Frequency-modulated Components Research Articles

Deep Neural Networks for Estimating Regularization Parameter in Sparse Time–Frequency Reconstruction

Time–frequency distributions (TFDs) are crucial for analyzing non-stationary signals. Compressive sensing (CS) in the ambiguity domain offers an approach for TFD reconstruction with high performance, but selecting the optimal regularization parameter for various signals remains challenging. Traditional methods for parameter selection, including manual and experimental approaches, as well as existing optimization procedures, can be imprecise and time-consuming. This study introduces a novel approach using deep neural networks (DNNs) to predict regularization parameters based on Wigner–Ville distributions (WVDs). The proposed DNN is trained on a comprehensive dataset of synthetic signals featuring multiple linear and quadratic frequency-modulated components, with variations in component amplitudes and random positions, ensuring wide applicability and robustness. By utilizing DNNs, end-users need only provide the signal’s WVD, eliminating the need for manual parameter selection and lengthy optimization procedures. Comparisons between the reconstructed TFDs using the proposed DNN-based approach and existing optimization methods highlight significant improvements in both reconstruction performance and execution time. The effectiveness of this methodology is validated on noisy synthetic and real-world signals, emphasizing the potential of DNNs to automate regularization parameter determination for CS-based TFD reconstruction in diverse signal environments.

Quantifying the frequency modulation in electrograms during simulated atrial fibrillation in 2D domains

Atrial fibrillation (AF) affects millions of people in the world, causing increased morbidity and mortality. Treatment involves antiarrhythmic drugs and catheter ablation, showing high success for paroxysmal AF but challenges for persistent AF. Experimental evidence suggests reentrant waves and rotors contribute to AF substrates. Ablation procedures rely on electroanatomical maps and electrogram (EGM) signals; however, current methods used in clinical practice lack consideration for time–frequency varying EGM components. The fractional Fourier transform (FrFT) can be adopted to capture time-varying frequency components, thereby enhancing the comprehension of arrhythmogenic substrates during AF for improved ablation strategies. To this end, a FrFT-based algorithm is developed to characterize non-stationary components in EGM signals from simulated AF episodes. The proposed algorithm comprises a pre-processing step to enhance the coarser features of the EGM waveform, a windowing process for dynamic assessment of the EGM, and a FrFT order optimization stage that seeks compact signal representations in fractional Fourier domains. The resulting order is related to the rate of frequency change in the signal, making it a useful indicator for frequency-modulated components. The FrFT-based algorithm is implemented on EGM signals from AF simulations in 2D domains representing a region of the atrial tissue. Consequently, the computed optimum FrFT orders are used to build maps that are spatially correlated to the underlying propagation dynamics of the simulated AF episode. The results evince that the extreme values in the optimum orders map pinpoint the localization of fibrillatory mechanisms, generating EGM activation waveforms with varying frequency content over time.

Convolutional Neural Networks for Local Component Number Estimation from Time–Frequency Distributions of Multicomponent Nonstationary Signals

Frequency-modulated (FM) signals, prevalent across various applied disciplines, exhibit time-dependent frequencies and a multicomponent nature necessitating the utilization of time-frequency methods. Accurately determining the number of components in such signals is crucial for various applications reliant on this metric. However, this poses a challenge, particularly amidst interfering components of varying amplitudes in noisy environments. While the localized Rényi entropy (LRE) method is effective for component counting, its accuracy significantly diminishes when analyzing signals with intersecting components, components that deviate from the time axis, and components with different amplitudes. This paper addresses these limitations and proposes a convolutional neural network-based (CNN) approach for determining the local number of components using a time–frequency distribution of a signal as input. A comprehensive training set comprising single and multicomponent linear and quadratic FM components with diverse time and frequency supports has been constructed, emphasizing special cases of noisy signals with intersecting components and differing amplitudes. The results demonstrate that the estimated component numbers outperform those obtained using the LRE method for considered noisy multicomponent synthetic signals. Furthermore, we validate the efficacy of the proposed CNN approach on real-world gravitational and electroencephalogram signals, underscoring its robustness and applicability across different signal types and conditions.

Multiscale dynamic graph signal analysis

We consider the problem of decomposing a time-varying graph signal into its constituent amplitude- and frequency-modulated components and inferring their dynamic functional connectivity structures in a data-driven manner, referred to as graph mode decomposition (GMD). The currently available method for GMD obtains static connectivity structures, limiting its applicability to real-life data. Further, the performance of the method relies critically on the accurate prior knowledge of the number of components to be extracted. We address those key limitations by presenting two approaches: (1) a two-stage method for obtaining the graph modes as well as corresponding connectivity structures by solving two separate optimization problems, and (2) a joint optimization formulation to achieve that task. The proposed optimization formulations include a prior to account for the time variation of graph edge weights. Moreover, we use a successive scheme to solve the problems which alleviates the limitation of having to specify the number of decomposed components a priori — improving the accuracy and data-driven capability while reducing the computational requirement of the methods. The performance of these methods is validated on a wide range of synthetic and real data sets. We also provide a public toolbox containing the MATLAB codes of the proposed methods.

Simulation method and spectrum modulation characteristic analysis of typical fault signals of inter-shaft bearing

In order to study the frequency spectrum characteristics of the vibration signal of the inter-shaft bearing defect fault in the aero-engine dual-rotor system, a vibration signal mathematical model is established based on the fault characteristic frequency of the inner and outer ring defects of the inter-shaft bearing, and the mutual modulation law of the signals during transmission is analyzed. A test bench for signal transmission path analysis is built to verify the calculation results. The results indicate that the fault signal of the inter-shaft bearing defect significantly attenuates during transmission, and the characteristic frequency of the inter-shaft bearing fault is modulated with the rotor rotation frequency. There are corresponding characteristic frequencies and modulation frequency components in the envelope spectrum of the inter-shaft bearing. The error between the experimental and simulation results is less than 1%, which verifies the accuracy of the simulation calculation results. After being transmitted to the rotor through the inter-shaft bearing, the rotor frequency includes the modulation frequency of bearing varying compliance frequency and rotation frequency, as well as the fault characteristic frequency of the inter-shaft bearing.

Refocusing Swing Ships in SAR Imagery Based on Spatial-Variant Defocusing Property

Synthetic aperture radar (SAR) is an essential tool for maritime surveillance in all weather conditions and at night. Ships are often affected by sea breezes and waves, generating a three-dimensional (3D) swinging motion. The 3D swing ship can thereby become severely defocused in SAR images, making it extremely difficult to recognize them. However, refocusing 3D swing ships in SAR imagery is challenging with traditional approaches due to different phase errors at each scattering point on the ship. In order to solve this problem, a novel method for refocusing swing ships in SAR imagery based on the spatial-variant defocusing property is proposed in this paper. Firstly, the spatial-variant defocusing property of a 3D swing ship is derived according to the SAR imaging mechanism. Secondly, considering the spatial-variant defocusing property, each azimuth line of the SAR 3D swing ship image is modeled as a multi-component linear frequency modulation (MC-LFM) signal. Thirdly, Fractional Autocorrelation (FrAc) is implemented in order to quickly calculate the optimal rotation order set for each azimuth line. Thereafter, Fractional Fourier Transform (FrFT) is performed on the azimuth lines to refocus their linear frequency modulation (LFM) components one by one. Finally, the original azimuth lines are replaced in the SAR image with their focused signals to generate the refocused SAR image. The experimental results from a large amount of simulated data and real Gaofen-3 data show that the proposed algorithm can overcome the spatial-variant defocusing of 3D swing ships. Compared with state-of-the-art algorithms, our approach reduces the image entropy by an order of magnitude, leading to a visible improvement in image quality, which makes it possible to recognize swing ships in SAR images.

Phase-Derived Ranging Based Fiber Transfer Delay Measurement Using a Composite Signal for Distributed Radars with Fiber Networks

Fiber transfer delay (FTD) variations influence the coherence of distributed radars with fiber networks, resulting in a performance degradation in target detecting and imaging. To measure and compensate for the variation, a phase-derived ranging based FTD measurement using a composite signal is proposed. The composite signal comprises a sinusoidal component and a linear frequency modulation (LFM) component. As the composite signal passes through a fiber under test (FUT), the sinusoidal component generates a phase shift that corresponds to the FTD. The phase shift can be represented by two parameters: the number of complete periods of 2π that can be estimated by using the LFM component, and a phase shift less than 2π that be measured employing the sinusoidal component. When using the proposed measurement system to measure FTD variations in a distributed radar, only an additional sinusoidal component is needed, which minimizes interference with radar signals. Moreover, the proposed measurement system can share core function modules such as signal generation and process modules with distributed radars, which enhances the compatibility and reduces the overall complexity. Experiments are carried out to measure a variable optical delay line and a long optical fiber. The experiment results verify the feasibility of the measurement system and show that a measurement range of more than 15 km, an accuracy of ±0.1 ps and a measurement time of 105 ms can be achieved.

Noise-induced vocal flexibility in Hipposiderid and Rhinolophid bats

Although James Simmons’s pioneering work on bats’ target ranging capability by echolocation has been widely acknowledged, his contributions to other fields of bat echolocation have often been underappreciated. For example, James Simmons was probably the first to observe that echolocating bats can employ remarkable vocal flexibilities to counter masking noise effects on target ranging [Simmons et al., https://doi.org/10.1121/1.1914154 (1974)], a research topic that has only gained popularity in the bioacoustics community in recent two decades or so. In this talk, we present the latest data on noise-induced vocal flexibility of five species of bats, including Hipposideros pratti and four Rhinolophids. All bats emit echolocation calls consisting of a constant frequency component and a frequency modulated component. We first show that both Rhinolophid and hipposiderid bats possess a highly developed vocal flexibility to counter noise interference. Then, with H. pratti we demonstrate that the expression of vocal flexibility by the same individual was affected by several factors, such as the behavioral context or task, and history of training, which were believed to mediate the noise-induced vocal flexibility of humans only. These results emphasize the value of the comparative approach in understanding the vocal production control of mammals.

Generalized Synchroextracting-Based Stepwise Demodulation Transform and Its Application to Fault Diagnosis of Rotating Machinery

The nonstationary characteristics of time-varying signals can be characterized by time–frequency analysis (TFA) accurately, which has been widely used in fault diagnosis of rotating machinery. However, some practical signals contain complex multicomponent modes and noise interference, which will pose challenges to traditional TFA methods. In this article, a novel technique called generalized synchroextracting-based stepwise demodulation (GSET-SD) transform is proposed. GSET-SD introduces a strategy that combines synchroextracting transform (SET) with a stepwise demodulation procedure, thereby solving the problem of detecting and retrieving the amplitude- and frequency-modulated (AM-FM) components of a multicomponent signal from the time–frequency representation (TFR), while allowing the signal to be reconstructed from the TFR. Furthermore, to increase the estimation accuracy of the initial instantaneous frequency (IF) in processing the strong modulation signals, SET is extended to the second-order or higher order domain, and the IF is accurately estimated by the higher order polynomial method, which can obtain higher resolution TFR. The proposed approach has been applied to numerical simulations and application research. The experimental results verify the effectiveness and superiority of GSET-SD in processing strong modulation signals and demonstrate its promise in the field of fault diagnosis of rotating machinery under time-varying speeds.

Data-driven nonstationary signal decomposition approaches: a comparative analysis

Signal decomposition (SD) approaches aim to decompose non-stationary signals into their constituent amplitude- and frequency-modulated components. This represents an important preprocessing step in many practical signal processing pipelines, providing useful knowledge and insight into the data and relevant underlying system(s) while also facilitating tasks such as noise or artefact removal and feature extraction. The popular SD methods are mostly data-driven, striving to obtain inherent well-behaved signal components without making many prior assumptions on input data. Among those methods include empirical mode decomposition and variants, variational mode decomposition and variants, synchrosqueezed transform and variants and sliding singular spectrum analysis. With the increasing popularity and utility of these methods in wide-ranging applications, it is imperative to gain a better understanding and insight into the operation of these algorithms, evaluate their accuracy with and without noise in input data and gauge their sensitivity against algorithmic parameter changes. In this work, we achieve those tasks through extensive experiments involving carefully designed synthetic and real-life signals. Based on our experimental observations, we comment on the pros and cons of the considered SD algorithms as well as highlighting the best practices, in terms of parameter selection, for the their successful operation. The SD algorithms for both single- and multi-channel (multivariate) data fall within the scope of our work. For multivariate signals, we evaluate the performance of the popular algorithms in terms of fulfilling the mode-alignment property, especially in the presence of noise.

Simulation of Friction Fault of Lightly Loaded Flywheel Bearing Cage and Its Fault Characteristics.

Because of the operating environment and load, the main fault form of flywheel bearing is the friction fault between the cage and the rolling elements, which often lead to an increase in the friction torque of the bearing and even to the failure of the flywheel. However, due to the complex mechanism of the friction fault, the characteristic frequencies often used to indicate cage failure are not obvious, which makes it difficult to monitor and quantitatively judge such faults. Therefore, this paper studies the mechanism of the friction fault of the flywheel bearing cage and establishes its fault feature identification method. Firstly, the basic dynamic model of the bearing is established in this paper, and the friction between the cage and the rolling elements is simulated by the variable stiffness. The influence law of the bearing vibration response reveals the relationship between the periodic fluctuation of cage-rolling element friction failure and the bearing load. After analyzing the envelope spectrum of the vibration data, it was found that when a friction fault occurred between the cage and the rolling element, the rotation frequency component of the cage modulated the rotational frequency component of the rolling element, that is, the side frequency components appeared on both sides of the characteristic frequency of the rolling element (with the characteristic frequency of the cage as the interval). In addition, the modulation frequency components of the cage and rolling element changed with the severity of the fault. Then, a modulation sideband ratio method based on envelope spectrum was proposed to qualitatively diagnose the severity of the cage-rolling element friction faults. Finally, the effectiveness of the presented method was verified by experiments.

Maintenance method of signal coherence in lidar and experimental validation.

According to the self-heterodyne signal obtained by lidar under different fiber delay times, the model of the local oscillator signal was established, and the maintenance method of signal coherence in lidar based on the digital delay was improved by using multiple sinusoidal frequency modulation components. An imaging detection experiment was carried out at a distance of 5.4 km. The coherence of the lidar signal was maintained by combining the transmitting reference channel correction method and the local oscillator reference channel compensation method, accompanied by the use of a phase spectrum to analyze the improvement effect. The processing results of the echo signal showed that the method could remove the high-order phase errors that cannot be compensated by the phase gradient autofocus algorithm and improve the signal coherence, which could be used for the detection and imaging of long-range targets.

A Time–Frequency Representation Approach of Undersampled Signals With Multiple Periodic FM Components

Periodic frequency-modulated (FM) interference signals, commonly employed by jammers and radars, may lead to the performance degradation or even failure of global navigation satellite systems and wireless communications. Time–frequency (TF) representations play an essential role in FM signal analysis and instantaneous frequency (IF) estimation, which is the basis of many nonstationary interference suppression algorithms. This article provides a TF representation approach for signals with multiple periodic FM components in the presence of sample loss. The proposed approach utilizes the periodicity and the sparsity of signal components in the TF domain to suppress cross-terms and artifacts. We reconstruct TF distributions of each component by time-averaging Wigner–Ville distribution. Then, the residual artifacts are eliminated by a low-complexity sparse-based adaptive directional TF filtering method. Simulation results confirm that the proposed approach provides an outstanding suppression of cross-terms and artifacts. The proposed TF representation approach can effectively improve the accuracy of the IF estimation of each signal component.

The Full Informational Spectral Analysis for Auditory Steady-State Responses in Human Brain Using the Combination of Canonical Correlation Analysis and Holo-Hilbert Spectral Analysis.

Auditory steady-state response (ASSR) is a translational biomarker for several neurological and psychiatric disorders, such as hearing loss, schizophrenia, bipolar disorder, autism, etc. The ASSR is sinusoidal electroencephalography (EEG)/magnetoencephalography (MEG) responses induced by periodically presented auditory stimuli. Traditional frequency analysis assumes ASSR is a stationary response, which can be analyzed using linear analysis approaches, such as Fourier analysis or Wavelet. However, recent studies have reported that the human steady-state responses are dynamic and can be modulated by the subject’s attention, wakefulness state, mental load, and mental fatigue. The amplitude modulations on the measured oscillatory responses can result in the spectral broadening or frequency splitting on the Fourier spectrum, owing to the trigonometric product-to-sum formula. Accordingly, in this study, we analyzed the human ASSR by the combination of canonical correlation analysis (CCA) and Holo-Hilbert spectral analysis (HHSA). The CCA was used to extract ASSR-related signal features, and the HHSA was used to decompose the extracted ASSR responses into amplitude modulation (AM) components and frequency modulation (FM) components, in which the FM frequency represents the fast-changing intra-mode frequency and the AM frequency represents the slow-changing inter-mode frequency. In this paper, we aimed to study the AM and FM spectra of ASSR responses in a 37 Hz steady-state auditory stimulation. Twenty-five healthy subjects were recruited for this study, and each subject was requested to participate in two auditory stimulation sessions, including one right-ear and one left-ear monaural steady-state auditory stimulation. With the HHSA, both the 37 Hz (fundamental frequency) and the 74 Hz (first harmonic frequency) auditory responses were successfully extracted. Examining the AM spectra, the 37 Hz and the 74 Hz auditory responses were modulated by distinct AM spectra, each with at least three composite frequencies. In contrast to the results of traditional Fourier spectra, frequency splitting was seen at 37 Hz, and a spectral peak was obscured at 74 Hz in Fourier spectra. The proposed method effectively corrects the frequency splitting problem resulting from time-varying amplitude changes. Our results have validated the HHSA as a useful tool for steady-state response (SSR) studies so that the misleading or wrong interpretation caused by amplitude modulation in the traditional Fourier spectrum can be avoided.

Induction Machine Bearing Fault Detection Using Empirical Wavelet Transform

The detection of faults related to the optimal condition of induction motors is an important task to avoid the malfunction or loss of the motor, thus avoiding high repair or replacement costs and faults in the efficiency of the process to which they belong. These faults are not limited to a single area; mechanical and electrical problems can cause a fault. Specifically, the bearing of a motor is subjected to several effects that cause bearing faults, which cause significant breakdowns in the machinery. This article proposes a methodology for detecting bearing faults on an induction motor. The first part of the methodology uses a signal processing method called empirical wavelet transform (EWT), which decomposes the vibration signal into multiple components to extract a series of amplitude and frequency modulated components (AM-FM) with a Fourier spectrum. First, the vibration signal data are collected in a normal operating condition and the other with bearing damage due to perforation. Then, three types of goodness-of-fit tests are used, Kuiper, Kolmogorov–Smirnov, and Pearson chi-square, to classify the signals and determine which ones belong to a damaged engine. Finally, the experimental results show that the EWT in conjunction with the proposed goodness tests achieves competitive precision and efficiency in diagnosing induction motor-bearing faults.

Dual tapered optical fiber for simultaneous detection of curvature and strain

We present a study of simultaneous detection of curvature and strain in optical fiber. This contains a micro tapered section and a nano tapered section. The transmission spectrum shows interference of multiple modes, and the frequency of the modulation can be used to distinguish and monitor specific physical parts of the fiber structure. The curvature detection is achieved using one specific modulation frequency component; this component shows an intensity modulation with a sensitivity of 0.26 dB/m−1. The strain information is extracted by applying a phase analysis over a second spatial frequency component; this analysis shows a sensitivity close to 8 mrad/με. The strain phase analysis exhibits a linear response, and the intensity curvature data indicates an exponential model. The proposed signal analysis can be employed for simultaneous detection in optical fiber interferometric sensors.

Echo reception in group flight by Japanese horseshoe bats, Rhinolophus ferrumequinum nippon.

The ability to detect behaviourally relevant sensory information is crucial for survival. Especially when active-sensing animals behave in proximity, mutual interferences may occur. The aim of this study was to examine how active-sensing animals deal with mutual interferences. Echolocation pulses and returning echoes were compared in spaces of various sizes (wide and narrow) in Rhinolophus ferrumequinum nippon flying alone or in a group of three bats. We found that in the narrow space, the group-flying bats increased the duration and bandwidth of the terminal frequency-modulated component of their vocalizations. By contrast, the frequency of the returning echoes did not differ in the presence of conspecifics. We found that their own echo frequencies were compensated within the narrow frequency ranges by Doppler shift compensation. By contrast, the estimated frequencies of the received pulses emitted by the other bats were much more broadly distributed than their echoes. Our results suggest that the bat auditory systems are sharply tuned to a narrow frequency to filter spectral interference from other bats.

A Fault Feature Extraction Method Based on LMD and Wavelet Packet Denoising

Aiming at the problem of fault feature extraction of a diaphragm pump check valve, a fault feature extraction method based on local mean decomposition (LMD) and wavelet packet transform is proposed. Firstly, the collected vibration signal was decomposed by LMD. After several amplitude modulation (AM) and frequency modulation (FM) components were obtained, the effective components were selected according to the Kullback-Leible (K-L) divergence of all component signals for reconstruction. Then, wavelet packet transform was used to denoise the reconstructed signal. Finally, the characteristics of the fault signal were extracted by Hilbert envelope spectrum analysis. Through experimental analysis, the results show that compared with other traditional methods, the proposed method can effectively overcome the phenomenon of mode aliasing and extract the fault characteristics of a check valve more effectively. Experiments show that this method is feasible in the fault diagnosis of check valve.

Rolling Bearing Fault Diagnosis Based on Component Screening Vector Local Characteristic-Scale Decomposition

The fault vibration signal of a bearing has nonstationary and nonlinear characteristics and can be regarded as the combination of multiple amplitude- and frequency-modulation components. The envelope of a single component contains the fault characteristics of a bearing. Local characteristic-scale decomposition (LCD) can decompose the vibration signal into a series of multiple intrinsic scale components. Some components can clearly reflect the running state of a bearing, and fault diagnosis is conducted according to the envelope spectrum. However, the conventional LCD takes a single-channel signal as the research object, which cannot fully reflect the characteristic information of the rotor, and the analysis results based on different channel signals of the same section will be inconsistent. To solve this problem, based on full vector spectrum technology, the homologous dual-channel information is fused. A vector LCD method based on cross-correlation coefficient component selection is given, and a simulation analysis is completed. The effectiveness of the proposed method is verified by simulated signals and experimental signals of a bearing, which provides a method for bearing feature extraction and fault diagnosis.

Epileptic seizure detection in EEG using mutual information-based best individual feature selection

Epilepsy is a group of neurological disorders that affect normal brain activities and human behavior. Electroencephalogram based automatic epileptic seizure detection has significant applications in epilepsy treatment and medical diagnosis. In this study, a novel epileptic seizure detection method is proposed with a combination of empirical mode decomposition, mutual information-based best individual feature (MIBIF) selection algorithm and multi-layer perceptron neural network. Initially, fixed length EEG epochs are decomposed into amplitude and frequency-modulated components called intrinsic mode functions (IMFs). Three features named ellipse area of second-order difference plot, variance and fluctuation index are calculated from first few IMFs. The most significant features are then selected from the calculated features using the MIBIF algorithm to produce a final feature set. Later, the generated feature set is fed into the multi-layer perceptron neural network (MLPNN) classifier. Two well-known benchmark epileptic EEG datasets are used in this study for experimental evaluations. The result of proposed approach shows a significant performance improvement compared to the recent state-of-the-art methods.