Detection of sleep arousal from STFT-based instantaneous features of single channel EEG signal.

OBJECTIVE: Sleep arousal, a frequent interruption in sleep with complete or partial wakefulness from sleep, may indicate a breathing disorder, neurological disorder, or sleep-related disorders. These phenomena necessitate the detection of sleep arousals. Uses of deep learning methods to detect features inhibits the scope to understand the specific distinctive nature of the signals and reduces the interpretability of the model. To evade these inconsistencies and to improve the classification performance of the sleep arousal detection model, a model has been proposed in this study on the prospect of understandable features that are useful in detecting sleep arousals. Approach: Time-frequency analysis of the electroencephalogram (EEG) signals was performed using Short-Time Fourier Transform (STFT). From the STFT coefficients, the spectrogram and instantaneous properties (frequency, bandwidth, power spectrum, band energy, local maxima, and band energy ratios) were investigated. From these properties, instantaneous features were generated by statistical analysis. Additive feature sets and reduced feature sets, formed by adding features successively and reducing features using the analysis of variance test respectively, were subjected to a tri-layered neural network classifier to evaluate the capability of the features to detect sleep arousal and normal sleep segments. Main results: The reduced feature set (Set 6) has proved to be efficacious in facilitating superior classification performance metrics (accuracy, sensitivity, specificity, and AUC of 89.14%, 83.52%, 89.49%, and 93.84% respectively). Significance: This efficient model can be incorporated with an automatic sleep apnea detection system where the estimation of hypopnea requires the detection of sleep arousal. .

Signal Separation Operator Based on Wavelet Transform for Non-Stationary Signal Decomposition.

This paper develops a new frame for non-stationary signal separation, which is a combination of wavelet transform, clustering strategy and local maximum approximation. We provide a rigorous mathematical theoretical analysis and prove that the proposed algorithm can estimate instantaneous frequencies and sub-signal modes from a blind source signal. The error bounds for instantaneous frequency estimation and sub-signal recovery are provided. Numerical experiments on synthetic and real data demonstrate the effectiveness and efficiency of the proposed algorithm. Our method based on wavelet transform can be extended to other time-frequency transforms, which provides a new perspective of time-frequency analysis tools in solving the non-stationary signal separation problem.

Unveil sleep spindles with concentration of frequency and time (ConceFT).

Objective.Sleep spindles contain crucial brain dynamics information. We introduce the novel non-linear time-frequency (TF) analysis tool 'Concentration of Frequency and Time' (ConceFT) to create an interpretable automated algorithm for sleep spindle annotation in EEG data and to measure spindle instantaneous frequencies (IFs).Approach.ConceFT effectively reduces stochastic EEG influence, enhancing spindle visibility in the TF representation. Our automated spindle detection algorithm, ConceFT-Spindle (ConceFT-S), is compared to A7 (non-deep learning) and SUMO (deep learning) using Dream and Montreal Archive of Sleep Studies (MASS) benchmark databases. We also quantify spindle IF dynamics.Main results.ConceFT-S achieves F1 scores of 0.765 in Dream and 0.791 in MASS, which surpass A7 and SUMO. We reveal that spindle IF is generally nonlinear.Significance.ConceFT offers an accurate, interpretable EEG-based sleep spindle detection algorithm and enables spindle IF quantification.

Machine-Learning-Assisted Instantaneous Frequency Measurement Method Based on Thin-Film Lithium Niobate on an Insulator Phase Modulator for Radar Detection.

A simple microwave photonic, reconfigurable, instantaneous frequency measurement system based on low-voltage thin-film lithium niobate on an insulator phase modulator is put forward and experimentally demonstrated. Changing the wavelength of the optical carrier can realize the flexibility of the frequency measurement range and accuracy, showing that during the ranges of 0-10 GHz, 3-15 GHz, and 12-18 GHz, the average measurement errors are 26.9 MHz, 44.57 MHz, and 13.6 MHz, respectively, thanks to the stacked integrated learning models. Moreover, this system is still able to respond to microwave signals of as low as -30 dBm with the frequency measurement error of 62.06 MHz, as that low half-wave voltage for the phase modulator effectively improves the sensitivity of the system. The general-purpose, miniaturized, reconfigurable, instantaneous frequency measurement modules have unlimited potential in areas such as radar detection and early warning reception.

Method for Automatic Estimation of Instantaneous Frequency and Group Delay in Time-Frequency Distributions with Application in EEG Seizure Signals Analysis.

Instantaneous frequency (IF) is commonly used in the analysis of electroencephalogram (EEG) signals to detect oscillatory-type seizures. However, IF cannot be used to analyze seizures that appear as spikes. In this paper, we present a novel method for the automatic estimation of IF and group delay (GD) in order to detect seizures with both spike and oscillatory characteristics. Unlike previous methods that use IF alone, the proposed method utilizes information obtained from localized Rényi entropies (LREs) to generate a binary map that automatically identifies regions requiring a different estimation strategy. The method combines IF estimation algorithms for multicomponent signals with time and frequency support information to improve signal ridge estimation in the time-frequency distribution (TFD). Our experimental results indicate the superiority of the proposed combined IF and GD estimation approach over the IF estimation alone, without requiring any prior knowledge about the input signal. The LRE-based mean squared error and mean absolute error metrics showed improvements of up to 95.70% and 86.79%, respectively, for synthetic signals and up to 46.45% and 36.61% for real-life EEG seizure signals.

Neural entrainment underpins sensorimotor synchronization to dynamic rhythmic stimuli.

Neural entrainment, defined as unidirectional synchronization of neural oscillations to an external rhythmic stimulus, is a topic of major interest in the field of neuroscience. Despite broad scientific consensus on its existence, on its pivotal role in sensory and motor processes, and on its fundamental definition, empirical research struggles in quantifying it with non-invasive electrophysiology. To this date, broadly adopted state-of-the-art methods still fail to capture the dynamic underlying the phenomenon. Here, we present event-related frequency adjustment (ERFA) as a methodological framework to induce and to measure neural entrainment in human participants, optimized for multivariate EEG datasets. By applying dynamic phase and tempo perturbations to isochronous auditory metronomes during a finger-tapping task, we analyzed adaptive changes in instantaneous frequency of entrained oscillatory components during error correction. Spatial filter design allowed us to untangle, from the multivariate EEG signal, perceptual and sensorimotor oscillatory components attuned to the stimulation frequency. Both components dynamically adjusted their frequency in response to perturbations, tracking the stimulus dynamics by slowing down and speeding up the oscillation over time. Source separation revealed that sensorimotor processing enhanced the entrained response, supporting the notion that the active engagement of the motor system plays a critical role in processing rhythmic stimuli. In the case of phase shift, motor engagement was a necessary condition to observe any response, whereas sustained tempo changes induced frequency adjustment even in the perceptual oscillatory component. Although the magnitude of the perturbations was controlled across positive and negative direction, we observed a general bias in the frequency adjustments towards positive changes, which points at the effect of intrinsic dynamics constraining neural entrainment. We conclude that our findings provide compelling evidence for neural entrainment as mechanism underlying overt sensorimotor synchronization, and highlight that our methodology offers a paradigm and a measure for quantifying its oscillatory dynamics by means of non-invasive electrophysiology, rigorously informed by the fundamental definition of entrainment.

Novel multivariate methods to track frequency shifts of neural oscillations in EEG/MEG recordings.

Instantaneous and peak frequency changes in neural oscillations have been linked to many perceptual, motor, and cognitive processes. Yet, the majority of such studies have been performed in sensor space and only occasionally in source space. Furthermore, both terms have been used interchangeably in the literature, although they do not reflect the same aspect of neural oscillations. In this paper, we discuss the relation between instantaneous frequency, peak frequency, and local frequency, the latter also known as spectral centroid. Furthermore, we propose and validate three different methods to extract source signals from multichannel data whose (instantaneous, local, or peak) frequency estimate is maximally correlated to an experimental variable of interest. Results show that the local frequency might be a better estimate of frequency variability than instantaneous frequency under conditions with low signal-to-noise ratio. Additionally, the source separation methods based on local and peak frequency estimates, called LFD and PFD respectively, provide more stable estimates than the decomposition based on instantaneous frequency. In particular, LFD and PFD are able to recover the sources of interest in simulations performed with a realistic head model, providing higher correlations with an experimental variable than multiple linear regression. Finally, we also tested all decomposition methods on real EEG data from a steady-state visual evoked potential paradigm and show that the recovered sources are located in areas similar to those previously reported in other studies, thus providing further validation of the proposed methods.

Acquisition of a single grid-based phase-contrast X-ray image using instantaneous frequency and noise filtering.

BACKGROUND: To obtain phase-contrast X-ray images, single-grid imaging systems are effective, but Moire artifacts remain a significant issue. The solution for removing Moire artifacts from an image is grid rotation, which can distinguish between these artifacts and sample information within the Fourier space. However, the mechanical movement of grid rotation is slower than the real-time change in Moire artifacts. Thus, Moire artifacts generated during real-time imaging cannot be removed using grid rotation. To overcome this problem, we propose an effective method to obtain phase-contrast X-ray images using instantaneous frequency and noise filtering. RESULT: The proposed phase-contrast X-ray image using instantaneous frequency and noise filtering effectively suppressed noise with Moire patterns. The proposed method also preserved the clear edge of the inner and outer boundaries and internal anatomical information from the biological sample, outperforming conventional Fourier analysis-based methods, including absorption, scattering, and phase-contrast X-ray images. In particular, when comparing the phase information for the proposed method with the x-axis gradient image from the absorption image, the proposed method correctly distinguished two different types of soft tissue and the detailed information, while the latter method did not. CONCLUSION: This study successfully achieved a significant improvement in image quality for phase-contrast X-ray images using instantaneous frequency and noise filtering. This study can provide a foundation for real-time bio-imaging research using three-dimensional computed tomography.

Estimation and Classification of NLFM Signals Based on the Time-Chirp Representation.

A new approach to the estimation and classification of nonlinear frequency modulated (NLFM) signals is presented in the paper. These problems are crucial in electronic reconnaissance systems whose role is to indicate what signals are being received and recognized by the intercepting receiver. NLFM signals offer a variety of useful properties not available for signals with linear frequency modulation (LFM). In particular, NLFM signals can ensure the desired reduction of sidelobes of an autocorrelation (AC) function and desired power spectral density (PSD); therefore, such signals are more frequently used in modern radar and echolocation systems. Due to their nonlinear properties, the discussed signals are difficult to recognize and therefore require sophisticated methods of analysis, estimation and classification. NLFM signals with frequency content varying with time are mainly analyzed by time-frequency algorithms. However, the methods presented in the paper belong to time-chirp domain, which is relatively rarely cited in the literature. It is proposed to use polynomial approximations of nonlinear frequency and phase functions describing signals. This allows for applying the cubic phase function (CPF) as an estimator of phase polynomial coefficients. Originally, the CPF involved only third-order nonlinearities of the phase function. The extension of the CPF using nonuniform sampling is used to analyse the higher order polynomial phase. In this paper, a sixth order polynomial is considered. It is proposed to estimate the instantaneous frequency using a polynomial with coefficients calculated from the coefficients of the phase polynomial obtained by CPF. The determined coefficients also constitute the set of distinctive features for a classification task. The proposed CPF-based classification method was examined for three common NLFM signals and one LFM signal. Two types of neural network classifiers: learning vector quantization (LVQ) and multilayer perceptron (MLP) are considered for such defined classification problem. The performance of both the estimation and classification processes was analyzed using Monte Carlo simulation studies for different SNRs. The results of the simulation research revealed good estimation performance and error-free classification for the SNR range encountered in practical applications.

Understanding Harmonic Structures Through Instantaneous Frequency.

The analysis of harmonics and non-sinusoidal waveform shape in time-series data is growing in importance. However, a precise definition of what constitutes a harmonic is lacking. In this paper, we propose a rigorous definition of when to consider signals to be in a harmonic relationship based on an integer frequency ratio, constant phase, and a well-defined joint instantaneous frequency. We show this definition is linked to extrema counting and Empirical Mode Decomposition (EMD). We explore the mathematics of our definition and link it to results from analytic number theory. This naturally leads to us to define two classes of harmonic structures, termed strong and weak, with different extrema behaviour. We validate our framework using both simulations and real data. Specifically, we look at the harmonic structures in shallow water waves, the FitzHugh-Nagumo neuronal model, and the non-sinusoidal theta oscillation in rat hippocampus local field potential data. We further discuss how our definition helps to address mode splitting in nonlinear time-series decomposition methods. A clear understanding of when harmonics are present in signals will enable a deeper understanding of the functional roles of non-sinusoidal oscillations.

A Comparative Study of Parameter Identification Methods for Asymmetric Nonlinear Systems with Quadratic and Cubic Stiffness.

Understanding the nonlinear dynamic characteristics of engineering structures is challenging, especially for the systems that exhibit asymmetric nonlinear behavior. This paper compared four parameter identification methods for asymmetric nonlinear systems incorporating quadratic and cubic stiffness nonlinearities. Hilbert transform, zero-crossing, direct quadrature, and wavelet transform were used to obtain the backbone, envelope, and restoring force curves from the free vibration time history. A nonlinear curve-fitting method was then applied to estimate the stiffness parameters of the asymmetric systems, and a linear least square fitting approach was utilized to estimate the damping parameters of the asymmetric systems. We used the Helmholtz-Duffing oscillator as a numerical example and a nonlinear vibration absorber with geometric imperfections to verify the feasibility and accuracy of these methods. The advantages and disadvantages of these methods and the deviations in estimated results are discussed.

A Non-Destructive Health Evaluation Method for Wooden Utility Poles with Frequency-Modulated Empirical Mode Decomposition and Laplace Wavelet Correlation Filtering.

Wooden utility poles are one of the most commonly used utility carriers in North America. Even though they are given different protection treatments, wooden utility poles are prone to have defects that are mainly caused by temperature, oxygen, moisture, and high potential hydrogen levels after decades of being exposed in open-air areas. In order to meet the growing demand regarding their maintenance and replacement, an effective health evaluation technology for wooden utility poles is essential to ensure normal power supply and safety. However, the commonly used hole-drilling inspection method always causes extra damage to wooden utility poles and the precision of health evaluation highly relies on technician experience at present. Therefore, a non-destructive health evaluation method with frequency-modulated empirical mode decomposition (FM-EMD) and Laplace wavelet correlation filtering based on dynamic responses of wooden utility poles was proposed in this work. Specifically, FM-EMD was used to separate multiple confusing closely-spaced vibration modes due to nonlinear properties of wooden utility poles into several single modes. The instantaneous frequency and damping factor of the decomposed signal of each single mode of the dynamic response of a wooden utility pole could be determined using Laplace wavelet correlation filtering with high precision. The health status of a wooden utility pole could then be estimated according to the extracted instantaneous frequency and damping factor of the decomposed signal of each single mode. The proposed non-destructive health evaluation method for wooden utility poles was tested in the field and achieved successful results.

Entropy-Based Concentration and Instantaneous Frequency of TFDs from Cohen's, Affine, and Reassigned Classes.

This paper explores three groups of time-frequency distributions: the Cohen's, affine, and reassigned classes of time-frequency representations (TFRs). This study provides detailed insight into the theory behind the selected TFRs belonging to these classes. Extensive numerical simulations were performed with examples that illustrate the behavior of the analyzed TFR classes in the joint time-frequency domain. The methods were applied both on synthetic and real-life non-stationary signals. The obtained results were assessed with respect to time-frequency concentration (measured by the Rényi entropy), instantaneous frequency (IF) estimation accuracy, cross-term presence in the TFRs, and the computational cost of the TFRs. This study gives valuable insight into the advantages and limitations of the analyzed TFRs and assists in selecting the proper distribution when analyzing given non-stationary signals in the time-frequency domain.

EEG alpha power predicts the temporal sensitivity of multisensory perception.

Pre-stimulus electroencephalogram (EEG) oscillations, especially in the alpha range (8-13 Hz), can affect the sensitivity to temporal lags between modalities in multisensory perception. The effects of alpha power are often explained in terms of alpha's inhibitory functions, whereas effects of alpha frequency have bolstered theories of discrete perceptual cycles, where the length of a cycle, or window of integration, is determined by alpha frequency. Such studies typically employ visual detection paradigms with near-threshold or even illusory stimuli. It is unclear whether such results generalize to above-threshold stimuli. Here, we recorded EEG, while measuring temporal discrimination sensitivity in a temporal-order judgement task using above-threshold auditory and visual stimuli. We tested whether the power and instantaneous frequency of pre-stimulus oscillations predict audiovisual temporal discrimination sensitivity on a trial-by-trial basis. By applying a jackknife procedure to link single-trial pre-stimulus oscillatory power and instantaneous frequency to psychometric measures, we identified a posterior cluster where lower alpha power was associated with higher temporal sensitivity of audiovisual discrimination. No statistically significant relationship between instantaneous alpha frequency and temporal sensitivity was found. These results suggest that temporal sensitivity for above-threshold multisensory stimuli fluctuates from moment to moment and is indexed by modulations in alpha power.

An Efficient and Accurate Multi-Sensor IF Estimator Based on DOA Information and Order of Fractional Fourier Transform.

Instantaneous frequency in multi-sensor recordings is an important parameter for estimation of direction of arrival estimation, source separation, and sparse reconstruction. The instantaneous frequency estimation problem becomes challenging when signal components have close or overlapping signatures and the number of sensors is less than the number of sources. In this study, we develop a computationally efficient method that exploits the direction of the IF curve in addition to the angle of arrival as additional features for the accurate tracking of IF curves. Experimental results show that the proposed scheme achieves better accuracy compared to the-state-of-art method in terms of mean square error (MSE) with a slight increase in the computational cost, i.e., the proposed method achieves MSE of -50 dB at the signal to noise ratio of 0 dB whereas the existing method achieves the MSE of -38 dB.

A novel combined model for prediction of daily precipitation data using instantaneous frequency feature and bidirectional long short time memory networks.

Meteorological events constantly affect human life, especially the occurrence of excessive precipitation in a short time causes important events such as floods. However, in case of insufficient precipitation for a long time, drought occurs. In recent years, significant changes in precipitation regimes have been observed and these changes cause socio-economic and ecological problems. Therefore, it is of great importance to correctly predict and analyze the precipitation data. In this study, a reliable and accurate precipitation forecasting model is proposed. For this aim, three deep neural network models, long short-time memory networks (LSTM), gated recurrent unit (GRU), and bidirectional long short time memory networks (biLSTM), were applied for one ahead forecasting of daily precipitation data and compared the performances of these models. Moreover, to increase the far ahead forecasting performance of the biLSTM model, the instantaneous frequency (IF) feature was applied as the input parameter for the first time in the literature. Therefore, a novel model ensemble of IF and biLSTM was employed for the aim of one-six ahead forecasting of daily precipitation data. The performance of the proposed IF-biLSTM model was evaluated using mean absolute error (MAE), mean square error (MSE), correlation coefficient (R), and determination coefficient (R2) performance parameter and spider charts were used to assess the model performances. According to the numerical results, the biLSTM model outperformed compared with the LSTM and GRU models. After the good score achieved with biLSTM model, IF feature applied to biLSTM and IF-biLSTM model has the best forecasting performance for daily precipitation data with R2 value 0.9983, 0.9827, 0.9092, 0.8508, 0.7827, and 0.7646, respectively, for one-six ahead forecasting of daily precipitation data. It has been observed that the IF-biLSTM model has higher forecasting performance than the biLSTM model, especially in far ahead forecasting studies, and the IF feature improves the estimation performance.

Power spectrum slope confounds estimation of instantaneous oscillatory frequency.

Oscillatory neural dynamics are highly non-stationary and require methods capable of quantifying time-resolved changes in oscillatory activity in order to understand neural function. Recently, a method termed 'frequency sliding' was introduced to estimate the instantaneous frequency of oscillatory activity, providing a means of tracking temporal changes in the dominant frequency within a sub-band of field potential recordings. Here, the ability of frequency sliding to recover ground-truth oscillatory frequency in simulated data is tested while the exponent (slope) of the 1/fx component of the signal power spectrum is systematically varied, mimicking real electrophysiological data. The results show that 1) in the presence of 1/f activity, frequency sliding systematically underestimates the true frequency of the signal, 2) the magnitude of underestimation is correlated with the steepness of the slope, suggesting that, if unaccounted for, slope changes could be misinterpreted as frequency changes, 3) the impact of slope on frequency estimates interacts with oscillation amplitude, indicating that changes in oscillation amplitude alone may also influence instantaneous frequency estimates in the presence of strong 1/f activity; and 4) analysis parameters such as filter bandwidth and location also mediate the influence of slope on estimated frequency, indicating that these settings should be considered when interpreting estimates obtained via frequency sliding. The origin of these biases resides in the output of the filtering step of frequency sliding, whose energy is biased towards lower frequencies precisely because of the 1/f structure of the data. We discuss several strategies to mitigate these biases and provide a proof-of-principle for a 1/f normalization strategy.

Adaptive instantaneous frequency ridge extraction based on target tracking for frequency-modulated signals.

The instantaneous frequency (IF) is an important feature for the analysis of non-stationary signals. However, extracting multiple IF ridges, crossing IF ridges, and discontinuous IF ridges simultaneously is still a challenging task. To solve this problem, an adaptive IF ridge extraction method is proposed. This method regards the IF ridge values at each time point as targets to be tracked. The tracking targets are defined as three states: survival, death, and birth. Firstly, the potential peaks in the time-frequency representation are found to reduce the noise effect. Secondly, an adaptive penalty function is constructed to determine the target state and track the ridge target. Thirdly, the crossing ridges are separated base on the slope information. This method is capable of simultaneously extracting multiple IF ridges, crossing IF ridges, and discontinuous IF ridges. The performance of the proposed method is investigated by a simulated signal and two experimental signals.

Within-cycle instantaneous frequency profiles report oscillatory waveform dynamics.

The nonsinusoidal waveform is emerging as an important feature of neuronal oscillations. However, the role of single-cycle shape dynamics in rapidly unfolding brain activity remains unclear. Here, we develop an analytical framework that isolates oscillatory signals from time series using masked empirical mode decomposition to quantify dynamical changes in the shape of individual cycles (along with amplitude, frequency, and phase) with instantaneous frequency. We show how phase-alignment, a process of projecting cycles into a regularly sampled phase grid space, makes it possible to compare cycles of different durations and shapes. "Normalized shapes" can then be constructed with high temporal detail while accounting for differences in both duration and amplitude. We find that the instantaneous frequency tracks nonsinusoidal shapes in both simulated and real data. Notably, in local field potential recordings of mouse hippocampal CA1, we find that theta oscillations have a stereotyped slow-descending slope in the cycle-wise average yet exhibit high variability on a cycle-by-cycle basis. We show how principal component analysis allows identification of motifs of theta cycle waveform that have distinct associations to cycle amplitude, cycle duration, and animal movement speed. By allowing investigation into oscillation shape at high temporal resolution, this analytical framework will open new lines of inquiry into how neuronal oscillations support moment-by-moment information processing and integration in brain networks.NEW & NOTEWORTHY We propose a novel analysis approach quantifying nonsinusoidal waveform shape. The approach isolates oscillations with empirical mode decomposition before waveform shape is quantified using phase-aligned instantaneous frequency. This characterizes the full shape profile of individual cycles while accounting for between-cycle differences in duration, amplitude, and timing. We validated in simulations before applying to identify a range of data-driven nonsinusoidal shape motifs in hippocampal theta oscillations.