Time-frequency Algorithm Research Articles

Robust Fractional Low‐Order Multiple Window STFT for Infinite Variance Process Environment

Mechanical fault vibration signal is a typical non‐Gaussian process, they can be characterized by the infinite variance process, and the noise within these signals may also be the process in complex environments. The performance of the traditional cross‐term reduction algorithm is compromised, sometimes yielding incorrect results under the infinite variance process environment. Several robust fractional lower order time–frequency representation methods are proposed including fractional low‐order smoothed pseudo Wigner (FLOSPW), fractional low‐order multi‐windowed short‐time Fourier transform (FLOMWSTFT), and improved fractional low‐order multi‐windowed short‐time Fourier transform (IFLOMWSTFT) utilizing fractional low‐order statistics and short‐time Fourier transform (STFT) to mitigate cross‐terms, enhance time–frequency resolution, and accommodate the infinite variance process environment. When compared to traditional methods, simulation results indicate that they effectively suppress the pulse noise and function effectively in lower mixed signal noise ratio (MSNR) in an infinite variance process environment. The efficacy of the proposed time–frequency algorithm is validated through its application to mechanical bearing outer ring fault vibration signals contaminated with Gaussian noise and subjected to an α infinite variance process.

An unsupervised online anomaly detection method for metal additive manufacturing processes via a statistical time-frequency domain algorithm

Anomalies often occur in metal additive manufacturing from processing inconsistencies and uncertainty. A robust fault detection system that uses sensor measurements such as melt pool imaging has the potential to improve part quality and save production time by anticipating print failure. Toward this goal, we develop and validate a fault detection technique using melt pool geometry-related measurements from an in situ near-infrared optical camera. This method is unsupervised and is trained on a small dataset, mitigating human error in classifying fault types, and reducing lead times for preparing training datasets. Furthermore, this method uses learned geometry-informed nominal behavior of the melt pool signal to make informed decisions on the process health. There are spatial-temporal characteristics embedded in the melt pool images, caused by the periodicity in the geometry-dependent raster pattern. These characteristics can be captured in the frequency domain using the signal spectrogram, a representation of the frequency content over time. Defects will appear in the spectrogram, disrupting the healthy spectral response. To quantify healthy spectrograms, we use principal component (PC) decomposition to extract the features of these spectrograms as a set of nominal basis vectors. Anomaly detection is then performed by calculating the error between the original and reconstructed spectrogram vector by projection of the spectrogram PCs onto the nominal basis. The reconstruction error for anomalous signals is larger than that from healthy signals, which is then used for fault detection. A one-tailed statistical test is used to determine the fault detection threshold for the reconstruction error signal. This method is tested on three raster patterns and performs better than a comparative time-series thresholding method. We demonstrate that this time-frequency algorithm can detect both temporal faults (which occur at a single time instant) and spatial faults (such as those introduced by an improper sintering), differentiating them from nominal operation.

Quantitative Electroencephalography as a Biomarker for Cognitive Dysfunction in Parkinson's Disease.

Background: Quantitative electroencephalography (qEEG) has been suggested as a biomarker for cognitive decline in Parkinson’s disease (PD).Objective: Determine if applying a wavelet-based qEEG algorithm to 21-electrode, resting-state EEG recordings obtained in a routine clinical setting has utility for predicting cognitive impairment in PD.Methods: PD subjects, evaluated by disease stage and motor score, were compared to healthy controls (N = 20 each). PD subjects with normal (PDN, MoCA 26–30, N = 6) and impaired (PDD, MoCA ≤ 25, N = 14) cognition were compared. The wavelet-transform based time-frequency algorithm assessed the instantaneous predominant frequency (IPF) at 60 ms intervals throughout entire recordings. We then determined the relative time spent by the IPF in the four standard EEG frequency bands (RTF) at each scalp location. The resting occipital rhythm (ROR) was assessed using standard power spectral analysis.Results: Comparing PD subjects to healthy controls, mean values are decreased for ROR and RTF-Beta, greater for RTF-Theta and similar for RTF-Delta and RTF-Alpha. In logistic regression models, arithmetic combinations of RTF values [e.g., (RTF-Alpha) + (RTF-Beta)/(RTF-Delta + RTF-Theta)] and RTF-Alpha values at occipital or parietal locations are most able to discriminate between PD and controls. A principal component (PC) from principal component analysis (PCA) using RTF-band values in all subjects is associated with PD status (p = 0.004, β = 0.31, AUC = 0.780). Its loadings show positive contribution from RTF-Theta at all scalp locations, and negative contributions from RTF-Beta at occipital, parietal, central, and temporal locations. Compared to cognitively normal PD subjects, cognitively impaired PD subjects have lower median RTF-Alpha and RTF-Beta values, greater RTF-Theta values and similar RTF-Delta values. A PC from PCA using RTF-band values in PD subjects is associated with cognitive status (p = 0.002, β = 0.922, AUC = 0.89). Its loadings show positive contributions from RTF-Theta at all scalp locations, negative contributions from RTF-Beta at central locations, and negative contributions from RTF-Delta at central, frontal and temporal locations. Age, disease duration and/or sex are not significant covariates. No PC was associated with motor score or disease stage.Significance: Analyzing standard EEG recordings obtained in a community practice setting using a wavelet-based qEEG algorithm shows promise as a PD biomarker and for predicting cognitive impairment in PD.

Interference Mitigation Based on Low Complexity Subspace Tracking Method for Vehicle Positioning

Advanced driver assistance systems and automatic driving have drawn lots of attentions due to user’s multiapplication needs. Among different technologies, the integration of Inertial Navigation System (INS) and Global Navigation Satellite System (GNSS) is a key technique with the decreasing costs of Inertial Measurement Unit (IMU) and the increasing deployment of GNSS for navigation applications. Although the integration may have immune ability to interference in a certain extent, interference suppression strategy applied on the integration system can greatly improve the performance. A complete framework including interference monitor, detection, and mitigation is provided jointly using subspace tracking method and Kalman filter measurements innovation of INS and GNSS. The proposed monitor is simple, efficient, and can decide when to start the interference mitigation procedure, which can reduce the computation complexity significantly; Subspace‐based method is introduced to track the interference basis matrix that can be feed to RootMUSIC to detect the frequency of interference, followed by the interference mitigation with a notch filter. The proposed framework has superior performance than the well‐known time‐frequency algorithm, such as short‐time Fourier transform (STFT) and smoothed pseudo Wigner‐Ville distribution (SPWVD), and can improve the performance of INS/GNSS system in the presence of interference with simulation verification.

Identification of boiling flow pattern in narrow rectangular channel based on TFA-CNN combined method

In this paper, an indirect flow pattern recognition method based on time-frequency analysis and neural networks is proposed to investigate the flow patterns in the narrow rectangular channel under heating and non-inertial conditions. Firstly, the adaptive optimal kernel algorithm is utilized to analyze on the typical pressure signal and convert it into time-frequency spectrograms. Then based on the concept of transfer learning strategy, convolutional neural networks are applied as feature extractors to classify flow patterns by the spectrogram images. The proposed method is verified by the visualized flow boiling experiment data. The results show that the adaptive time-frequency algorithm can effectively reflect the characteristics of different flow pattern signals, and several chosen neural network models show high recognition accuracy after training. Among them, VGG-16 network with small convolution kernels and strong transferability has the highest recognition rate. In addition, the network based on data of static conditions remains identifying more than 75% spectrograms of rolling conditions, exhibiting the generalization ability of the method under different flow conditions.

A Hybrid Approach for Parkinson’s Disease diagnosis with Resonance and Time-Frequency based features from Speech signals

Parkinson’s Disease (PD) is a progressive neurological disorder that affects the functioning of the brain. As PD progresses, there arises a problem of maintaining coordination between brain and different parts of the body. Subjects have the problem of performing daily activities. Its early diagnosis is important to improve the quality of life of Parkinson’s patients. Most of Parkinson’s patients are likely to have voice disorders in the early stages. Therefore, the analysis of voice recordings with machine learning-based models can improve the diagnosis process. Voice signals are non-linear, non-stationary signals which exhibit oscillatory behavior. In this paper, a hybrid approach is proposed to extract features from resonance-based and time-frequency based information. A combination of Resonance based Sparse Signal Decomposition (RSSD) + Time-Frequency (T-F) algorithm is proposed. Two datasets are collected for the study. The first dataset D1 is a public dataset consisting of 16 PD + 21 Healthy Controls (HC) and the second dataset D2 is collected from 20 HC to explore the effect of diversity in the diagnosis process. To explore the potential of deep learning techniques in diagnosing speech impairments in PD patients, the potential of Convolution Neural Network (CNN) is also explored. To evaluate the method, we conducted several experiments with state-of-the-art feature extraction and classification techniques. The proposed hybrid approach distinguished PD and HC with a validation accuracy of 99.37%. We have also explored the effect of diversity in the data collection process and it is observed that diversity in the socio-cultural group plays very important role to put the system in the clinical practice.

Multi-synchrosqueezing S-transform for fault diagnosis in rolling bearings

Rolling bearings are one of the most significant components of much large machinery, and also one of the components prone to failure. Advanced time–frequency analysis (TFA) methods can provide time–frequency (TF) graphs with more significant features that are critical for fault diagnosis of rolling bearings. In this paper, we propose a new TF algorithm, called the multi-synchrosqueezing S-transform, in which an S-transform is embedded into a multi-synchrosqueezing framework, by reassigning the TF coefficients of the S-transform result in frequency multiple times to achieve the ideal TFA. Using the Rényi entropies to measure the resolution of the TFA and determine iteration, this method can get a better time–frequency representation (TFR) with fewer iterations. The results show that the algorithm can produce TFRs with higher TFR resolution while inheriting the advantages of the S-transform. Through simulation signals and field signals, the effectiveness of the method is verified.

Modeling and parameter identification of linear time-varying systems based on adaptive chirplet transform under random excitation

In this paper, a time–frequency algorithm based on adaptive chirplet transform for parameter modeling and identification of Linear Time-Varying (LTV) systems under random excitation is presented. It is assumed that the solution of responses of LTV structures is expressed as the sum of multicomponent Linear Frequency Modulated (LFM) signals in a short-time. Then the measured acceleration response is used to perform the adaptive chirplet transform, in which an integral algorithm is employed to reconstruct the velocity and displacement responses. The vibration differential equation with time-varying coefficients is transformed into a simple linear equation. Furthermore, for systems under random excitation, the input–output relation based on correlation function is also derived to estimate the parameters including physicals parameters and instantaneous modal parameters. The full procedure of the method is presented and validated by using simulated responses. The results show that the presented method is accurate and robust for various LTV systems under random excitation.

Hybrid time–frequency algorithm for active sound quality control of vehicle interior noise based on stationary discrete wavelet transform

Active sound quality control (ASQC) of vehicle interior noise is to reshape the sound spectrum by considering human perception. But current ASQC method mainly controls the interior noise amplitude, ignoring the time–frequency characteristics, and active control of sharpness is a problem. According to psychoacoustic indices, the original noise needs to be decomposed into subbands to obtain targeted control. Thus, this study presents a hybrid time–frequency domain active noise equalization (TFD-ANE) algorithm based on stationary discrete wavelet transform. For get a supporting effect, a variable step-size FxLMS (VS-FxLMS) and a normalized frequency-domain block FxLMS are inspected and determined for each subband noise suppression. It can be found NFB-FxLMS can control higher frequency noise well, while VS-FxLMS just shows better control effect on the lowest frequency subband. To verify the effectiveness of proposed method, ASQC simulations are performed by using the basic ANE, VS-ANE, NFB-ANE and TFD-ANE algorithms. Moreover, three psychoacoustic indices, loudness, sharpness, and roughness, with the utmost impact on the interior sound quality, are considered to quantify the noise improvement effect. Results show that TFD-ANE achieves the optimum performance, where the loudness and roughness are further reduced by more than 38% and 46% compared with other three algorithms. In terms of sharpness, the ANE and VS-ANE are ineffective, and the NFB-FxLMS cannot improve the sharpness of nonstationary interior noise. However, the proposed TFD-ANE can reduce the sharpness by approximately 40%, which suggests a promising approach to the ASQC of vehicle interior noises and other sound-related fields in engineering.

SGM: a novel time-frequency algorithm based on unsupervised learning improves high-frequency oscillation detection in epilepsy

Objective. We propose a novel automated method called the S-Transform Gaussian Mixture detection algorithm (SGM) to detect high-frequency oscillations (HFO) combining the strengths of different families of previously published detectors. Approach. This algorithm does not depend on parameter tuning on a subject (or database) basis, uses time-frequency characteristics, and relies on non-supervised classification to determine if the events standing out from the baseline activity are HFO or not. SGM consists of three steps: the first stage computes the signal baseline using the entropy of the autocorrelation; the second uses the S-Transform to obtain several time-frequency features (area, entropy, and time and frequency widths); and in the third stage Gaussian mixture models cluster time-frequency features to decide if events correspond to HFO-like activity. To validate the SGM algorithm we tested its performance in simulated and real environments. Main results. We assessed the algorithm on a publicly available simulated stereoelectroencephalographic (SEEG) database with varying signal-to-noise ratios (SNR), obtaining very good results for medium and high SNR signals. We further tested the SGM algorithm on real signals from patients with focal epilepsy, in which HFO detection was performed visually by experts, yielding a high agreement between experts and SGM. Significance. The SGM algorithm displayed proper performance in simulated and real environments and therefore can be used for non-supervised detection of HFO. This non-supervised algorithm does not require previous labelling by experts or parameter adjustment depending on the subject or database considered. SGM is not a computationally intensive algorithm, making it suitable to detect and characterize HFO in long-term SEEG recordings.

Modeling of synthetic-aperture radar in X and P-band

Synthetic-aperture radar is usually a complex software and hardware system. It allows obtaining images in radio range, comparable in resolution with optical systems. The advantage of radio waves is that the images are of high quality, despite cloudiness and dark time. The development of algorithms for such systems is a rather complex process. Mathematical modeling applied in purpose to reduce costs. In this paper, we give an overview of early created systems. We discuss the methods for calculating the scattered electromagnetic field. We choose methods that are most suitable for simulating a synthetic aperture radar. Combination of different approximation methods allows us to process large scenes. We take into account the various effects that arise when propagating radio waves. Also, we describe algorithms for a synthesis of radar images. In particular, we consider range-migration algorithm and time-frequency processing algorithm. We show that the frequency-time processing algorithm is preferable for synthesis a radio image in the X-band due to its speed. In opposite, the range-migration effect in P-band is too strong to ignore it. The time-frequency algorithm gives not focused image with serious artifacts. It is better to use the range-migration algorithm for P-band.

Underdetermined convolutive blind separation of sources integrating tensor factorization and expectation maximization

Underdetermined convolutive blind separation of sources is a challenging topic in speech and audio processing. In plenty of conventional separation algorithms, the source signal estimation is performed in the frequency-domain, thus leading to permutation problems and poor separation results. In this paper, to solve the permutation alignment and obtain better source separation results, we exploit the algebraic structure of tensor factorization model and expectation–maximization (EM) to provide a new time-frequency algorithm. This is because tensor factorization has an advantage to estimate the channel for the underdetermined convolutive mixture case, and EM algorithm is conducive to faster converge to the desired solution and better source separating property. In the proposed algorithm, we first estimate the mixing matrix by using tensor decomposition, while permutation alignment algorithm is used to deal with the permutation problems. Then, the model parameters are updated using EM algorithm for improving source separation performance. At the same time, the spatial images of source signals are obtained using Wiener filters constructed from the estimated parameters. Furthermore, the time-domain source signals can be obtained through inverse short-time Fourier transform. Finally, a series of simulations show that compared with some existing separation algorithms, the proposed algorithm achieves better separation performance.

Diagnosis of Encephalopathy Based on Energies of EEG Subbands Using Discrete Wavelet Transform and Support Vector Machine.

EEG analysis in the field of neurology is customarily done using frequency domain methods like fast Fourier transform. A complex biomedical signal such as EEG is best analysed using a time-frequency algorithm. Wavelet decomposition based analysis is a relatively novel area in EEG analysis and for extracting its subbands. This work aims at exploring the use of discrete wavelet transform for extracting EEG subbands in encephalopathy. The subband energies were then calculated and given as feature sets to SVM classifier for identifying cases of encephalopathy from normal healthy subjects. Out of various combinations of subband energies, energy of delta subband yielded highest performance parameters for SVM classifier with an accuracy of 90.4% in identifying encephalopathy cases.

A Novel Adaptive Joint Time Frequency Algorithm by the Neural Network for the ISAR Rotational Compensation

We propose a novel adaptive joint time frequency algorithm combined with the neural network (AJTF-NN) to focus the distorted inverse synthetic aperture radar (ISAR) image. In this paper, a coefficient estimator based on the artificial neural network (ANN) is firstly developed to solve the time-consuming rotational motion compensation (RMC) polynomial phase coefficient estimation problem. The training method, the cost function and the structure of ANN are comprehensively discussed. In addition, we originally propose a method to generate training dataset sourcing from the ISAR signal models with randomly chosen motion characteristics. Then, prediction results of the ANN estimator is used to directly compensate the ISAR image, or to provide a more accurate initial searching range to the AJTF for possible low-performance scenarios. Finally, some simulation models including the ideal point scatterers and a realistic Airbus A380 are employed to comprehensively investigate properties of the AJTF-NN, such as the stability and the efficiency under different signal-to-noise ratios (SNRs). Results show that the proposed method is much faster than other prevalent improved searching methods, the acceleration ratio are even up to 424 times without the deterioration of compensated image quality. Therefore, the proposed method is potential to the real-time application in the RMC problem of the ISAR imaging.

Real-Time Segmentation and Feature Extraction of Electromyography: Towards Control of a Prosthetic Hand

Surface electromyographic (sEMG) signals can be used as inputs to control a myoelectric prosthetic hand. This requires the discrimination of sEMG associated with different hand movements. The signals for key unilateral hand movements such as wrist extension, wrist flexion, and power grip are similar, making the classification and control of these hand movements challenging. This preliminary study explores the viability of classifying the sEMG signals of these hand movements in real-time, in order to control a software simulation of a prosthetic hand. sEMG data was recorded from two bipolar electrodes for offline classifier training purposes. A novel segmentation technique was used to separate the muscle contraction and rest periods of the sEMG time-series data. A time-frequency algorithm was then applied for the first time to extract sEMG-based features from the segmented data. Features were used to train four support vector machines offline, in a one-versus-all architecture. The classification system was tested offline and in real-time. The system yielded accuracies of 89.39% and 84.93% for offline and real-time testing respectively. Real-time classification was done in 10.2 ms when processing 0.5 s of input sEMG data. This shows that the system is accurate and computationally efficient, even with limited electrodes. Thus, it can serve as a foundation for further work in the implemented segmentation and feature extraction methods, for an inexpensive alternative to commercial myoelectric prosthetic devices.

Automated and High Accuracy Out-Of-Hospital Heart Diseases Early Detection System

Background: ECG measurement and analysis being performed in-hospital normally check patients with obvious symptoms. Asymptomatic patients, for example, those with silent ischemia, paroxysmal atrial fibrillation and Brugada syndrome are very difficult to detect using in-hospital ECG system. To make matter worst, conventional ECG analysis techniques only focuses in time domain that limits the sensitivity, specificity and accuracy of the interpretation due to ECG signals non-stationary nature. Most recent researches have proposed linear joint time-frequency analysis to overcome these limitations, however, their linear methods limit their accuracy. Objective: The main objective is to enable automated and high accuracy out-of-hospital ECG analysis for early detection of heart disease. Materials & Methods: MIT-BIH ECG databases are used to test the performance of the proposed system. The data is pre-processed for amplitude normalization and frequency resampling. The pre-processed output is then fed to the non-linear joint time-frequency algorithm for analysis. The outcome of the analysis is further classified by the machine learning algorithm. Before the classification can be performed, the intelligent classifier is trained using control data that contains 52 normal and 148 patients data. After that, it is used for classifying 40 normal and 88 patients with ischaemia. The entire processes is automated inside a computer. The main disadvantage of the proposed non-linear joint time-frequency technique together with the intelligent classification is that it requires huge amount of computing system resources (big data problem). To solve this issue the system can be connected to the cloud to further enhance the performance and the accuracy of the system. Results: The analysis is performed on 421632 normal and 863282 patients ECG beats. The results obtained show that the system gives high performance of accuracy, sensitivity and specificity with values of 99.03%, 99.59% and 99.57%, respectively. Conclusions: The proposed method operates in joint time-frequency in non-linear fashion. Hence it produces more accurate interpretation compared to the conventional time domain and the more recent linear time-frequency techniques. The high accuracy together with the automated capability of the system can help detect heart problems at the early stages even before the patients pay visit to the hospital.

Micro-Doppler Signal Time-Frequency Algorithm Based on STFRFT.

This paper proposes a time-frequency algorithm based on short-time fractional order Fourier transformation (STFRFT) for identification of a complicated movement targets. This algorithm, consisting of a STFRFT order-changing and quick selection method, is effective in reducing the computation load. A multi-order STFRFT time-frequency algorithm is also developed that makes use of the time-frequency feature of each micro-Doppler component signal. This algorithm improves the estimation accuracy of time-frequency curve fitting through multi-order matching. Finally, experiment data were used to demonstrate STFRFT’s performance in micro-Doppler time-frequency analysis. The results validated the higher estimate accuracy of the proposed algorithm. It may be applied to an LFM (Linear frequency modulated) pulse radar, SAR (Synthetic aperture radar), or ISAR (Inverse synthetic aperture radar), for improving the probability of target recognition.

Atrial flutter and atrial tachycardia detection using Bayesian approach with high resolution time–frequency spectrum from ECG recordings

Contemporary methods of atrial flutter (AFL), atrial tachycardia (AT), and atrial fibrillation (AF) monitoring, although superior to the standard 12-lead ECG and symptom-based monitoring, are unable to accurately discriminate between AF, AFL and AT. Thus, there is a need to develop accurate, automated, and comprehensive atrial arrhythmia detection algorithms using standard ECG recorders. To this end, we have developed a sensitive and real-time realizable algorithm for accurate AFL and AT detection using any standard electrocardiographic recording. Our novel method for automatic detection of atrial flutter and atrial tachycardia uses a Bayesian approach followed by a high resolution time–frequency spectrum. We find the TQ interval of the electrocardiogram (ECG) corresponding to atrial activity by using a particle filter (PF), and analyze the atrial activity with a high resolution time–frequency spectral method: variable frequency complex demodulation (VFCDM). The rationale for using a high-resolution time–frequency algorithm is that our approach tracks the time-varying fundamental frequency of atrial activity, where AT is within 2.0–4.0Hz, AFL is within 4.0–5.3Hz and NSR is found at frequencies less than 2.0Hz. For classifications of AFL (n=22), AT (n=10) and normal sinus rhythms (NSR) (n=29), we found that our approach resulted in accuracies of 0.89, 0.87 and 0.91, respectively; the overall accuracy was 0.88.

Modeling and Analysis of LPI Radar Signal

Radar Emitter Signal recognition is one of the key procedures of signal processing in Electronic Warfare (EW) Receiver. As there is an intense growth in the activities of modern Electronic Warfare, advanced radars are increasing and becoming main component of radars gradually. These modern radars called Low Probability of Intercept (LPI), use different complex waveforms to mask their presence from the enemy while accomplishing their mission. These waveforms cannot be detected by the use of traditional recognition algorithms and methods thus posing a major challenge to the Electronic Warfare designer. This paper presents simulation of different types of LPI signals, generation of those signals and development of Time Frequency Algorithm to analyze those signals.

Dual-time-scale method for modeling of the nonlinear amplitude-modulated ultrasound fields

This study focuses on modeling of the nonlinear acoustic wave propagation in situations when the amplitude of the focused ultrasound field is modulated by a low-frequency signal. This problem is relevant to both ultrasound imaging applications entailing the use of the acoustic radiation force, and treatment applications such as histotripsy. The difficulty of predicting the pressure wavefield lies in a fact that the excessive length of the low-frequency modulated signal may significantly increase the computational effort. To tackle the problem, this study utilizes the dual-time-scale approach, where two temporal variables are introduced to distinguish between ultrasound-scale and modulation-scale variations. In this case, the Westervelt-type equation can be effectively solved using hybrid time-frequency algorithm for any transient (sufficiently smooth) modulation envelope. To validate the proposed approach, the Khokhlov-Zabolotskaya-Kuznetsov equation was solved in the time domain for an example pressure profile on the boundary. A comparison between the time-domain and hybrid calculations demonstrates that the latter are notably faster, require significantly less memory, and have satisfactory accuracy for the ratios between the modulation and carrier ultrasound frequencies below 0.1.