Weak Periodic Signal Detection Research Articles

Weak signal detection technique based on Durbin-Watson test and one-bit sampling.

Correlation-based detection techniques are widely used in the weak periodic signal detection field. Traditionally, they are based on extracting the correlation of a weak signal from noise. Considering the impact of a weak signal on the randomness of background noise, this article takes the opposite approach and proposes a weak signal detection technique based on the Durbin-Watson (DW) test and one-bit sampling, detecting the weak signal due to the extent to which the randomness of noise is affected. The randomness of noise is analyzed through the DW test, which is a method for detecting the randomness of data sequences through first-order autocorrelation. One-bit sampling is adopted to reduce the complexity of the sampling circuit and data processing algorithm. The effectiveness of the DW test in the situation of one-bit sampling is demonstrated through simulation and analysis. Simulation results show that the proposed technique is capable of detecting weak sinusoidal and square-wave signals with a signal-to-noise ratio (SNR) above -30 dB, and the frequency or SNR of a weak signal can be further estimated based on mutual constraints. The measured results confirm the capability. In addition, the factors of coherent sampling, noise bandwidth, and comparator threshold that influence the performance of the proposed technique are simulated and discussed in detail.

Parameter-tuning stochastic resonance as a tool to enhance wavelength modulation spectroscopy using a dense overlapped spot pattern multi-pass cell.

The parameter-tuning stochastic resonance (SR) method can convert part of the noise energy into the signal energy to suppress the noise and amplify the signal, comparing with traditional weak periodic signal detection methods (e.g., time average method, filtering method, and correlation analysis method). In this work, the numerical calculation is conducted to find the optimal resonance parameters for applying the SR method to the wavelength modulation spectroscopy (WMS). Under the stochastic resonance state, the peak value of 2f signal (a constant concentration of CH4∼20 ppm) is effectively amplified to ∼0.0863 V, which is 3.8 times as much as the peak value of 4000-time average signal (∼0.0231 V). Although the standard deviation also increases from ∼0.0015 V(1σ) to ∼0.003 V(1σ), the SNR can be improved by 1.83 times (from ∼25.9 to ∼15.8) correspondingly. A linear spectral response of SR 2f signal peak value to raw 2f signal peak value is obtained. It suggests that the SR method is effective for enhancing photoelectric signal under strong noise background.

A field programmable gate array based high speed real-time weak periodic signal detection technique

The detection of a high repetition rate weak signal is studied in this paper. Owing to the characteristics of the signal of interest, both high speed analog-to-digital converter (ADC) and low computational complexity data processing techniques are required for high speed real-time weak signal detection. In this paper, a novel field programmable gate array (FPGA) based high speed real-time periodic weak signal detection technique is presented. Cascaded comparators outside the FPGA and cascaded flip flops in the FPGA are used to implement a one-bit ADC, which performs quantization first followed by sampling. Based on this novel design, a time-interleaved structure with several sub-channels is further proposed to significantly improve the sampling rate of the one-bit ADC, which does not require calibration for offset, gain, and sample-time mismatches between sub-channels. Each sub-channel has a long-time coherent integration structure to coherently integrate the sampled one-bit data. A full layer clearance mechanism that only operates on specific bits of the integrated sums is proposed to overcome the influence of a noise baseline drift on the weak signal detection. Compared with the traditional adaptive threshold, this mechanism has a significantly lower computational complexity. A prototype with three sub-channels performing 1.5 Gs/s sampling is implemented to verify the proposed technique. The results obtained confirm its high sampling rate and noise baseline drift tolerance in weak signal detection.

Automated system for weak periodic signal detection based on Duffing oscillator

The periodic signals that have predictable and deterministic characteristics are used in the analysis and modelling of dynamical systems in diverse fields. These signals can be detected as the weak signals within the time series obtained from the measurable processes of dynamical systems. The Duffing oscillator is effective in detecting weak periodic signals with a very low signal-to-noise ratio. In this study, the authors present a method to automate the weak periodic signal detection of the Duffing oscillator using a quantitative index for the classification of the periodic and non-periodic signals. In this method, the authors use the wavelet scale index as the quantitative index in the classification of signals. Thus, they are able to plot the wavelet scale index spectrum of the Duffing oscillator where the frequency values of the weak periodic signals correspond to near-zero wavelet scale index parameters. First, the authors perform simulations using the method and detect weak periodic signals embedded in noise. Then, they employ two electroencephalogram signals to demonstrate the feasibility of the proposed method in the empirical data. Lastly, they compare the method to the periodogram power spectral density estimate based on fast Fourier transform.

Method of Rolling Bearing Fault Detection Based on Two-Dimensional Tri-Stable Stochastic Resonance System

To solve the problem that it is difficult to detect the weak bearing fault signal from high-intensity noise, a method of bearing fault detection based on the two-dimensional tri-stable system (TDTS) is proposed. The analytical expression for the spectral power amplification (SPA) of the TDTS is derived using the probabilistic flow method. The stochastic resonance (SR) mechanism of the TDTS is studied with the SPA as a measure index. The fourth-order Runge–Kutta method and the genetic algorithm are utilized to carry out the numerical simulation. Apply the TDTS to the weak periodic signal detection and the bearing fault detection. In this work, the potential field structure of the TDTS is discussed. The SPA of the TDTS to the periodic driving force is derived. The influence of the coupling coefficient, the driving frequency, and the driving force amplitude on the SPA is analyzed. The performance of the TDTS and the ODATS to detect weak signals from intense noise are compared. The theoretical analysis shows that SR phenomena occur in the TDTS. As the noise intensity increases, the SPA presents a unimodal trend, that is, the noise of a specific intensity can enhance the response of the TDTS to the weak external driving force. Moreover, the enhancement effect is proportional to the amplitude of the driving force and the coupling coefficient, and inversely proportional to the driving frequency. The experimental results indicate that the TDTS can effectively detect the weak periodic signal and detect the inner and outer ring faults of the bearings. The detection effects are preferable to that of the one-dimensional asymmetric tri-stable system (ODATS). The effectiveness and advancement of the proposed method are proved.

The Analysis of Periodic Signal Detection Method Based on Duffing System Chaotic Dynamics

This article presents the analysis of periodic signal detection method based on Duffing system sensitivity to weak influences. The described signal detection method is developed with using of Duffing system that oscillates in chaotic state, without transitions to periodic state. The main advantage of such method is the absence of periodic oscillation modes with low sensitivity. The divergence of Duffing system phase trajectories is investigated with influences of different periodic signals under low signal-to-noise ratio values. The estimation of phase trajectories divergence is performed with using of numeric integration. The signal detection method is analyzed with different forms of input signal: sinusoidal, square, triangle. The analysis shows that a reliable detection of periodic signal can be performed for any of the three presented forms of signal with repeating frequency near the frequency of the driving signal. The obtained results show wide capabilities of Duffing system applications for detection of weak periodic signals.

Weak periodic signal detection by sine-Wiener-noise-induced resonance in the FitzHugh-Nagumo neuron.

Based on the FitzHugh-Nagumo (FHN) neuron model subjected to sine-Wiener (SW) noise, impacts of SW noise on weak periodic signal detection are investigated by calculating response measure Q for characterizing synchronization between the input signal and the output temporal activities of the neuron. It is numerically demonstrated that the response measure Q can achieve the optimal value under appropriate and moderate intensity or correlation time of SW noise, suggesting the occurrence of SW-noise-induced stochastic resonance. Furthermore, the optimal value of Q is sensitive to correlation time. Consequently, the correlation time of SW noise has a great influence on the performance of signal detection in the FHN neuron.

Detecting weak periodic signals in EEG time series

Recently many attempts had been devoted to the detection of weak periodic signals embedded in noisy chaotic signals using simulation methods and Duffing Oscillator System. In this paper, weak periodic signals in electroencephalogram (EEG) time series are investigated using a Duffing Equation based method. The EEG signals are collected from FR1-F3 and FR2-F4 channels in the scalp of an epileptic patient. In order to excite the Duffing equation by outer signals, the data is scaled down to a compatible range with the equation by multiplying it with a constant. After running the data with the Duffing Equation, weak periodic signals are obtained. As a result, the presence of weak periodic signals is observed in EEG time series. The amplitude and frequency values of the found weak periodic signals are calculated. Presence of weak periodic signals within the EEG signals can give us insight about the dynamic structure of the brain and functional brain activity.

Delayed feedback and detection of weak periodic signals in a stochastic Hodgkin–Huxley neuron

We study the effect of the delayed feedback loop on the weak periodic signal detection performance of a stochastic Hodgkin–Huxley neuron. We consider an electrical autapse characterized by its coupling strength and delay time. The stochastic Hodgkin–Huxley neuron exhibits subthreshold oscillations, and thus has an intrinsic time scale with the subthreshold oscillations. Therefore, we investigate the interplay of the subthreshold oscillations, coupling strength and delay time on the weak periodic signal detection. Results indicate that the delayed feedback either enhances or suppresses the weak signal detection depending on its parameters, when compared to that without the feedback. The delayed feedback augments the weak periodic signal detection for the optimal values of the intrinsic noise and the coupling strength when the delay time is close to the integer multiples of the period of the intrinsic oscillations, due to the multiple resonance among the weak signal, the intrinsic oscillations, and the delayed feedback.We analyze the interspike interval histograms and show that the delayed feedback enhances or suppresses the weak periodic signal detection by increasing or decreasing the phase locking (synchronization) between the spiking and the weak periodic signal. We also show that an optimal phase locking is obtained when the delay time is close to the period of the intrinsic oscillations, leading a single dominant time scale in the spike trains.

Dynamic analysis and numerical simulation of a discrete model of a bistable system

Numerical simulation is the generally used method for studying stochastic resonance (SR), which is a kind of non-linear phenomenon that usually occurs in non-linear bistable systems. It has been found that the input signal needs to be over-sampled during the numerical simulation of SR. In this paper we provide an explanation of this phenomenon based on a stability analysis of the bistable system. We begin by studying the stability of a discrete model of a bistable system in numerical simulations. We then give a theoretical derivation of the stability conditions for the simulation model with different parameters, and carry out numerical experiments to show that the results coincide with the predictions of the theory. We explain why the input signal needs to be over-sampled in the simulation and provides guidelines for the choice of system parameters for the bistable system and the sampling time step in the numerical simulation of SR. Finally, we present the results of simulations showing an example of SR occurring in a bistable system and an example of weak periodic signal detection when it is processed by a bistable system.

Effects of time-periodic modulation of cross-correlation intensity between noises on stochastic resonance of over-damped linear system

For an over-damped linear system subjected to correlated additive and multiplicative noise and a periodic signal, when the cross-correlation intensity between noises is a time-periodic function, the analytical expression of the output signal-to-noise ratio (SNR) is derived by means of the stochastic averaging method. It is found that this system has richer dynamic behaviors than the linear systems in which cross-correlation intensity between noises is constant, that the evolution of the output SNR with the cross-correlation modulation frequency presents periodic oscillation, and that the parameters of cross-correlation intensity between noises diversify the stochastic resonance phenomena.The time-periodic modulation of cross-correlation intensity between noises is conductive to enhancing the sensitivity to weak periodic signal detection and implementing the frequency estimation of weak periodic signal.

Study on weak signal detection method with Duffing oscillators

By numerical simulations we find that the Duffing state transition from big-cycle motion to chaotic motion is more suited to weak signal detection. Based on this, in this paper, we propose a new weak periodic signal detection method from the angle of theoretical analysis. The principle of the proposed method is introduced and its feasibility is analyzed. Then, the proposed method and the traditional method are compared and analyzed both in transition zone effect and detection probability, and then a contrast simulation is carried out. The analysis and simulation results both indicate, the Duffing oscillator state transition from big-cycle motion to chaotic motion is affected less by transition zone under the same condition, based on which the proposed detection method possesses better detection capability. The simulation data also show that weak signal detection with Duffing oscillator must be based on unilateral state transition. The frequency difference detection based on intermittent chaos is suited only for the case where the signal-to-noise ratio of the detected signal is relatively high.

Detection of Weak Signal in Strong Noise Based on NBS Chaos System

Based on the principle of chaos suppression with the piecewise periodic perturbation, detection of weak periodic signals in strong noise is realized with controlled NBS (Novel butterfly-shaped) model. First, according to the parametric equivalent relationship obtained using segment control mechanism, the parameter range is determined in different periodic states of the chaotic system. Second, combined with Lyapunov exponent criterion, the critical values of detection parameters are determined, which lead to a sudden change of the system dynamical behavior from chaotic state to periodic 3. Finally, the numerical simulation and the measured signals experiment are performed. The results show that the method reacts sensitively for weak signals, possesses the better inhibitory action on the noise, and can effectively improve the signal-to-noise ratio.

Abrupt change of synchronization of ring coupled Duffing oscillator

The ring coupled Duffing oscillator was investigated, a phenomenon was observed when analyzing the synchronization evolution between coupled oscillators, which shows that if all oscillators are driven by the same periodic driving force,the motion trajectory between weakly coupled oscillators will generate two abrupt changes from synchronization to non-synchronization and then to synchronization in the phase transition of period-doubling bifurcation, chaotic state and large-scale periodic state. Any synchronous abrupt change can be used to rapidly identify system phase transition, and thus a weak periodic signal detection method was proposed based on the phase transition of period-doubling bifurcation and chaotic state.

Weak Signal Detection Principle Based on Chaotic Duffing Oscillator and its Simulation Method

Based on Matlab as the software platform, chaos detection principle and methods used for weak signals detection are studied. The model used for simulation is established, then the simulation results of weak periodic signal detection in strong noise atmosphere are given and the steps for detecting weak signals with chaos method are listed. Furthermore, the influence of sampling period on system’s performance is studied. Simulation results show that the chao detection approach proposed in this paper can detect the signal even if it is small to 10-10v, and even when it is in the environment with strong noise, small signal with magnitude of only 5×10-9 v can be found. Chaos method has strong capability for weak signal detection which lay important foundation for exploiting virtual instrument.

Evidence of stochastic resonance in an auditory discrimination task may reflect response bias

Stochastic resonance is a mechanism that improves the detection of weak periodic signals when an optimal level of background noise is present. This counterintuitive concept is thought to involve a cooperative effect that arises out of a physical coupling between deterministic and random dynamics in nonlinear systems. We report the results of three psychophysical experiments designed to probe the auditory system for evidence of stochastic resonance. In all three experiments, participants judged which of two 1000-Hz tones was greater in intensity, with one of the tones embedded in a background of Gaussian noise. Experiment 1 used a two-alternative forced choice task and provided evidence of enhanced discriminability at an optimal level of noise. The aim of Experiment 2 was to determine whether the apparent enhancement observed in Experiment 1 was due to sensory processes or to a response bias. Receiver operating characteristic analysis supported an explanation based on decision processes, rather than a genuine sensory enhancement. An additional experiment (Experiment 3) was used to discount experimental artifacts.

Frequency sensitivity in Hodgkin-Huxley systems.

The frequency sensitivity of weak periodic signal detection has been studied via numerical simulations for both a single neuron and a neuronal network. The dependence of the critical amplitude of the signal upon its frequency and a resonance between the intrinsic oscillations of a neuron and the signal could account for the frequency sensitivity. In the presence of both a subthreshold periodic signal and noise, the signal-to-noise ratio (SNR) of the output of either a single neuron or a neuronal network present the typical characteristics of stochastic resonance. In particular, there exists a frequency-sensitive range of 30-100 Hz, and for signals with frequencies within this range the SNRs have large values. This implies that the system under consideration (a single neuron or a neuronal network) is more sensitive to the detection of periodic signals, and the frequency sensitivity may be of a functional significance to signal processing.

Detection of Weak Periodic Signals from Irregularly Spaced Observations

AbstractWe perform time series analysis on irregularly spaced data with large gaps. Our algorithm is based on multidimensional nonlinear optimisation. Particular emphasis is given to the selection and deletion of frequencies. The final result is checked by various statistical tests.

Noise enhancement of information transfer in crayfish mechanoreceptors by stochastic resonance.

In linear information theory, electrical engineering and neurobiology, random noise has traditionally been viewed as a detriment to information transmission. Stochastic resonance (SR) is a nonlinear, statistical dynamics whereby information flow in a multi-state system is enhanced by the presence of optimized, random noise. A major consequence of SR for signal reception is that it makes possible substantial improvements in the detection of weak periodic signals. Although SR has recently been demonstrated in several artificial physical systems, it may also occur naturally, and an intriguing possibility is that biological systems have evolved the capability to exploit SR by optimizing endogenous sources of noise. Sensory systems are an obvious place to look for SR, as they excel at detecting weak signals in a noisy environment. Here we demonstrate SR using external noise applied to crayfish mechanoreceptor cells. Our results show that individual neurons can provide a physiological substrate for SR in sensory systems.

Probability of alarm detection in a search and rescue system

Diagnostic systems are often based on the detection of weak periodic signals buried in noise. As an illustrative example, a maritime search and rescue system is described. Here, alarms consist of frequency-modulated signals where the carrier frequency may vary in a certain range due to Doppler shifts. The signals are strongly corrupted by additive noise and by fading. For a given averaging time, the probability of missed alarms is computed and minimised, comparing different receiver structures and detection schemes. The theoretical investigations were verified in practical tests with striking accuracy.