Aperiodic Signals Research Articles

Longitudinal changes in aperiodic and periodic activity in electrophysiological recordings in the first seven months of life

Neuronal oscillations emerge in early human development. These periodic oscillations are thought to rapidly change in infancy and stabilize during maturity. Given their numerous connections to physiological and cognitive processes, understanding the trajectory of oscillatory development is important for understanding healthy human brain development. This understanding is complicated by recent evidence that assessment of periodic neuronal oscillations is confounded by aperiodic neuronal activity, an inherent feature of electrophysiological recordings. Recent cross-sectional evidence shows that this aperiodic signal progressively shifts from childhood through early adulthood, and from early adulthood into later life. None of these studies, however, have been performed in infants, nor have they been examined longitudinally. Here, we analyzed longitudinal non-invasive EEG data from 22 typically developing infants, ranging between 38 and 203 days old. We show that the progressive flattening of the EEG power spectrum begins in very early development, continuing through the first months of life. These results highlight the importance of separating the periodic and aperiodic neuronal signals, because the aperiodic signal can bias measurement of neuronal oscillations. Given the infrequent, bursting nature of oscillations in infants, we recommend using quantitative time domain approaches that isolate bursts and uncover changes in waveform properties of oscillatory bursts.

“Empirical Prewhitening” Spectral Analysis Detects Periodic but Inconsistent Signals in Abyssal Hill Morphology at the Southern East Pacific Rise

AbstractThe existence, or not, of periodicities in abyssal hill morphology has been vigorously debated in recent publications, and some have hypothesized that such periodicities are evidence of the impact of Milankovitch cycle‐caused sea level fluctuations on the volcanic construction process at mid‐ocean ridges. Periodicities are detected by the presence of spectral peaks that rise significantly above the random variations of sample power spectra associated with an aperiodic, continuous spectrum process, typically modeled as a band‐limited fractal (von Kármán model). Here, I formulate and test a new algorithm to “empirically prewhiten” the sample power spectrum which, without needing to model the continuous spectrum, flattens it to a zero‐mean process. This greatly simplifies definition of the null hypothesis, and additional modeling approximates standard deviation levels that provide a conservative basis for detecting peaks that may be indicative of periodicity. The algorithm is applied to extensive bathymetric data flanking the southern East Pacific Rise. Significant periodicities are detected on many profiles analyzed, but the periods vary widely, and do not cluster at Milankovitch periods. The most substantial harmonic signals detected exhibit periods ∼0.082–0.216 my, with root‐mean square (RMS) heights approximately a quarter to a third of the RMS height for the aperiodic signal. It is hypothesized that the dominant aperiodic component of abyssal hills corresponds to morphology constructed by faults that follow a random distribution governed by scaling laws, whereas longer‐scale periodic signals are associated with crustal thickness variations controlled internally by variations in melt supply.

Modified Recurrence Plot for Robust Condition Monitoring of Electrode Tips in a Resistance Spot Welding System

Degraded electrodes in a resistance spot welding system should be replaced to ensure that weld quality is maintained. Welding electrodes are subjected to different environmental and operational loading conditions during use. When they are replaced with a fixed interval, replacement may occur too early (raising maintenance costs) or too late (leading to quality issues). This motivates condition monitoring strategies for resistance spot welding electrode tips. Thus, this paper proposes a modified recurrence plot (RP) for robust condition monitoring of welding electrode tips in resistance spot welding systems. The overall procedure for the proposed condition monitoring approach consists of three steps: (1) transformation of a one-dimensional signal to a two-dimensional image, (2) unsupervised feature extraction with LeNet architecture-based convolutional neural networks, and (3) health indicator calculation. RP methods convert dynamic resistance waveforms to RPs. The original RP method provides an image with binary-colored pixels (i.e., black or white) that makes this method insensitive to the change of the waveform signal. The proposed RP method is devised to be sensitive to the change of the waveform signal, while enhancing robustness to external noise. The performance of the proposed RP method is evaluated by examining simulated aperiodic waveform signals with and without external noise. A case study is presented to examine the proposed method’s ability to monitor the condition of resistance spot welding electrodes. The results show that the proposed method outperforms handcrafted, feature-based condition monitoring methods. This study can be used to accurately determine the lifetime of welding electrodes in real time during the spot welding process.

Voltage stability assessment accounting for current-limited converters

This paper investigates how current-limited converters influence system stability. An improved approach for assessing voltage stability is introduced, which determines the maximum deliverable power to a load by accounting for changes in the Thévenin voltages. The new approach is able to detect voltage instability well before the traditional approach based on Thévenin impedance matching. A new stability boundary is discovered that describes the aperiodic small signal stability boundary for current-limited converters. The improved approach was modified to account for current-limited converters. The detection of voltage and rotor angle instability during current limitation were demonstrated on a seven bus system, where test cases were performed. The test cases showed that voltage instability can lead to aperiodic small signal instability, when the converter has reached its current limit and loss of synchronism in the unstable region during current-limitation causes the system voltages to collapse.

A Chaotic Circuit for Producing Gaussian Random Numbers

One of the main applications for chaotic circuits is the production of aperiodic signals with many of the characteristics of noise for secure communications and similar uses. However, the probability distribution function (pdf) of such signals is usually far from Gaussian. This paper describes a new chaotic circuit based on the recently proposed signum thermostat that produces signals whose pdf is accurately Gaussian. Data from the constructed circuit are analyzed and shown to be in agreement with the theoretical prediction.

Aperiodic electro-optic time lens for spectral manipulation of single-photon pulses

Electro-optic time lenses are promising experimental components for photonic spectral-temporal processing of quantum information. We report a stable method to realize an electro-optic time lens, which relies on the amplification of an electronic response of a fast photodiode. The method does not require a repetitive clock and may be applied to aperiodic optical signals. We experimentally demonstrate the approach using single-photon pulses, and directly verify its aperiodicity. The approach will enable the construction of complex electro-optic temporal optical systems.

On the Aperiodic Signal Amplification by Rescaled Vibrational Resonance in Fractional-Order Duffing Oscillators

AbstractIn the former works of Yang et al., they put forward two vibrational resonance (VR) methods in fractional Duffing oscillators to amplify the weak harmonic character signal with arbitrary high-frequency. Moreover, the aperiodic character signal is also a common signal form in practical engineering. For the “fast-changing” aperiodic character signal in time domain, the classical VR method is difficult to amplify it effectively. To solve this problem, an aperiodic signal amplification method based on rescaled VR in fractional-order Duffing oscillators is proposed. Take the bipolar binary random signals with arbitrary minimal pulse width as an example, the rescaled VR under the overdamped and underdamped conditions can be realized by matching the signal parameters and system parameters effectively, and the amplification of aperiodic signal can be achieved.

Formation of Minimax Ensembles of Aperiodic Gold Codes

Introduction. Signals constructed on the basis of ensembles of code sequences are widely used in digital communication systems. During development of such systems, the most attention is paid to analysis, synthesis and implementation of periodic signal ensembles. Theoretic methods for synthesis of periodic signal ensembles are developed and are in use. Considerably fewer results are received regarding construction of aperiodic signal ensembles with given properties. Theoretical methods for synthesis of such ensembles are practically nonexistent.Aim. To construct aperiodic Gold code ensembles with the best ratios of code length to ensemble volume among the most known binary codes.Materials and methods. Methods of directed search and discrete choice of the best ensemble based on unconditional preference criteria are used.Results. Full and truncated aperiodic Gold code ensembles with given length and ensemble volume were constructed. Parameters and shape of auto- and mutual correlation functions were shown for a number of constructed ensembles. Comparison of the paper results with known results for periodic Gold code ensembles has been conducted regarding growth of minimax correlation function values depending on code length and ensemble volume.Conclusion. The developed algorithms, unlike the known ones, make it possible to form both complete ensembles and ensembles taking into account the limitation of their volume. In addition, the algorithms can be extended to the tasks of forming ensembles from other families, for example, assembled from code sequences belonging to different families.

Stochastic resonance induced by an unknown linear frequency modulated signal in a strong noise background.

Stochastic resonance (SR) is widely used as a signal enhancement technique in recovering and enhancing periodic or aperiodic signals submerged in noise. However, system parameters and noise intensity tend to influence the SR performance. To achieve better resonance performance, several indices are often used to determine these parameters, including signal-to-noise, amplification factor, and cross-correlation coefficient. Nevertheless, for a linear frequency modulated (LFM) signal, such indices may no longer work and consequently make SR unable to recover the unknown LFM signal from raw signals. Thus, this limits the application of SR to some extent. To deal with this problem, we define here a new index to characterize the unknown LFM signal with the help of the fractional Fourier transform. Guided by this index, SR is thus able to recover the unknown LFM signal from the raw signal. In addition, a cloud model based genetic algorithm is used to achieve an adaptive SR in order to improve the effectiveness of signal processing.

A Synchronization Approach Based on Bidirectional Correlation Search for Aperiodic Chaotic Direct Sequence Spread Spectrum Signals

The chaotic direct sequence spread spectrum (CD3S) is one of the distinguished techniques providing physical layer secrecy and low probability of intercept (LPI) in wireless communication. Due to the noise-like and aperiodic characteristics of chaotic signals, the synchronization of CD3S signals is a challenging issue. A synchronization approach for aperiodic CD3S signals based on bidirectional correlation search (BDCS) is proposed. Through a joint acquisition of forward frequency domain matched filtering (FDMF) and backward FDMF, the synchronization module aligns received CD3S signals with local chaotic sequences without aid of the pilot signal. The probability distribution of correlator output is derived with additive white Gaussian noise and narrowband jamming. The probability of detection, probability of false alarm, and bit error rate are analyzed mathematically. An approximate solution of the local optimal acquisition threshold coefficient is obtained. These theoretical analyses are verified by numerical simulations, the results of which demonstrate that the proposed synchronization approach enables the CD3S system to resist interception and adapt to the environment with low signal-to-noise and signal-to-jammer ratios.

Extended Target Echo Detection Based on KLD and Wigner Matrices.

With the development of airborne radar radio frequency stealth (RFS) technology, the method of improving the RFS performance of airborne radar by optimizing target detection performance has been extensively studied. However, for wideband radar signals, the traditional point target model appears as an extended target model in the range-dimension, which is unfavorable to the detection of target echoes. To overcome the existing drawbacks, this paper devises an efficient echo detection algorithm from the perspective of information theory and random matrix. Firstly, aperiodic agile wideband radar signals are utilized to observe targets. Then, one frame of echo signals in the same range gate is reconstructed into a data form conforming to the Wigner matrix spectral decomposition. Finally, according to the signal detection theory, Kullback-Leibler Divergence (KLD) is used as the test statistic to complete the echo detection of the stealthy extended targets. By statistical analysis and comparison with other established echo detection algorithms, simulation results manifest that the proposed algorithm has superior detection performance and strong robustness, which not only makes up for the deficiency of traditional narrowband radar detection algorithms, but also increases the detection probability of radar system when it is faced with stealthy extended targets.

Observer‐based modified repetitive control for fractional‐order non‐linear systems with unknown disturbances

This study investigates the problem of observer-based modified repetitive control for a class of fractional-order non-linear systems in the presence of unknown external disturbances. An equivalent-input-disturbance estimator is incorporated into the controller block to compensate the unknown external disturbances. The main objective of this study is to design a modified repetitive controller for the addressed system such that the system output can exactly trace the given periodic reference signal by attenuating both periodic and aperiodic disturbances. To be precise, by employing the Lyapunov stability theory together with the linear matrix inequality approach, sufficient conditions that ensure the existence of such a controller are obtained. It is to be noted that the advantage of using equivalent-input-disturbance estimator in the controller design is that it can reject both periodic and aperiodic disturbance signals effectively without requiring any prior knowledge of them. Finally, two numerical simulation examples are provided to illustrate the effectiveness and applicability of the proposed control technique.

Detection and Prevention of Aperiodic Small Signal Angle Instability at an Early Stage

This paper explores the method of early detection and prevention of aperiodic small signal rotor angle (ASD) instability. A criterion for ASD stability detection is tested on a synthetic system. Sensitivity analysis is utilized to seek the node that would have the most influence on the generator undergoing said instability. The assessment of a suggested countermeasure is carried out to determine whether the system will sustain the stable state. Three case studies on the synthetic system, in the form of generator fault, three phase symmetrical fault and double line to ground fault, are also performed to test the method of early detection.

Aperiodic Stochastic Resonance in the Fractional-Order Bistable System

The aperiodic stochastic resonance (ASR) in the bistable fractional-order system is further studied when the fractional-order lies in the interval (0, 2). In previous works, the ASR can only process aperiodic binary signal with large pulse width. However, for the signal with small pulse width, the method cannot work. Actually, the signals with small pulse width are also common in the information transmission field. It greatly limits the application of the fractional stochastic resonance. Hence, we mainly focus on the enhancement of aperiodic binary signal with small pulse width. To solve the aforementioned technical problem, the general scale transformation is introduced, which allows us to achieve the ASR successfully. By this method, the equivalent system with large system parameters is able to match the input character signal with arbitrary small pulse width well, where the scale parameter is a key to achieve resonance. During the process, the fractional-order system presents rich dynamical behaviors in processing the aperiodic binary signals. Especially, as the order increases, the output signal at optimal noise intensity might be better and be more similar to the input one. This indicates the fractional order can optimize the stochastic resonance. The results might provide some reference to the engineering field, such as digital transmission and image processing field.

Weak Transient Electromagnetic Radiation Signal Detection Method Considering the New Watershed Image Segmentation Algorithm

In order to study the detection methods of weak transient electromagnetic radiation signals, a detection algorithm integrating generalized cross-correlation and chaotic sequence prediction is proposed in this paper. Based on the dual-antenna test and cross-correlation information estimation method, the detection of aperiodic weak discharge signals under low signal-to-noise ratio is transformed into the estimation of periodic delay parameters, and the noise is reduced at the same time. The feasibility of this method is verified by simulation and experimental analysis. The results show that under the condition of low signal-to-noise ratio, the integrated method can effectively suppress the influence of 10 noise disturbances. It has a high detection probability for weak transient electromagnetic radiation signals, and needs fewer pulse accumulation times, which improves the detection efficiency and is more suitable for long-distance detection of weak electromagnetic radiation sources.

Multiple mechanisms link prestimulus neural oscillations to sensory responses.

Spontaneous fluctuations of neural activity may explain why sensory responses vary across repeated presentations of the same physical stimulus. To test this hypothesis, we recorded electroencephalography in humans during stimulation with identical visual stimuli and analyzed how prestimulus neural oscillations modulate different stages of sensory processing reflected by distinct components of the event-related potential (ERP). We found that strong prestimulus alpha- and beta-band power resulted in a suppression of early ERP components (C1 and N150) and in an amplification of late components (after 0.4 s), even after controlling for fluctuations in 1/f aperiodic signal and sleepiness. Whereas functional inhibition of sensory processing underlies the reduction of early ERP responses, we found that the modulation of non-zero-mean oscillations (baseline shift) accounted for the amplification of late responses. Distinguishing between these two mechanisms is crucial for understanding how internal brain states modulate the processing of incoming sensory information.

Spatiotemporal data fusion and manifold reconstruction in Hall thrusters**Distribution Statement A: Approved for Public Release. Distribution is Unlimited. PA# 18635.

A critical breakthrough in the understanding of Hall effect thrusters (HETs) has been the emergence of mapping techniques to fuse multiple time-varying plasma measurements from spatially distributed probes into a unified reconstruction describing the full spatiotemporal dynamics of the HET plasma. The most basic requirement for generating such a spatiotemporal reconstruction is a robust and accurate method to build a map between a single input and a single output signal. This work describes a new nonlinear phase space based mapping technique, the shadow manifold interpolation (SMI) technique, and assesses its performance versus traditional linear FFT-based mapping. Results demonstrate the superiority of the SMI reconstruction for short, noisy and aperiodic signals. Analysis in conjunction with the convergent cross mapping methodology (Sugihara et al 2012 Science 338 496–500) provides theoretical justification for the physical relevance of SMI application to a given signal reconstruction.

Vibrational resonance without tuning in a neuronal parallel array

This paper investigates the propagation of the weak aperiodic signal in a parallel array of FitzHugh–Nagumo (FHN) neurons with heterogenous aperiodic high-frequency (HAHF) disturbances. Different from the traditional vibrational resonance, where the optimal amplitudes of the HF driving signal should be tuned for individual elements, the ability of the proposed averaging parallel array network for weak signal detection can be optimized at a fixed amplitude of the HAHF disturbance, regardless of the nature of the input signal. Local connections in the parallel array network are found to be important for the propagation of weak signal in parallel array. Besides, the characteristics of high-frequency signal such as heterogeneity and frequency, can also modulate the propagation of aperiodic signal in parallel array.

Detection and parameter estimation of weak pulse signal based on strongly coupled Duffing oscillators

Pulse signal detection is widely used in nuclear explosion electromagnetic pulse detection, lightning signal detection, power system partial discharge detection, electrostatic discharge detection, and other fields. The signal strength becomes weak with the increase of the detection distance and may be submerged in strong Gaussian noise for remote detection. Therefore, the detection and recovery of the weak signals, especially the weak pulse signals, have important applications in signal processing area. Some methods have been reported to detect and estimate weak pulse signals in strong background noise. Coupled Duffing oscillators are usually used in processing periodic signals, though it is still in an exploration stage for aperiodic transient signals. There remain some problems to be solved, for example, the system performance depends on some initial values, results are valid only for the period-doubling bifurcation state, the waveform time domain information cannot be accurately estimated, etc. In this paper, we explain the reasons why there exist these inherent defects in the current weakly coupled Duffing oscillators. In order to solve the above-mentioned problems, a new signal detection and recovery model is constructed, which is characterized by coupling the restoring force and damping force of the two oscillators simultaneously. A large coupling coefficient is applied to the two Duffing oscillators, and a generalized " in-well out-of-synchronization”phenomenon arises between the oscillators which conduces to detecting and recovering the weak pulse signals, and also overcoming the defects mentioned above. Using the metrics of signal-to-noise ratio improvement (SNRI) and waveform similarity, the effects of amplitude and period of periodic driving force, coupling coefficient, step size and damping coefficient on signal detection and waveform recovery are studied. Finally, experiments are performed to detect and recover the following three kinds of pulses: square wave pulses, double exponential pulses, and Gaussian derivative pulses. The input SNR thresholds of these three waveforms are –15, –12, and –16 dB, respectively, under the detection probabilities and waveform similarity all being greater than 0.9 simultaneously. The maximum error of the pulse amplitude and pulse width are both less than 5% of their corresponding true values. In summary, the strongly coupled Duffing system has advantages of being able to operate in any phase-space state and being no longer limited by the initial values. Especially, the time domain waveform of weak pulse signals can be well recovered in the low SNR case, and the error and the minimum mean square error are both very low.

Improving amplitude-modulated signals by re-scaled and twice sampling vibrational resonance methods

We present the re-scaled vibrational resonance (VR) method and the twice sampling VR method to improve the amplitude-modulated signal. Two different kinds of signals are considered. One is the amplitude-modulated harmonic signal. The other is the amplitude-modulated aperiodic binary signal. Both the VR methods have an excellent effect on the signal improvement. For the re-scaled VR method, the scale parameter is the key factor to determine the resonance output. For the twice sampling VR method, the frequency reduced ratio or the minimal random pulse width stretched ratio is the crucial factor. By choosing appropriate key factors, the output can achieve the strongest resonance and lead to the optimal signal improvement.