negatively correlated with the weather‐scale spectral intensity of the CUHII. CWs and HWs can increase the CUHII for a long duration. Plain Language Summary The canopy urban heat island (CUHI) phenomenon can affect human health and the ecological environment, and its multi‐timescale variability brings great uncertainty to the study of urban climates worldwide. In this study, taking the megacity of Beijing as an example, a novel short‐time Fourier transform (STFT) method was used to extract the multi‐timescale pattern of the CUHI intensity (CUHII) during 2000–2020. The STFT of CUHII showed a close relationship between the CUHI and the background meteorological forcing at intra‐annual, weather and intra‐daily scales. The intra‐annual spectrum of CUHII showed an increasing trend with a V‐shaped mode. The local climatic backgrounds of different cities can lead to differences in the seasonal development of the CUHI. The intra‐daily spectrum of CUHII showed an increasing trend due to the asymmetry in the day/night development of the CUHI. Increasing Western Pacific Subtropical High Intensity can enhance the seasonal and diurnal fluctuations of CUHII. The weather‐scale spectrum of CUHII was mainly controlled by weather system evolution, showing that cold waves and heat waves can increase the CUHII over a long duration. Our findings indicate that the evolution of CUHII is a nonlinear and complex process that is directly related to multi‐timescale background climate forcing. Key Points Using a short‐time Fourier transform to study the multi‐timescale evolution of the canopy urban heat island intensity (CUHII) Close relationships existed between CUHII and the background meteorological forcing at intra‐annual, intra‐daily, and weather scales The frequency of cold/heat waves in Beijing showed a significant negative correlation with the weather‐scale spectral intensity of the CUHII

The frequent switching of pump mode and turbine mode of the pump turbine leads to frequent transient phenomena. To ensure the safe and stable operation of the unit, a detailed study on the exhaust and pressurization process when the unit switches from turbine mode to the pump mode has been carried out. Based on the Shear Stress Transfer model (SST) k–ω turbulent model, the numerical simulations are processed both in a steady and unsteady state. The visualization results of gas–liquid two phases distribution in the dynamic process of exhaust and pressurization are given, and the characteristic references of each stage are also carried out. The transient characteristics of the torque, axial, and radial force of the runner and guide vane are analyzed by combining the short‐time Fourier transform. The results show that the main frequencies in this transient process are the blade passing frequency and its harmonic frequency. This process also presents a high amplitude band at all frequency values, which may be caused by the entrainment and centrifugal action of the runner on the free liquid surface. The exhaust and pressurization process when switching from turbine mode to pump mode of pump turbine units is studied. Based on the computational fluid dynamics numerical simulation method, visualization of the gas–liquid two‐phase distribution in this dynamic process was achieved. Combined with the short‐time Fourier transform, the transient characteristics of the torque, axial force, and radial force of the runner and guide vane in this process were analyzed, and the reasons for their formation were also demonstrated.

Liquefied hydrogen storage vessels (LHSVs) are vulnerable to surface-crack initiation, propagation, and fracture on their surfaces because they are under high-pressure, low-temperature conditions. Defects can also occur in the coatings of the storage containers used to prevent hydrogen permeation, and these lead to surface defects such as pitting corrosions. Together, these increase the probability of liquid hydrogen leaks and can cause serious accidents. Therefore, it is important to detect surface defects during periodic surface inspections of LHSVs. Among the candidate non-destructive evaluation (NDE) techniques, testing using guided waves (GWs) is effective for detecting surface defects. Because of the ability of GWs to travel long distances without significant acoustic attenuation, GW testing has attracted much attention as a promising structural monitoring technique for LHSVs. In this study, an ultrasonic NDE method was designed for detecting surface defects of 304SS plate, which is the main material used for fabricating LHSVs. It involves the use of linear discriminant analysis (LDA) based on short-time Fourier transform (STFT) pixel information produced from GW data. To accomplish this, the differences in the number of STFT pixels between sound and defective specimens were used as a major factor in distinguishing the two groups. Consequently, surface defects could be detected and classified with 97% accuracy by the newly developed pixel-based mapping method. This indicates that the newly developed NDE method with LDA can be used to detect defects and classify LHSVs as either sound or defective.

This paper presents an effective signal processing scheme of hand gesture recognition with a superior accuracy rate of judging identical and dissimilar hand gestures. This scheme is implemented with the air sonar possessing a pair of cost-effective ultrasonic emitter and receiver along with signal processing circuitry. Through the circuitry, the Doppler signals of hand gestures are obtained and processed with the developed algorithm for recognition. Four different hand gestures of push motion, wrist motion from flexion to extension, pinch out, and hand rotation are investigated. To judge the starting time of hand gesture occurrence, the technique based on continuous short-period analysis is proposed. It could identify the starting time of the hand gesture with small-scale motion and avoid faulty judgment while no hand in front of the sonar. Fusing the short-time Fourier transform spectrogram of hand gesture to the image processing techniques of corner feature detection, feature descriptors, and Hamming-distance matching are the first-time, to our knowledge, employed to recognize hand gestures. The results show that the number of matching points is an effective parameter for classifying hand gestures. Based on the experimental data, the proposed scheme could achieve an accuracy rate of 99.8% for the hand gesture recognition.

In this paper we consider the directional short-time Fourier transform (DSTFT) that was introduced and investigated in (Giv in J. Math. Anal. Appl. 399:100-107, 2013 ). We analyze the DSTFT and its transpose on test function spaces S ( R n ) and S ( Y 2 n ) , respectively, and prove the continuity theorems on these spaces. Then the obtained results are used to extend the DSTFT to spaces of distributions.

Low-cost and user-friendly benchtop low-field nuclear magnetic resonance (NMR) spectrometers are typically used to monitor food processes in the food industry. Because of excessive spectral overlap, it is difficult to characterize food mixtures using low-field NMR spectroscopy. In addition, for standard compounds, low-field benchtop NMR data are typically unavailable compared to high-field NMR data, which have been accumulated and are reusable in public databases. This work focused on NMR parameter visualization of the chemical structure and mobility of mixtures and the use of high-field NMR data to analyze benchtop NMR data to characterize food process samples. We developed a tool to easily process benchtop NMR data and obtain chemical shifts and T2 relaxation times of peaks, as well as transform high-field NMR data into low-field NMR data. Line broadening and time–frequency analysis methods were adopted for data processing. This tool can visualize NMR parameters to characterize changes in the components and mobilities of food process samples using benchtop NMR data. In addition, assignment errors were smaller when the spectra of standard compounds were identified by transferring the high-field NMR data to low-field NMR data rather than directly using experimentally obtained low-field NMR spectra.

We introduce the directional short-time fractional Fourier transform (DSTFRFT) and prove an extended Parseval’s identity and a reconstruction formula for it. We also investigate the continuity of both the directional short-time fractional Fourier transform and its synthesis operator on the appropriate space of test functions. Using the obtained continuity results, we develop a distributional framework for the DSTFRFT on the space of tempered distributions S ′ ( R n ) . We end the article with a desingularization formula.

Electric power utilities must ensure a consistent and undisturbed supply of power, with the voltage levels adhering to specified ranges. Any deviation from these supply specifications can lead to malfunctions in equipment. Monitoring the quality of supplied power is crucial to minimize the impact of fluctuations in voltage. Variations in voltage or current from their ideal values are referred to as \"power quality (PQ) disturbances,\" highlighting the need for vigilant monitoring and management. Signal processing methods are widely used for power system applications which include understanding of voltage disturbance signals and used for retrieval of signal information from the signals Different signal processing methods are used for extracting information about a signal. The method of Fourier analysis involves application of Fourier transform giving frequency information. The method of Short-Time Fourier analysis involves application of Short-Time Fourier transform (STFT) giving time–frequency information. The method of continuous wavelet analysis involves application of Continuous Wavelet transform (CWT) giving signal information in terms of scale and time where frequency is inversely related to scale. The method of discrete wavelet analysis involves application of Discrete Wavelet transform (DWT) giving signal information in terms of approximations and details where approximations and details are low and high frequency representation of original signal. In this paper, an attempt is made to perceive power quality disturbances in MATLAB using Fourier, Short-Time Fourier, Continuous Wavelet and Discrete Wavelet Transforms. Proper understanding of the signals can be possible by transforming the signals into different domains. An emphasis on application of signal processing techniques can be laid for power quality studies. The paper compares the results of each transform using MATLAB-based visualizations. The discussion covers the advantages and disadvantages of each technique, providing valuable insights into the interpretation of power quality disturbances. As the paper delves into the complexities of each method, it takes the reader on a journey of signal processing complexities, culminating in a nuanced understanding of power quality disturbances and their representations across various domains. The outcomes of this research, elucidated through energy values, 3D plots, and comparative analyses, contribute to a comprehensive understanding of power quality disturbances. The findings not only traverse theoretical domains but also find practical utility in real-world scenarios.

A hybrid deep learning approach was designed that combines deep learning with enhanced short-time Fourier transform (STFT) spectrograms and continuous wavelet transform (CWT) scalograms for pipeline leak detection. Such detection plays a crucial role in ensuring the safety and integrity of fluid transportation systems. The proposed model leverages the power of STFT and CWT to enhance detection capabilities. The pipeline’s acoustic emission signals during normal and leak operating conditions undergo transformation using STFT and CWT, creating scalograms representing energy variations across time–frequency scales. To improve the signal quality and eliminate noise, Sobel and wavelet denoising filters are applied to the scalograms. These filtered scalograms are then fed into convolutional neural networks, extracting informative features that harness the distinct characteristics captured by both STFT and CWT. For enhanced computational efficiency and discriminatory power, principal component analysis is employed to reduce the feature space dimensionality. Subsequently, pipeline leaks are accurately detected and classified by categorizing the reduced dimensional features using t-distributed stochastic neighbor embedding and artificial neural networks. The hybrid approach achieves high accuracy and reliability in leak detection, demonstrating its effectiveness in capturing both spectral and temporal details. This research significantly contributes to pipeline monitoring and maintenance and offers a promising solution for real-time leak detection in diverse industrial applications.

Successful applications of brain-computer interface (BCI) approaches to motor imagery (MI) are still limited. In this paper, we propose a classification framework for MI electroencephalogram (EEG) signals that combines a convolutional neural network (CNN) architecture with a variational autoencoder (VAE) for classification. The decoder of the VAE generates a Gaussian distribution, so it can be used to fit the Gaussian distribution of EEG signals. A new representation of input was developed by combining the time, frequency, and channel information from the EEG signal, and the CNN-VAE method was designed and optimized accordingly for this form of input. In this network, the classification of the extracted CNN features is performed via the deep network VAE. Our framework, with an average kappa value of 0.564, outperforms the best classification method in the literature for BCI Competition IV dataset 2b with a 3% improvement. Furthermore, using our own dataset, the CNN-VAE framework also yields the best performance for both three-electrode and five-electrode EEGs and achieves the best average kappa values 0.568 and 0.603, respectively. Our results show that the proposed CNN-VAE method raises performance to the current state of the art.