Time-frequency Representation Research Articles

Investigation and evaluation of cross-term reduction in masked Wigner-Ville distributions using S-transforms.

Non-linear and non-stationary signals are analyzed and processed in the time-frequency (TF) domain due to interpretation simplicity. Wigner-Ville distribution (WVD) delivers a very sharp resolution of non-stationary signals in the TF domain. However, cross-terms occur between true frequency modes due to their bilinear nature. Masked WVD reduces cross-terms by multiplying the time-frequency representation (TFR) obtained from the WVD with the TFR of the same signal obtained from another method, while S-transform (ST) is a linear signal analysis method that combines the advantages of short-time Fourier transform (STFT) and wavelet transform (WT). This paper investigated WVD masking with both original and modified STs to compare their cross-term reduction results. Moreover, additional parameters are integrated into the ST to deliver the better resolution of the ST and, consequently, more satisfactory cross-term reduction. However, these parameters must be carefully optimized by expert users in their respective application fields.

Comparison of dry and wet electroencephalography for the assessment of cognitive evoked potentials and sensor-level connectivity

BackgroundMultipin dry electrodes (dry EEG) provide faster and more convenient application than wet EEG, enabling extensive data collection. This study aims to compare task-related time-frequency representations and resting-state connectivity between wet and dry EEG methods to establish a foundation for using dry EEG in investigations of brain activity in neuropsychiatric disorders.MethodsIn this counterbalanced cross-over study, we acquired wet and dry EEG in 33 healthy participants [n = 22 females, mean age (SD) = 24.3 (± 3.4) years] during resting-state and an auditory oddball paradigm. We computed mismatch negativity (MMN), theta power in task EEG, and connectivity measures from resting-state EEG using phase lag index (PLI) and minimum spanning tree (MST). Agreement between wet and dry EEG was assessed using Bland–Altman bias.ResultsMMN was detectable with both systems in time and frequency domains, but dry EEG underestimated MMN mean amplitude, peak latency, and theta power compared to wet EEG. Resting-state connectivity was reliably estimated with dry EEG using MST diameter in all except the very low frequencies (0.5–4 Hz). PLI showed larger differences between wet and dry EEG in all frequencies except theta.ConclusionDry EEG reliably detected MMN and resting-state connectivity despite a lower signal-to-noise ratio. This study provides the methodological basis for using dry EEG in studies investigating the neural processes underlying psychiatric and neurological conditions.

Masked Time-Frequency Representation and Composite Priors Enabled Mixed-Mode Signal Decomposition Algorithm

Masked Time-Frequency Representation and Composite Priors Enabled Mixed-Mode Signal Decomposition Algorithm

Traveling wave mode analysis of a coherence collapse regime semiconductor laser with optical feedback

A highly developed traveling wave model for a semiconductor laser system supports sophisticated mode analysis of the coherence collapse regime in semiconductor lasers with delayed optical feedback. The concept of instantaneous optical modes is used. Time-frequency representations of chaotic trajectories are constructed and interpreted. This involves synthesizing the calculated optical modes with their corresponding steady states, analysis of the mode driving and coupling sources, and field expansion into modal components. The results support detailed physical interpretation of the optical and radiofrequency spectra throughout the coherence collapse regime. This includes simulation results for the transition out of coherence collapse at high optical feedback. Also key frequencies observed in the radiofrequency spectrum of the chaotic output are linked to the modes that mix to generate them.

Noise robust damage detection of laminated composites using multichannel wavelet-enhanced deep learning model

This paper presents a noise-robust damage detection framework for composite structures via a commonly used vibration-based non-destructive testing (NDT) method. Recently, deep learning-based models have shown promising performance in the autonomous damage detection of laminated composites; however, the poor noise robustness of these models has plagued data-driven damage detection. Moreover, none of the existing studies on damage detection in laminated composites focus on noise-robust deep learning models with high generalization ability. Therefore, this study proposes a hybrid deep learning framework called a multi-channel convolutional autoencoder-support vector machine (MC-CAE-SVM) based on empirical mode decomposition (EMD) and correlation analysis for noise-robust damage detection. This framework aims to first decompose the vibrational signal from multiple health states into intrinsic mode functions (IMFs). Secondly, highly correlated IMFs were extracted using correlation analysis to remove noisy IMFs. Finally, these IMFs were transformed into a time-frequency representation using continuous wavelet transform (CWT) and input to the MC-CAE-SVM model for feature learning and damage detection. Additionally, the accuracy and sensitivity of the model to damage are enhanced by optimizing the MC-CAE-SVM model hyperparameters. Moreover, anti-noise analysis is performed to check the noise-robustness of the proposed model by incorporating noise at various levels. The results showed that the proposed model can provide better damage detection performance compared to conventional models with excellent noise robustness.

Dynamic mode decomposition-based technique for cross-term suppression in the Wigner-Ville distribution

This paper presents a new method for time-frequency representation (TFR) using dynamic mode decomposition (DMD) and Wigner-Ville distribution (WVD), which is termed as DMD-WVD. The proposed method helps in removing cross-term in WVD-based TFR. In the suggested method, the DMD decomposes the multi-component signal into a set of modes where each mode is considered as mono-component signal. The analytic modes of these obtained mono-component signals are computed using the Hilbert transform. The WVD is computed for each analytic mode and added together to obtain cross-term free TFR based on the WVD. The effectiveness of the proposed method for TFR is evaluated using Rényi entropy (RE). Experimental results for synthetic signals namely, multi-component amplitude modulated signal, multi-component linear frequency modulated (LFM) signal, multi-component nonlinear frequency modulated (NLFM) signal, multi-component signal consisting of LFM and NLFM mono-component signal, multi-component signal consisting of sinusoidal and quadratic frequency modulated mono-component signals, and synthetic mechanical bearing fault signal and natural signals namely, electroencephalogram (EEG) and bat echolocation signals are presented in order to show the effectiveness of the proposed method for TFR. It is clear from the results that the proposed method suppresses cross-term effectively as compared to the other existing methods namely, smoothed pseudo WVD (SPWVD), empirical mode decomposition (EMD)-WVD, EMD-SPWVD, variational mode decomposition (VMD)-WVD, VMD-SPWVD, and DMD-SPWVD.

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Warped time-frequency systems have recently been introduced as a class of structured continuous frames for functions on the real line. Herein, we generalize this framework to the setting of functions of arbitrary dimensionality. After showing that the basic properties of warped time-frequency representations carry over to higher dimensions, we determine conditions on the warping function which guarantee that the associated Gramian is well-localized, so that associated families of coorbit spaces can be constructed. We then show that discrete Banach frame decompositions for these coorbit spaces can be obtained by sampling the continuous warped time-frequency systems. In particular, this implies that sparsity of a given function f in the discrete warped time-frequency dictionary is equivalent to membership of f in the coorbit space. We put special emphasis on the case of radial warping functions, for which the relevant assumptions simplify considerably.

Fault Diagnosis Method for Marine Electric Propulsion Systems Based on Zero-Crossing Tacholess Order Tracking

In marine electric propulsion systems (MEPS) driven by variable-frequency drives, motor current signals often exhibit complex modulation components, ambiguous spectra, and severe noise interference, rendering it challenging to extract fault-related modulation components. To address this issue, we propose a zero-crossing tacholess order tracking method based on motor current signals. This method utilizes zero-crossing estimation of the instantaneous frequency to perform angular resampling of stator current signals and demodulates the envelope spectrum to extract fault characteristic spectra, enabling the diagnosis of mechanical faults in MEPS. Given the synchronization of the synchronous motor speed with the inverter fundamental frequency, this method estimates instantaneous frequencies in the time domain without requiring integration or time–frequency representation, which is simple and computationally efficient. Data validation on a small-scale marine electric propulsion test platform demonstrates that the proposed method exhibits good robustness under variable-speed conditions and effectively detects imbalance faults caused by propeller breakages and gear faults resulting from bevel gear tooth defects. Therefore, the proposed method can be applied to diagnose faults in downstream mechanical equipment driven by motors.

High performance method for COPD features extraction using complex network.

Objectives. The paper proposes a novel methodology for the classification of Chronic Obstructive Pulmonary Disease (COPD) utilizing respiratory sound attributes.Methods. The approach involves segmenting respiratory sounds into individual breaths and conducting extensive studies on this dataset. Spectral Transforms, various Wavelet Transforms are applied to capture distinct signal features. Complex Network is also employed to extract characteristic elements, generating novel representations of spectrogram data based on graph factors, including entropy, density, and position. The normalized and enriched data is then used to develop COPD classifiers using six machine learning algorithms, fine-tuning with appropriate training details and hyperparameter tuning.Results. Our results demonstrate robust performance, with ROC curves consistently exhibiting an Area Under the Curve (AUC) > 96% across different time-frequency transformations. Notably, the Random Forest algorithm achieves an AUC of 99.67%, outperforming other algorithms. Moreover, the Wavelet Daubechies 2 (Db2) consistently approaches 98% accuracy, particularly noteworthy in conjunction with the Naive Bayes algorithm.Conclusion. This study diagnosis patients through spectrogram images extracted from lung sounds. The application of Inverse Transforms, Complex Network, and Optimized Classification Algorithms yielded results beyond expectations. This methodology provides a promising approach for accurate COPD diagnosis, leveraging Machine Learning techniques applied to respiratory sound analysis.

An adaptive parameter-free seismic data denoising approach by combining general cross-validation thresholding and pixel connectivity in synchrosqueezed domain

High signal-to-noise ratio (SNR) seismic waveform data are conductive to various studies in seismology. Seismic denoising aims to enhance SNR by eliminating additive noise through signal processing while preserving important features of the seismic signal. Conventional parametric seismic denoising methods often require selecting appropriate parameters to achieve optimal results, which may be limiting when dealing with various types and scales of seismic data. Here, we develop an adaptive parameter-free denoising method by combining general cross-validation (GCV) thresholding and pixel connectivity in synchrosqueezed (SS) domain. In this denoising framework, the synchrosqueezed continuous wavelet transform (SS-CWT) is first applied to obtain a high-resolution time–frequency representation. Then, the GCV approach, which allows for choosing the (nearly) optimal threshold without relying on any prior knowledge about the noise level, is employed to attenuate most of the low-energy noise. After that, the relatively isolated high-energy residual noise remaining in the SS-CWT spectrum is removed using pixel connectivity thresholding. Finally, the inverse SS-CWT is applied to the thresholded spectrum to obtain the denoised seismic record. As the thresholds for GCV and pixel connectivity are derived from the spectrum characteristics of the data being analyzed, the proposed denoising approach is highly adaptive and parameter-free. We demonstrate the effectiveness and versatility of the proposed denoising framework using synthetic data and real seismic data from diverse monitoring scenarios, including land, ocean, and emerging distributed acoustic sensing (DAS). The results indicate that the method is a stable and efficient tool for seismic data denoising.Graphical

Methodology for the automated selection of time-frequency representations

Data preprocessing is a key step in extracting useful information from sound and vibration data and often involves selecting a time-frequency representation. No single time-frequency representation is always optimal, and no standard method exists for selecting the appropriate time-frequency representation, so selecting the time-frequency representation requires expert knowledge and is susceptible to human bias. To address this, this work introduces a methodology to automate the selection of a time-frequency representation for a dataset using only a subset of the healthy, or normal, class of data. To select the parameters for each type of time-frequency representation, Bayesian optimization is used. With a candidate from each type of time-frequency representation, the average similarity is used to select the final candidate. Additionally, the use of multiple time-frequency representations within a single model is explored. Because there is currently no objective method to compare the selected time frequency representations against, the proposed methodology is evaluated in two case studies. In the case studies, the time frequency representations are used as inputs to a simple convolutional neural network that achieved 100% accuracy in classifying bearing faults and 94% accuracy in classifying the contact tip to workpiece distance in wire arc additive manufacturing. Additionally, the proposed methodology presents a 75% and 94% reduction in the data size for the two case studies. This offers further benefits for reducing costs of data transmission and storage in modern digital manufacturing architectures.

RU-Net, Multi-Scale Feature Fusion and Transfer Learning: Unlocking the Potential of Cuffless Blood Pressure Monitoring with PPG and ECG.

This study introduces an innovative deep-learning model for cuffless blood pressure estimation using PPG and ECG signals, demonstrating state-of-the-art performance on the largest clean dataset, PulseDB. The rU-Net architecture, a fusion of U-Net and ResNet, enhances both generalization and feature extraction accuracy. Accurate multi-scale feature capture is facilitated by short-time Fourier transform (STFT) time-frequency distributions and multi-head attention mechanisms, allowing data-driven feature selection. The inclusion of demographic parameters as supervisory information further elevates performance. On the calibration-based dataset, our model excels, achieving outstanding accuracy (SBP MAE ± std: 4.49 ± 4.86 mmHg, DBP MAE ± std: 2.69 ± 3.10 mmHg), surpassing AAMI standards and earning a BHS Grade A rating. Addressing the challenge of calibration-free data, we propose a fine-tuning-based transfer learning approach. Remarkably, with only 10% data transfer, our model attains exceptional accuracy (SBP MAE ± std: 4.14 ± 5.01 mmHg, DBP MAE ± std: 2.48 ± 2.93 mmHg). This study sets the stage for the development of highly accurate and reliable wearable cuffless blood pressure monitoring devices.

Agile manipulation of the time-frequency distribution of high-speed electromagnetic waves

Controlling the temporal evolution of an electromagnetic (EM) wave’s frequency components, the so-called time-frequency (TF) distribution, in a versatile and real-time fashion remains very challenging, especially at the high speeds (> GHz regime) required in contemporary communication, imaging, and sensing applications. We propose a general framework for manipulating the TF properties of high-speed EM waves. Specifically, the TF distribution is continuously mapped along the time domain through phase-only processing, enabling its user-defined manipulation via widely-available temporal modulation techniques. The time-mapping operations can then be inverted to reconstruct the TF-processed signal. Using off-the-shelf telecommunication components, we demonstrate arbitrary control of the TF distribution of EM waves over a full bandwidth approaching 100 GHz with nanosecond-scale programmability and MHz-level frequency resolution. We further demonstrate applications for mitigating rapidly changing frequency interference terms and the direct synthesis of fast waveforms with customized TF distributions. The reported method represents a significant advancement in TF processing of EM waves and it fulfills the stringent requirements for many modern and emerging applications.

Short-time adaptive compact kernel distribution for fault diagnosis under variable working condition bearing

Time-frequency distribution (TFD) methods are extensively employed in the diagnosis of bearings operating under variable working conditions. However, these methods often face high computational complexity, limited time-frequency resolution, and cross-terms. To address these issues, this paper presents a new approach called Short-Time Adaptive Compact Kernel Distribution (STACKD). Based on the characteristics of the vibration signals, we designed Chirp-modulated Gaussian Window and used them to segment the overall signal into small segments. Then, we used a two-step Bayesian optimization method to obtain adaptive compact kernel distributions (ACKD) for these small segments of the signal. Finally, we recombined the ACKD of these small segments into a global STACKD. Results from simulations and experiments demonstrate that STACKD offers improved robustness against interference signals, lower computational complexity, and higher time-frequency resolution without cross-term effects. This method is tailored for diagnosing rolling bearings under variable working conditions, providing enhanced visualization of diagnostic processes with superior time-frequency resolution.

Time-frequency analysis of speech signals using the Stockwell transform for the detection of upper respiratory tract infection

The acoustic properties of speech demonstrate modifications in the presence of different health states. Biomedical engineering has great promise for creating non-invasive diagnostic processes that use speech as a biomarker. The use of speech indications to screen for upper respiratory tract infections (URTIs), such as the common cold, may have potential advantages in terms of limiting transmission. In this study, we have employed the Stockwell transform -based time-frequency (TF) analysis of speech signals for URTI detection. The Stockwell transform is applied on speech signals to derive their TF representation. Using a TF matrix, the various statistics of magnitude and phase are calculated and used as features for classifying speech of healthy speakers and speakers with URTI. The URTIC database is employed for evaluating the proposed features. The utilization of an ensemble of support vector machines (SVM) is proposed as a classification approach to address the issue of class imbalance. The results show that the proposed method produces comparable outcomes to state-of-the-art approaches. The proposed features obtain 66.53% and 64.65% UARs on the development and test partitions of the URTIC database.

High‐speed algorithm for fault detection and location in DC microgrids based on a novel time–frequency analysis

AbstractProtecting DC microgrids (DCMGs) from faults is critical due to the rapid current changes that occur in milliseconds. However, ensuring fast and accurate protection in DCMGs is more challenging than in AC systems. This study proposes a novel protection algorithm using traveling waves (TWs) for fault detection and localization. The high‐order synchrosqueezing transform (FSSTH) is applied to precisely identify TWs at the relay location. FSSTH offers a sharp time–frequency representation, enhancing the accuracy and speed of fault detection. This method can accurately detect transient phenomena like TWs in DCMGs, even with noise and variable fault resistance. By using the spectral envelope with FSSTH, ridges in time–frequency representations are extracted, improving fault diagnosis. The approach differentiates external from internal faults and recognizes fault direction by assessing TW polarity. Testing on two different DCMGs showed this algorithm's high efficiency and accuracy, with fault location errors ranging from 1 to 50 meters in low‐voltage and 13 to 64 meters in medium‐voltage DCMGs, even under challenging conditions like high resistance (up to 500 Ω) and low signal‐to‐noise ratio (5 dB). These results demonstrate the method's superior accuracy and robustness compared to existing techniques.

A novel synchrosqueezing transform associated with linear canonical transform

Synchrosqueezing transforms have aroused great attention for its ability in time–frequency energy rearranging and signal reconstruction, which are post-processing techniques of the time–frequency distribution. However, the time–frequency distributions, such as short-time Fourier transform and short-time fractional Fourier transform, cannot change the shape of the time–frequency distribution. The linear canonical transform (LCT) can simultaneously rotate and scale the time–frequency distribution, which enlarges the distance between different signal components with proper parameters. In this study, a convolution-type short-time LCT is proposed to present the time–frequency distribution of a signal, from which the signal reconstruction formula is given. Its resolutions in time and LCT domains are demonstrated, which helps to select suitable window functions. A fast implementation algorithm for the short-time LCT is provided. Further, the synchrosqueezing LCT (SLCT) transform is designed by performing synchrosqueezing technique on the short-time LCT. The SLCT inherits many properties of the LCT, and the signal reconstruction formula is obtained from the SLCT. Adaptive selections of the parameter matrix of LCT and the length of the window function are introduced, thereby enabling proper compress direction and resolution of the signal. Finally, numerical experiments are presented to verify the efficiency of the SLCT.

Non-stationary mechanical sound source separation: An all-neural beamforming network driven by time–frequency convolution and self-attention

To tackle the challenging task of extracting target signal features amidst significant interference from complex, time-varying non-stationary noise in industrial scenarios, we propose a novel time-domain all-neural beamforming network tailored for non-stationary mechanical sound source separation, named TFANBNet. Leveraging time–frequency convolution and self-attention, TFANBNet promised robust performance in challenging acoustic environments. First, the proposed time–frequency convolution module employs parameterized complex-valued convolutional layers to simulate time–frequency transformations, thereby implicitly extracting time–frequency features. Then, the proposed adaptive attention transformer network enhances local attention interaction by integrating intermediate features, effectively enhancing long-range context modeling. Third, the beamforming module utilizes deep neural networks for beamforming weight estimation, replacing conventional noise covariance matrix computations, which have inherent performance limitations. Finally, the experimental results on the multi-channel spatial reverberation dataset synthesized from the MIMII dataset show that the proposed TFANBNet yields superior separation performance and generalization capabilities compared to the considered competitive methods.

An Adaptive Chirp Mode Decomposition-Based Method for Modal Identification of Time-Varying Structures

Modal parameters are inherent characteristics of civil structures. Due to the effect of environmental factors and ambient loads, the physical and modal characteristics of a structure tend to change over time. Therefore, the effective identification of time-varying modal parameters has become an essential topic. In this study, an instantaneous modal identification method based on an adaptive chirp mode decomposition (ACMD) technique was proposed. The ACMD technique is highly adaptable and can accurately estimate the instantaneous frequencies of a structure. However, it is important to highlight that an initial frequency value must be selected beforehand in ACMD. If the initial frequency is set incorrectly, the resulting instantaneous frequencies may lack accuracy. To address the aforementioned problem, the Welch power spectrum was initially developed to extract a high-resolution time–frequency distribution from the measured signals. Subsequently, the time–frequency ridge was identified based on the maximum energy position in the time–frequency distribution plot, with the frequencies associated with the time–frequency ridge serving as the initial frequencies. Based on the initial frequencies, the measured signals with multiple degrees of freedom could be decomposed into individual time-varying components with a single degree of freedom. Following that, the instantaneous frequencies of each time-varying component could be calculated directly. Subsequently, a sliding window principal component analysis (PCA) method was introduced to derive instantaneous mode shapes. Finally, vibration data collected under various operational scenarios were used to validate the proposed method. The results demonstrated the effective identification of time-varying modal parameters in real-world civil structures, without missing modes.

Synchronous Decomposition Match-Reassigning Transform and Its Application in Planetary Gearbox Fault Diagnosis

Abstract Under time-varying operating conditions, the instantaneous frequency (IF) of the vibration signal of the planetary gearbox exhibits non-stationary time-varying closely spaced characteristics as well as non-proportional and non-synchronous characteristics, making it difficult for traditional time-frequency analysis (TFA) methods to accurately identify its fault features and obtain accurate time-frequency representations (TFR). To address this challenge, this paper proposes a TFA method based on Synchronous Decomposition Match-Reassigning Transform (SDMRT). Firstly, the successive variational mode decomposition (SVMD) is used to adaptively separate non-synchronous frequency components in the original vibration signal. Then, the chirp rate (CR) describing the signal harmonic structure is used to synchronously match each frequency component, obtaining the TFR corresponding to each component. Next, all TFRs are merged to obtain a complete TFA result. Finally, Finally, the energy spread is re-aggregated to the ridge of the IF using the reassignment principle, resulting in a new frequency estimation operator called the Synchronous Decomposition Match-Reassigning Operator (SDMRO). SDMRT can adaptively separate non-proportional and non-synchronous IFs and achieve precise matching of time-varying closely spaced IFs, thereby completing the TFR of the vibration signal generated by the planetary gearbox. By analyzing simulated signals and measured vibration signals from planetary gearboxes, the method proposed in this paper is significantly superior to other TFA methods, thereby validating the effectiveness and superiority of SDMRT.