Time-frequency Representation Research Articles

LoRa Radio Frequency Fingerprinting with Residual of Variational Mode Decomposition and Hybrid Machine-Learning/Deep-Learning Optimization

RFF refers to the technique for identifying and classifying wireless devices on the basis of their physical characteristics, which appear in the digital signal transmitted in space. Small differences in the radio frequency front-end of the wireless devices are generated across the same wireless device model during the implementation and manufacturing process. These differences create small variations in the transmitted signal, even if the wireless device is still compliant with the wireless standard. By using data analysis and machine-learning algorithms, it is possible to classify different electronic devices on the basis of these variations. This technique has been well proven in the literature, but research is continuing to improve the classification performance, robustness to noise, and computing efficiency. Recently, DL has been applied to RFF with considerable success. In particular, the combination of time-frequency representations and CNN has been particularly effective, but this comes at a great computational cost because of the size of the time-frequency representation and the computing time of CNN. This problem is particularly challenging for wireless standards, where the data to be analyzed is extensive (e.g., long preambles) as in the case of the LoRa (Long Range) wireless standard. This paper proposes a novel approach where two pre-processing steps are adopted to (1) improve the classification performance and (2) to decrease the computing time. The steps are based on the application of VMD where (in opposition to the known literature) the residual of the VMD application is used instead of the extracted modes. The concept is to remove the modes, which are common among the LoRa devices, and keep with the residuals the unique intrinsic features, which are related to the fingerprints. Then, the spectrogram is applied to the residual component. Even after this step, the computing complexity of applying CNN to the spectrogram is high. This paper proposes a novel step where only segments of the spectrogram are used as input to CNN. The segments are selected using a machine-learning approach applied to the features extracted from the spectrogram using the LBP. The approach is applied to a recent LoRa radio frequency fingerprinting public data set, where it is shown to significantly outperform the baseline approach based on the full use of the spectrogram of the original signal in terms of both classification performance and computing complexity.

Impact location of metal structures based on time–frequency image features and deep residual network

Impact location detection plays an important role in the structural health monitoring of metal materials. However, the methods of metal material impact location detection based on physical analysis are often limited by the extraction accuracy of some parameters such as material and structure parameters and time difference calculation. Therefore, this paper develops a deep residual network method for impact location detection, time–frequency characteristic deep residual network (TF-DRN). This method takes the four-channel short-time Fourier transform time–frequency graph as input, uses the unique residual network architecture to automatically extract the advanced features, and then uses the global average pooling layer and the full connection layer to establish the mapping between the advanced features and the impact location, so as to detect the impact location. By introducing regularization and batch normalization, the problems of gradient disappearance and gradient explosion are alleviated, and the generalization and efficiency of impact location detection are further improved. The experimental results show that on an 800 mm × 800 mm × 2.5 mm aluminum plate, the average error of the validation set and the test set are 0.85 cm and 1.33 cm respectively, and the performance of the method is significantly better than that of CNN, ResNet18 and ResNet33 networks.

High-resolution ground motion generation with time–frequency representation

High-resolution ground motion generation with time–frequency representation

Entropy-Aided Meshing-Order Modulation Analysis for Wind Turbine Planetary Gear Weak Fault Detection under Variable Rotational Speed

As one of the most vital energy conversation systems, the safe operation of wind turbines is very important; however, weak fault and time-varying speed may challenge the conventional monitoring strategies. Thus, an entropy-aided meshing-order modulation method is proposed for detecting the optimal frequency band, which contains the weak fault-related information. Specifically, the variable rotational frequency trend is first identified and extracted based on the time–frequency representation of the raw signal by constructing a novel scaling-basis local reassigning chirplet transform (SLRCT). A new entropy-aided meshing-order modulation (EMOM) indicator is then constructed to locate the most sensitive modulation frequency area according to the extracted fine speed trend with the help of order tracking technique. Finally, the raw vibration signal is bandpass filtered via the corresponding optimal frequency band with the highest EMOM indicator. The order components resulting from the weak fault can be highlighted to accomplish weak fault detection. The effectiveness of the proposed EMOM analysis-based method has been tested using the experimental data of three different gear fault types of different fault levels from a planetary test rig.

A study of oil–water two-phase flow pattern recognition based on thermal sensors

To understand the flow characteristics and kinetic modelling of oil–water two-phase flow(OWTPF), this paper employs thermal array sensors to identify the flow pattern (FP) in OWTPF horizontal pipelines. Firstly, the thermal array sensor installation was constructed. Secondly, the time-varying characteristics of multi-feature signals were qualitatively analyzed using the adaptive optimal kernel time–frequency representation (AOK-TFR) method and unthresholded recurrence plot (URP) method. Finally, the sparrow search algorithm-support vector machine (SSA-SVM) machine learning algorithm is used for quantitative prediction of multi-feature classification, which leads to high prediction accuracy. The experiment proves that the correct rate of the thermal method in recognizing six types of OWTPF is above 91%, the correct rate of five types of flow is above 97.33%. This paper adopts the thermal method to identify the multiphase FP, which is a major innovation in this paper and also lays the foundation for recognizing the flow characteristics of multiphase flow.

A Novel Time-frequency Representation Method: The Generalized W Transform

The time-frequency representation (TFR) of seismic data is an effective technology for the detection of hydrocarbon reservoirs. To obtain the TFR of a seismic trace, a mathematical transform tool must be used to perform the decomposition of the seismic trace. This paper introduces an effective time-frequency decomposition method: the generalized W transform (GWT). We prove that the GWT is not a strictly reversible mathematical transform. The numerical experiment of a simulated seismic trace shows that the reconstruction relative error of inverse GWT could reach up to 20%. Nevertheless, the time-frequency spectrum obtained from its forward transform is particularly suitable for identifying oil and gas reservoirs. The presented GWT has three advantages: (1) Its time-frequency spectrum has a high temporal resolution even at low frequencies; (2) The spectral centroid corresponds to the peak frequency of the wavelet; (3) It eliminates the singularity of the original W transform (WT) at the peak frequency of the waveform. Compared with the wavelet transform and the S transform, the generalized W transform can more accurately characterize reservoirs. A real data example illustrates that the GWT provides better TFR performance and can more effectively identify hydrocarbon reservoirs.

Development of a 90–600 MHz Meter-wave Solar Radio Spectrometer

Radio observation is important for understanding coronal mass ejections (CMEs), coronal shock waves, and high-energy electron acceleration. Here, we developed a new Chashan broadband solar radio spectrometer at a meter wavelength for observing the (super)fine structure of the solar radio burst spectrum. In the signal-receiving unit, we adopt an antenna system consisting of a 12 m large-aperture parabolic reflector and dual-line polarized logarithmic periodic feed source, as well as a high-precision Sun-tracking turntable system, all of which ensure the high-precision acquisition of solar radiation signals. For the digital receiver, we use a high-speed analog-to-digital converter with a sampling rate of 1.25 GSPS to directly sample the signal amplified and filtered by the analog receiver, simplifying the structure of the analog receiver, and design a 16k-point fast Fourier transform algorithm in the field programmable gate array to perform time–frequency transformation on the sampled signals. The default frequency and temporal resolution of the system are 76.294 kHz and 0.839 ms (up to 0.21 ms), respectively. The noise coefficient of the system is less than 1 dB, the dynamic range is more than 60 dB, and the sensitivity is as high as 1 sfu. We have observed a large number of radio bursts, including type I radio storms, hundreds of type III, ∼20 type II, and ∼15 type IV bursts in the past year. These high-quality data are useful in the further study of CMEs and associated particle acceleration and the origins of solar radio bursts.

Unsupervised recognition of radar signals combining multi-block TFR with subspace clustering

In the realm of radar systems, the proliferation of new modulation techniques introduces an increased level of complexity in the identification of both existing and potentially novel modulation schemes. Conventional supervised recognition methodologies, which rely heavily on labeled datasets, exhibit limitations in distinguishing amongst a multitude of unlabeled signals. This paper introduces a novel framework that synergizes Subspace Clustering (SC) with Multi-Block Time-Frequency Representations (TFRs, denoted as mT), referred to as SC-mT. This framework leverages subspace clustering for the unsupervised categorization of radar modulations and employs an innovative multi-block strategy to augment classification precision. The process commences with the generation of TFR datasets for radar signals, followed by the construction of two distinct multi-block models, Model-A and Model-B. These models segment the radar TFRs into overlapping multi-block sets, utilizing the concept of random receptive fields. The subspace clustering algorithm is then applied to each block within the sub-TFR sets to procure an affinity matrix. The culmination of this process involves the aggregation of the affinity matrices from all blocks, facilitating the derivation of classification outcomes via spectral clustering. Empirical analyses affirm that the sequential integration of the SC-mT algorithm surpasses the classification efficacy of various conventional and cutting-edge algorithms. Notably, this algorithm attains a classification accuracy surpassing 90% for ten unlabeled signals, even in scenarios where the signal-to-noise ratio (SNR) is as low as -4 dB.

DTP-Net: Learning to Reconstruct EEG Signals in Time-Frequency Domain by Multi-Scale Feature Reuse.

Electroencephalography (EEG) signals are prone to contamination by noise, such as ocular and muscle artifacts. Minimizing these artifacts is crucial for EEG-based downstream applications like disease diagnosis and brain-computer interface (BCI). This paper presents a new EEG denoising model, DTP-Net. It is a fully convolutional neural network comprising Densely-connected Temporal Pyramids (DTPs) placed between two learnable time-frequency transformations. In the time-frequency domain, DTPs facilitate efficient propagation of multi-scale features extracted from EEG signals of any length, leading to effective noise reduction. Comprehensive experiments on two public semi-simulated datasets demonstrate that the proposed DTP-Net consistently outperforms existing state-of-the-art methods on metrics including relative root mean square error (RRMSE) and signal-to-noise ratio improvement ( ∆SNR). Moreover, the proposed DTP-Net is applied to a BCI classification task, yielding an improvement of up to 5.55% in accuracy. This confirms the potential of DTP-Net for applications in the fields of EEG-based neuroscience and neuro-engineering. An in-depth analysis further illustrates the representation learning behavior of each module in DTP-Net, demonstrating its robustness and reliability.

Automatic Estimation of the Interference Subspace Dimension Threshold in the Subspace Projection Algorithms of Magnetoencephalography Based on Evoked State Data

A class of algorithms based on subspace projection is widely used in the denoising of magnetoencephalography (MEG) signals. Setting the dimension of the interference (external) subspace matrix of these algorithms is the key to balancing the denoising effect and the degree of signal distortion. However, most current methods for estimating the dimension threshold rely on experience, such as observing the signal waveforms and spectrum, which may render the results too subjective and lacking in quantitative accuracy. Therefore, this study proposes a method to automatically estimate a suitable threshold. Time–frequency transformations are performed on the evoked state data to obtain the neural signal of interest and the noise signal in a specific time–frequency band, which are then used to construct the objective function describing the degree of noise suppression and signal distortion. The optimal value of the threshold in the selected range is obtained using the weighted-sum method. Our method was tested on two classical subspace projection algorithms using simulation and two sensory stimulation experiments. The thresholds estimated by the proposed method enabled the algorithms to achieve the best waveform recovery and source location error. Therefore, the threshold selected in this method enables subspace projection algorithms to achieve the best balance between noise removal and neural signal preservation in subsequent MEG analyses.

Maritime Moving Target Reconstruction via MBLCFD in Staggered SAR System

Imaging maritime targets requires a high resolution and wide swath (HWRS) in a synthetic aperture radar (SAR). When operated with a variable pulse repetition interval (PRI), a staggered SAR can realize HRWS imaging, which needs to be reconstructed due to echo pulse loss and a nonuniformly sampled signal along the azimuth. The existing reconstruction algorithms are designed for stationary scenes in a staggered SAR mode, and thus, produce evident image defocusing caused by complex target motion for moving targets. Typically, the nonuniform sampling and complex motion of maritime targets aggravate the spectrum aliasing in a staggered SAR mode, causing inevitable ambiguity and degradation in its reconstruction performance. To this end, this study analyzed the spectrum of maritime targets in a staggered SAR system through theoretical derivation. After this, a reconstruction method named MBLCFD (Modified Best Linear Unbaised and Complex-Lag Time-Frequency Distribution) is proposed to refocus the blurred maritime target. First, the signal model of the maritime target with 3D rotation accompanying roll–pitch–yaw movement was established under the curved orbit of the satellite. The best linear unbiased (BLU) method was modified to alleviate the coupling of nonuniform sampling and target motion. A precise SAR algorithm was performed based on the method of inverse reversion to counteract the effect of a curved orbit and wide swath. Based on the hybrid SAR/ISAR technique, the complex-lag time-frequency distribution was exploited to refocus the maritime target images. Simulations and experiments were carried out to verify the effectiveness of the proposed method, providing precise refocusing performance in staggered mode.

A sparse time-frequency reconstruction approach from the synchroextracting domain

Synchroextracting, including frequency-extracting and transient-extracting, offers a sparse time-frequency (TF) representation for multi-component signals. However, it is susceptible to amplitude modulation (AM) and frequency modulation (FM) when reconstructing the raw signal through the TF ridge. This paper proposes a new signal reconstruction approach (SRA) in the synchroextracting domain to address this limitation. This approach performs synchroextracting on the short-time Fourier transform (STFT) domain. We incorporate the extracting operator in the inverse STFT to establish the mathematical relationship between the synchroextracting representation and the retrieved signal, thus enabling the reconstruction of each mode in the synchroextracting domain. The proposed SRA is theoretically derived, and its reconstruction performance is evaluated in the frequency-extracting and transient-extracting domains. Two synthetic signals are utilized to demonstrate that compared with some advanced reconstruction methods, the SRA has a high reconstruction accuracy, strong noise robustness, and is less affected by AM-FM features and the window length. The application of the bat signal further clarifies the advantages of the SRA and its feasibility in practical applications. Moreover, this study also provides a new reconstruction framework and reference for other synchroextracting-type methods.

Dynamic Response of Phase Change Heat Exchange Unit with Layered Porous Media for Pulsed Electronic Equipment

Effective heat dissipation challenges transient high-power electronic devices in hypersonic vehicle cabins. This study introduces a Phase Change Heat Exchange Unit with Layered Porous Media (PCHEU–LPM) employing pulsed heat flow at the top and forced convection at the bottom. The primary aim was a comparative parametric study analyzing the thermal response of the heating surface under pulsed heat flow conditions. The geometric model was generated using electron microscopy images of manufactured objects and the numerical model was established based on the enthalpy–porosity method. Numerical simulations explored amplitude and frequency effects on pulsed thermal excitation, evaluating temperature and phase fields. A comprehensive time-frequency transformation assessed the temperature response. The results indicated an initial decrease and subsequent increase in interface temperature fluctuation with pulse heat flux amplitude growth. Temperature field uniformity correlated with natural convection strength in two-phase and liquid-phase regions. At mid and low frequencies, the phase change process increasingly suppressed interface temperature fluctuations. Optimal pulse thermal excitation selection was crucial for minimizing temperature fluctuations while maintaining the interface temperature within the expected phase transition range. In conclusion, a novel design concept is posited herein, aiming to enhance surface temperature uniformity and broaden the applicability of electronic devices through the manipulation of porosity rates.

Multi scale encoder-decoder network with Time Frequency Attention and S-TCN for single channel speech enhancement

The goal of speech enhancement is to restore clean speech in noisy environments. Acoustic scenarios with low signal-to-noise ratios (SNR) make it quite challenging to extract the target speech from its noise. In the current study, to enhance noisy speech, we propose a feature recalibration based multi-scale convolutional encoder-decoder architecture with squeeze temporal convolutional networks (S-TCN) bottleneck. Each multi-scale convolutional layer in encoder and decoder is followed by time-frequency attention module (TFA). The recalibration based multi-scale 2D convolution layers are used to extract local and contextual information. Additionally, the recalibration network is equipped with a gating mechanism to control the flow of information among the layers, enabling weighting of the scaled features for noise suppression and speech retention. The fully connected layer (FC) in the bottleneck part of encoder-decoder contains a few neurons, which capture the global information from the multi-scale 2D convolution layer and reduce parameters. A S-TCN, inspired by the popular temporal convolutional neural network (TCNN), is inserted between the encoder and the decoder to model long-term dependencies in speech. The TFA is a highly efficient network component, that operates through two simultaneous attentions, one focused on time frames, and the other on frequency channels. These attentions work together to explicitly exploit positional information to create a two-dimensional attention map to effectively capture the significant time-frequency distribution of speech. Utilizing the common voice dataset, our proposed model consistently enhances results compared to the current benchmarks, as demonstrated by two extensively utilized objective measures PESQ and STOI. The proposed model shows significant improvements, with average PESQ and STOI scores increasing by 45.7% and 23.8% respectively for seen background noises, and by 43.5% and 21.4% for unseen background noises, when compared to the quality of noisy speech. Tests validate that the proposed approach outperforms numerous cutting-edge algorithms.

A novel spectrogram based lightweight deep learning for IoT spectrum monitoring

The integration of cognitive radio network (CRNet) with internet of things (IoT) holds tremendous potential for creating more intelligent and advanced technological ecosystems. By allowing IoT devices to dynamically access and utilize the available radio spectrum, CRNet-based IoT systems can enable transparent connectivity, faster data transmission, and efficient resource utilization. The successful deployment of CRNet-based IoT systems highly depends on spectrum sensing implementation, which makes selecting the appropriate spectrum sensing technique extremely critical. However, several challenges are associated with the current spectrum sensing techniques, including limited representation of signal features, susceptibility to noise, inadequate hardware compatibility, and significant performance degradation using deep learning models. To deal with these issues, a novel approach is proposed integrating spectrogram representation and lightweight convolutional neural network models. Unlike raw digital representation, spectrograms allow efficient and consistent feature extraction using time–frequency representation of the received signals. Lightweight convolutional neural network models leverage advanced deep learning techniques to achieve fast and accurate predictions from spectrograms. They require few parameters to process while reduce the computational burden. The proposed approach is a promising solution for performing spectrum sensing in resource-constrained environments paving the way for efficient use of radio spectrum in IoT networks. The performance of the proposed approach is evaluated and compared to the existing techniques. Spectrogram based lightweight deep learning achieved high efficiency while required less computational resources.

Bearings fault diagnosis under variable speed conditions by hypothesis-based FRFT technique

The vibration signals of faulty bearings under non-stationary conditions are inherently multi-component and time-varying, which presents a challenge for effective fault diagnosis. Considering the vibration characteristics of rolling bearings under non-stationary conditions and taking advantage of the Fractional Fourier Transform (FRFT), a novel diagnosis method based on the hypothesis-based FRFT has been proposed to separate the fault components. First, the fault characteristic frequencies (FCFs) are extracted from the time-frequency representation of the vibration signals, and the Vold-Kalman filtering is employed to eliminate the influence of noises and other interference components. Subsequently, the fractional feature model is constructed to obtain speed information by the hypothesis approach, whose central idea is that the rotational frequency (RF)-related frequencies under different fault types are estimated, based on the extracted FCFs and the fault characteristic orders. Finally, fault diagnosis is completed by the RF-related peaks in the final spectrum. The method eliminates the need for rotational speed measurement devices and angular resampling. Simulation and experiment estimation results show that the hypothesis-based FRFT method can accurately locate fault characteristic components of bearings under non-stationary conditions.

A Data Augmentation Method for Motor Imagery EEG Signals Based on DCGAN-GP Network.

Motor imagery electroencephalography (EEG) signals have garnered attention in brain-computer interface (BCI) research due to their potential in promoting motor rehabilitation and control. However, the limited availability of labeled data poses challenges for training robust classifiers. In this study, we propose a novel data augmentation method utilizing an improved Deep Convolutional Generative Adversarial Network with Gradient Penalty (DCGAN-GP) to address this issue. We transformed raw EEG signals into two-dimensional time-frequency maps and employed a DCGAN-GP network to generate synthetic time-frequency representations resembling real data. Validation experiments were conducted on the BCI IV 2b dataset, comparing the performance of classifiers trained with augmented and unaugmented data. Results demonstrated that classifiers trained with synthetic data exhibit enhanced robustness across multiple subjects and achieve higher classification accuracy. Our findings highlight the effectiveness of utilizing a DCGAN-GP-generated synthetic EEG data to improve classifier performance in distinguishing different motor imagery tasks. Thus, the proposed data augmentation method based on a DCGAN-GP offers a promising avenue for enhancing BCI system performance, overcoming data scarcity challenges, and bolstering classifier robustness, thereby providing substantial support for the broader adoption of BCI technology in real-world applications.

A micro-Doppler spectrogram denoising algorithm for radar human activity recognition

Radar signal recognition based on micro-Doppler spectrogram has been widely used in human action recognition tasks. However, in practical application scenarios, radar signals inevitably have noise, which leads to different degrees of deformation of the spectrogram graph structure and affects the accuracy of subsequent recognition algorithms. In this paper, we present “ACFL”, a novel algorithm for micro-Doppler spectrogram denoising, which aims to reduce the impact of noise on human action recognition. ACFL employs amplitude–frequency two-dimensional clustering and fuzzy logic clustering selection mechanism to remove noise elements from the spectrogram. Moreover, to address the issue of noise leakage or target missing under time-varying noise and action conditions, ACFL adopts spectrogram segmentation based on short-term Rényi entropy. By dividing the spectrogram into intervals with different time–frequency distributions, the dynamic spectrogram denoise over time is achieved. Simulation and measured data experiments demonstrate that the proposed algorithm not only achieves a higher-quality denoised spectrogram but also significantly improves the accuracy of human action recognition under noisy conditions.

Altered neural oscillations in classical galactosaemia during sentence production.

Classical galactosaemia (CG) is a hereditary disease in galactose metabolism that despite dietary treatment is characterized by a wide range of cognitive deficits, among which is language production. CG brain functioning has been studied with several neuroimaging techniques, which revealed both structural and functional atypicalities. In the present study, for the first time, we compared the oscillatory dynamics, especially the power spectrum and time-frequency representations (TFR), in the electroencephalography (EEG) of CG patients and healthy controls while they were performing a language production task. Twenty-one CG patients and 19 healthy controls described animated scenes, either in full sentences or in words, indicating two levels of complexity in syntactic planning. Based on previous work on the P300 event related potential (ERP) and its relation with theta frequency, we hypothesized that the oscillatory activity of patients and controls would differ in theta power and TFR. With regard to behavior, reaction times showed that patients are slower, reflecting the language deficit. In the power spectrum, we observed significant higher power in patients in delta (1-3 Hz), theta (4-7 Hz), beta (15-30 Hz) and gamma (30-70 Hz) frequencies, but not in alpha (8-12 Hz), suggesting an atypical oscillatory profile. The time-frequency analysis revealed significantly weaker event-related theta synchronization (ERS) and alpha desynchronization (ERD) in patients in the sentence condition. The data support the hypothesis that CG language difficulties relate to theta-alpha brain oscillations.

Control of quantum paths in harmonic generation through orthogonal fields specific frequency ratios

By solving a two-dimensional, time-dependent Schrödinger equation, we investigate high-order harmonic generation for the H2+ molecular ion in orthogonally polarized two-color laser pulses. We find that harmonic generation depends on the frequency ratio n=ωyωx . When the wavelength is 800 nm and n = 1.2, the harmonic plateau becomes smoother, and the quantum orbital interference decreases. We change the fundamental wavelength and find that the harmonic spectrum exhibits a supercontinuum structure, and the quantum orbital is controllable. When the wavelength is 1600 nm and 2000 nm, and n = 1.2, we gain a deeper understanding of the physical process of harmonics. We have provided the time-frequency distribution and the probability density of an electron wave packet picture. Next, we analyzed the impact of the carrier-envelope phase on harmonics, and we combined Lissajous figures to continue our analysis. The research results find that when the carrier-envelope phase is 0, 0.5π, π, and 1.5π, the harmonic intensity becomes higher, and all exhibit a supercontinuum structure. We chose certain orders of harmonics, and isolated attosecond pulses can be synthesized.