Band-limited Gaussian White Noise Research Articles

Stimulator compensation and generation of Gaussian noise stimuli with defined amplitude spectra for studying input-output relations of sensory systems.

Gaussian noise is an important stimulus for the study of biological systems, especially sensory and neural systems. Since these systems are inherently nonlinear, the properties of the noise strongly influence the outcome of the analysis. Therefore, it is crucial to use a well-defined and controlled noise stimulus. In this paper, we first use the example of an insect filiform sensillum, a simple mechanoreceptor with a single sensory cell, to show that changes in the amplitude and spectral properties of the noise stimulus indeed affect the linear transfer function of the sensillum. We then explain step-by-step how to use the inverse fast Fourier transform to generate a Gaussian noise that has an arbitrary user-defined amplitude spectrum, including a band-limited white noise with a perfectly sharp cutoff edge. Finally, we demonstrate how such a perfect band-limited Gaussian white noise stimulus can also be generated with a non-perfect stimulator using a simple procedure that compensates for the filtering properties of the stimulator. With this approach, one can generate well-defined Gaussian noise stimuli that can be adapted to any application. For example, one can generate visual, sound, or vibrational stimuli for experimental research in visual physiology, auditory physiology, and biotremology, as well as inputs for testing various models in theoretical research.

Residual Strength Analysis of C/SiC Ceramic Matrix Composite Panels Subjected to Combined Thermal-Acoustic Loadings

A study was undertaken to develop a methodology for assessing the residual strength of C/SiC ceramic matrix composite panels subjected to combined thermal-acoustic loadings. A 2D plain-woven C/SiC ceramic matrix composite panel subjected to spatially uniform thermal loading and band-limited Gaussian white noise is chosen as the computational test article, with its geometric nonlinear response determined via numerical simulation. As the input, the material properties (static strength, residual strength, and fatigue life) of this material are fully characterized under tensile and compression loads, for fiber direction at elevated temperature in static and fatigue loading conditions. Based on the methodology, a computer code is developed that simulates the cycle-by-cycle behavior of composite panels under fatigue loadings. The methodology is validated with the residual strength test of 2D plain-woven C/SiC composite panel subjected to combined thermal-acoustic loadings. It has been shown that the results of residual strength predicted by the methodology are well correlated with the experimental results.

The benefits of a magnetically coupled asymmetric monostable dual-cantilever energy harvester under random excitation

Piezoelectric vibration energy harvesting is a promising technique to power wireless sensor networks. This article originally presents a magnetically coupled asymmetric monostable dual-cantilever piezoelectric energy harvester consisting of a generating piezoelectric cantilever beam and an auxiliary cantilever beam. Theoretical and experimental results both verify that the asymmetric harvester has the superior performance compared with the conventional magnetically coupled symmetric bistable dual-cantilever piezoelectric energy harvester, yielding higher voltage output under different magnetic coupling intensities and different power densities of the band-limited Gaussian white noise random excitation. More importantly, the mechanical strain of the asymmetric harvester is much smaller than that of the symmetric harvester, being lower than half of the latter one under strong magnetic coupling. Therefore, due to its higher energy conversion efficiency and better durability, the proposed asymmetric harvester is beneficial for practical environment vibration energy harvesting.

Implementation of Dryden Continuous Turbulence Model into Simulink for LSA-02 Flight Test Simulation

Turbulence is a movement of air on small scale in the atmosphere that caused by instabilities of pressure and temperature distribution. Turbulence model is integrated into flight mechanical model as an atmospheric disturbance. Common turbulence model used in flight mechanical model are Dryden and Von Karman model. In this minor research, only Dryden continuous turbulence model were made.Dryden continuous turbulence model has been implemented, it refers to the military specification MIL-HDBK-1797. The model was implemented into Matlab Simulink. The model will be integrated with flight mechanical model to observe response of the aircraft when it is flight through turbulence field. The turbulence model is characterized by multiplying the filter which are generated from power spectral density with band-limited Gaussian white noise input.In order to ensure that the model provide a good result, model verification has been done by comparing the implemented model with the similar model that is provided in aerospace blockset. The result shows that there are some difference for 2 linear velocities (vg and wg), and 3 angular rate (pg, qg and rg). The difference is instantly caused by different determination of turbulence scale length which is used in aerospace blockset. With the adjustment of turbulence length in the implemented model, both model result the similar output.

Nonlinear Response and Fatigue Life of Thin Plates Subjected to Non-Uniform Temperature Distributions and Acoustic Excitations

A finite element formulation is presented for the prediction of nonlinear response of thin plates under a steady-state non-uniform temperature change over the thin plate and band limited Gaussian white noise. Thermal buckling temperatures and thermal deflections are obtained to explain the stability of panels, and modal frequencies of thermally buckled plate are obtained to explain the stiffness characteristics of panels. The stress responses of panels under thermo-acoustic loadings exhibit complex nonlinear characteristics. Miner linear accumulation damage theory and improved Rainflow counting cycle method are used for estimation of fatigue life of panels under combined thermo-acoustic loadings. Results show that the fatigue life decreases till the end of snap-through and then gives a rise trend. Afterward, the fatigue life reaches a steady state at low peak temperature area. As the peak temperature goes up sequentially, the fatigue life rises suddenly, and then reaches a steady state at high peak temperature area.

GPS Output Signal Processing considering both Correlated/White Measurement Noise for Optimal Navigation Filtering

In this paper, a dynamic modeling for the velocity and position information of a single frequency stand-alone GPS(Global Positioning System) receiver is described. In static condition, the position error dynamic model is identified as a first/second order transfer function, and the velocity error model is identified as a band-limited Gaussian white noise via non-parametric method of a PSD(Power Spectrum Density) estimation in continuous time domain. A Kalman filter is proposed considering both correlated/white measurements noise based on identified GPS error model. The performance of the proposed Kalman filtering method is verified via numerical simulation.

Limitations of Equivalent Circuit Models in Data-Driven Simulation of the Neuron-Electrode Interface

Noninvasive neuroelectronic interfacing has important applications in the fields of neural prosthetics, biological computation and biosensors. Traditionally, neuron-electrode interfaces have been modeled as linear point or area contact equivalent circuits but such models have not been able to explain the shapes and magnitudes of the experimentally recorded extracellular signals. Also, previous work with Volterra-Wiener characterization of the planar neuron-microelectrode junction using bandlimited Gaussian white noise had shown that the mechanism of signal transduction across the nanoscale neuron-microelectrode cleft region might be nonlinear. In this optimization based study we compared and contrasted experimental and simulation data for point contact models of the extracellular ‘on-cell’ neuron-patch electrode and the planar neuron-microelectrode interface. The nonlinear contributions of the neurons to the dynamics of the equivalent circuit representation of the interfacial medium were systematically isolated by an independent estimation of the ion-channel parameters through a fitting of the simulated intracellular signals to the experimentally recorded voltage and current clamp signals. These ion-channel parameters were then employed in the optimization of the cell-electrode interface parameters based on extracellular recordings obtained from a neuron simultaneously interfaced to the ‘on-cell’ patch-electrode and the planar microelectrode using sub- and supra-threshold stimuli. An examination of the optimized model parameters for the experimental extracellular recordings from sub- and supra-threshold stimulations of the neuron-electrode junctions allowed us to draw important distinctions between the ‘on-cell’ neuron-patch electrode and neuron-microelectrode interfaces that could be attributed to the presence of electric double layer (EDL) and ionic electrodiffusion effects. Based on these results, we then discuss and point out the limitations of the equivalent circuit models in their failure to take account of the nonlinear EDL and ionic electrodiffusion effects occurring during the process of signal transduction at the neuron-electrode interface.

A White Noise Approach To System Analysis In Demembranated Muscle Mechanics

Measuring the force response to sinusoidal length perturbations in muscle enables calculating the viscoelastic properties of the tissue over a wide range of frequencies. Coupling these empirical results with complementary mathematical and computational models describes the kinetics of force-generating actomyosin cross-bridges. This sinusoidal analysis requires system linearity, a constraint confining length stimuli to very small amplitudes in demembranated (skinned) muscle preparations because larger length perturbations produce a non-linear force response. Therefore, it becomes difficult to examine cross-bridge cycling kinetics during length transients that are comparable with sarcomeric strains experienced during contraction in living muscles. Here we introduce a white noise method of system analysis that facilitates extracting the linear and non-linear components of the system response. Building upon Wiener theory, this method estimates the system response to a band-limited Gaussian white noise length stimulus through cross-correlation techniques (Lee-Schetzen approach). To examine and develop this approach, we computer simulated the response of a pre-defined system consisting of both linear and non-linear components and were able to estimate the expected linear response of the system. These simulations demonstrate the powerful utility of this technique to separate the linear and non-linear system responses in both the time or frequency domains. We also examined the experimental applicability of these methods using small strips of skinned muscle tissue, from which we estimated the linear and non-linear components of the system response in calcium-activated muscle. This linear component is consistent with the linear system response calculated from comparable measurements using sinusoidal length perturbation analysis. These computational and experimental methods provide a platform for characterizing cross-bridge cycling behavior, and permits distinguishing between linear and non-linear components of the complicated force responses following length transients associated with normal muscle contraction.

On Characterization of Continuous Mixing of Particulate Materials

The concept of heterogeneity in relation to axial mixing in continuous mixers is investigated. The state of the mixture along the axial direction can be described by an axial heterogeneity function. It is shown that this function can be decomposed into two independent components. The first component describes the fluctuations caused by the feeding system. The second component is the fluctuations due to the particulate nature of the material. In addition, the second component, or the random component, can be modeled as a band-limited Gaussian white noise. Moreover, the variogram function is shown to be a useful tool in determining the variance of the random component. A linear time-invariant (LTI) model is proposed for continuous mixers. This model also implies that the Danckwerts-Weinekötter formula is applicable for the variance reduction ratio (VRR). However, it is shown that the Danckwerts formula for VRR is more appropriate for determination of mixer efficiency.

OPTIMAL DAMPING OF STAYS IN CABLE-STAYED BRIDGES FOR IN-PLANE VIBRATIONS

Significant vibrations have been reported in stays of recently constructed cable stayed bridges. The vibrations appear as in-plane vibrations that may be caused by rain–wind- induced aeroelastic interaction or by resonance excitation of the cables from the motion of the pylons. The stays of modern cable-stayed bridges are often designed as twin cables with a spacing of, say 1m. In such cases, it is suggested in the paper to suppress the mentioned in-plane types of vibrations by means of a tuned mass–damper (TMD) placed between the twin cables at their midpoints. The TMD divides the stay into four half-cables, and resonance may occur in each of the half-cables as well as in the entire stay. The optimal tuning of the TMD is investigated based on a mathematical model, where the motion of the support points on the pylons is considered to be the main cause of excitation. The indicated motion is modelled as a band-limited Gaussian white noise process. Three load scenarios are considered: narrow-banded excitations, with the central frequency of the autospectrum close to the lowest eigenfrequency of each of the two cables constituting the stay, and a broadbanded excitation which encompasses both of the mentioned frequencies. The spring and the damper constants of the TMD are optimized so that the variances of the displacement of the adjacent four half-cables, the support point of the TMD and the secondary mass are minimized. At optimal design, it is shown that the variances reduce below 14% of those of the unprotected stay.

A spectral representation based model for Monte Carlo simulation

A new model is proposed for generating samples of real-valued stationary Gaussian processes. The model is based on the spectral representation theorem stating that a weakly stationary process can be viewed as a superposition of harmonics with random properties. The classical use of this theorem for Monte Carlo simulation is based on models consisting of a superposition of harmonics with fixed frequencies but random amplitude and phase. The resulting samples have the same period depending on the discretization of the frequency band. In contrast, the proposed model consists of a superposition of harmonics with random amplitude, phase, and frequency so that different samples have different periods depending on the particular sample values of the harmonic frequencies. A band limited Gaussian white noise process is used to illustrate the proposed Monte Carlo simulation algorithm and demonstrate that the estimates of the covariance function based on the samples of the proposed model are not periodic.

Signal-to-noise ratio gain by stochastic resonance in a bistable system

It was shown recently that the signal-to-noise ratio (SNR) could be improved by stochastic resonance (SR) in certain monostable systems and certain systems with monotonous nonlinearity working in the nonlinear response (NLR) regime. Here we demonstrate that a simple bistable system driven by periodic pulse train and band-limited Gaussian white noise can also provide an SNR gain. We show the reasons why SNR gain had not been found in double well potential systems, despite strong efforts made during the last 15 years.

Categorization of Gerbil auditory fiber responses

This ongoing work is concerned with what the gerbil's ear tells the gerbil's brain. The responses of over 600 auditory nerve fibers to band-limited Gaussian white noise were recorded, and a smoothed, linear estimate of each fiber's impulse response was derived using a reverse correlation procedure and a state space model. In this paper, we investigate the impulse responses’ dependence on animal, stimulus amplitude, and tuning frequency. Despite great fiber response variability, we conclude that their responses tend to be briefer and more asymmetric for moderate to high frequencies.

Dynamic nonlinear vago-sympathetic interaction in regulating heart rate

Although the characteristics of the static interactions between the sympathetic and parasympathetic nervous systems in regulating heart rate have been well established, how the dynamic interaction modulates the heart rate response remains unknown. Thus, we investigated the dynamic interaction by estimating the transfer function from nerve stimulation to heart rate, using band-limited Gaussian white noise, in anesthetized rabbits. Concomitant tonic vagal stimulation at 5 and 10 Hz increased the gain of the transfer function relating dynamic sympathetic stimulation to heart rate by 55.0%+/-40.1% and 80.7%+/-50.5%, respectively (P < 0.05). Concomitant tonic sympathetic stimulation at 5 and 10 Hz increased the gain of the transfer function relating dynamic vagal stimulation to heart rate by 18.2%+/-17.9% and 24.1%+/-18.0%, respectively (P < 0.05). Such bidirectional augmentation was also observed during simultaneous dynamic stimulation of the sympathetic and vagal nerves independent of their stimulation patterns. Because of these characteristics, changes in sympathetic or vagal tone alone can alter the dynamic heart rate response to stimulation of the other nerve. We explained this phenomenon by assuming a sigmoidal static relationship between autonomic nerve activity and heart rate. To confirm this assumption, we identified the static and dynamic characteristics of heart rate regulation by a neural network analysis, using large-amplitude Gaussian white noise input. To examine the mechanism involved in the bidirectional augmentation, we increased cytosolic adenosine 3',5'-cyclic monophosphate (cAMP) at the postjunctional effector site by applying pharmacological interventions. The cAMP accumulation increased the gain of the transfer function relating dynamic vagal stimulation to heart rate. Thus, accumulation of cAMP contributes, at least in part, to the sympathetic augmentation of the dynamic vagal control of heart rate.

A Stochastic Approach in Estimating the Pseudo-Relative Spectral Velocity

In the prediction of ground motion from seismological model by random vibration theory, the basic assumption as that the ground motion process is a bandlimited Gaussian white noise (BGWN). For pseudo-response spectral values, the estimation is based on the response of a single-degree-of-freedom (SDOF) system due to the input of BGWN. The function of an SDOF is a narrowband filter. Therefore, the response of an SDOF is a narrowband process that no longer satisfies the assumption of bandlimited random process. The property of a narrowband process is significantly different from that of a bandlimited process and should be incorporated into the estimation of pseudo-spectral values. A stochastic methodology is proposed to estimate the spectral values on the basis of narrowband Gaussian stationary process. A key feature of the method is the use of envelope crossings in lieu of press crossings of the ground motion amplitude level. This substitution makes the estimation of spectral values more accurate. Comparing our results with those of previous research studies, we will illustrate that our proposed approach is in a good agreement with that of the simulation of time domain.

A stochastic resonator is able to greatly improve signal-to-noise ratio

After a decade of doubts, for the first time in the history of stochastic resonance (SR), we demonstrate that a simple stochastic resonator does greatly improve the signal-to-noise ratio (SNR) of a periodic signal with additive Gaussian noise. The particular stochastic resonator is a level-crossing detector (LCD) driven by the sum of a periodic spike train signal and a band-limited Gaussian white noise. To reach the improvement of the SNR, the stochastic resonator has to work in the strongly nonlinear response limit and the noise has to have a high cut-off frequency compared to the reciprocal duration of the spikes. We demonstrate by analog and computer simulations that the SNR gain goes beyond four orders of magnitude at practical conditions. These findings get a particular importance due the fact that simplest neurone models behave very similarly to our arrangement, so the results might have direct applications in neural systems.

Third-order reverse correlation analysis of muscle spindle primary afferent fiber responses to random muscle stretch.

The response of primary muscle spindle afferent fibers to muscle stretch is nonlinear. Now spindle responses (trains of action potentials) to band-limited Gaussian white noise length perturbations of the gastrocnemius muscles (input signal) are described in cats. The input noise upper cutoff frequency was clearly above the frequency range of physiological length changes in cat hindleg muscles. The input-output relation was analyzed by means of peri-spike averages (PSAs), which could be shown to correspond to the kernels of Wiener's white noise approach to systems identification. The present approach (the reverse correlation analysis) was applied up to the third order. An experiment consisted of two recordings: one (the source recording) to determine PSAs and the other (the test recording) to provide an input signal for predicting responses. The predictions of different orders were compared with the actual neuronal response (the observation) of the test recording. Four different approximation procedures were developed to adapt prediction and observation and to determine weighting factors for the predictions of different orders. The approximations also yielded the value of the power density P of the input noise signal: at a variety of stimulus parameters, P from approximations had the same magnitude as P determined directly from the input signal amplitude spectrum. The prediction of a sequence of action potentials improved the higher the order of components. 37 of 42 action potentials of a test recording (the observation) could be confidently predicted from PSAs or kernels. Compared with the size of the linear first-order prediction curve, the relative sizes of the second and third-order prediction curves were: 1.0:0.47:0.26.

Dynamics of neurons controlling movements of a locust hind leg: Wiener kernel analysis of the responses of proprioceptive afferents

1. The response properties of proprioceptive sensory neurons providing input to the local circuits controlling leg movements of the locust have been analysed by the Wiener kernel method. The proprioceptor, the femoral chordotonal organ, encodes the position and movements of the tibia about the femorotibial joint. 2. Intracellular recordings were made from sensory neurons while the apodeme of the organ was moved with a band-limited Gaussian white noise signal with a cutoff frequency of 27, 58, or 117 Hz. To define the input-output characteristics of the neurons, the first- and second-order Wiener kernels were computed by a cross-correlation between the spike response of the afferents and the white noise stimulus. 3. White noise stimulation elicited sustained spiking in 50 out of 54 afferents throughout the 20 s periods of stimulation and recording. The first-order kernels, the linear response properties, of these afferents were of six basic types that were dependent on the cutoff frequency of the white noise stimulus. These included 1) flexion-sensitive afferents that were primarily position sensitive irrespective of stimulus frequency, 2) flexion-sensitive afferents that were position sensitive at low frequencies but also coded velocity at higher frequencies, 3) flexion-sensitive afferents that coded velocity at all stimulus frequencies, 4) flexion-sensitive afferents that coded velocity at low stimulus frequencies but also acceleration at high frequencies, 5) extension-sensitive afferents that coded velocity at all stimulus frequencies, and 6) extension-sensitive afferents that coded velocity at low stimulus frequencies and acceleration at high frequencies. A seventh type contained the four remaining afferents that adapted rapidly to the stimulus within 3-5 s. These were all extension-acceleration sensitive irrespective of stimulus frequency. 4. The gain curves (produced by Fourier transform of the 1st-order kernels) and the power spectra of the linear models (produced by convolving the 1st-order kernels with the white noise) demonstrated that responses in the position-sensitive afferents are representative of a constant gain low-pass filter with a cutoff frequency of approximately 80 Hz, whereas those in the velocity- and acceleration-sensitive afferents are band passed, having peaks at 80 Hz. 5. The main nonlinearity was a signal compression in which the diagonal peak(s) of the second-order nonlinear kernels offset one or more peaks of the first-order kernels and represents a rectification or directional sensitivity of the afferents.(ABSTRACT TRUNCATED AT 400 WORDS)

Reverse correlation analysis of the stretch response of primary muscle spindle afferent fibers

The nonlinear responses of deefferented primary muscle spindle afferent fibers to muscle stretching consisted of a train of action potentials which was analyzed when random changes in muscle length (band-limited gaussian white noise) were applied in cats. The upper cutoff frequency of the applied noise (the source stimulus) was varied between 1.6 and 570 Hz; the amplitude of the random input was varied between 0.002 and 1.2 mm. In a previous report the reverse correlation of 1st and 2nd order was studied for its ability to analyze data of a continuous input signal and pulsatile events in the output. Computations of the Wiener kernels h1 and h2 or their equivalents, the perispike averages of the 1st and 2nd order, were computed from the random stretch responses of muscle-spindle afferents. Then the 1st- and the 2nd-order predictions and the summation of both to random muscle stretch was estimated. A general finding was that the 1st-order component was approximately 10 times that of the 2nd-order component, when both were combined in approximation procedures to give the closest prediction of observed responses to random test stimuli. The approximation was poor when the source stimulus was less than 0.03 mm and improved when it was greater. With the increase in the upper cutoff frequency of the random source input, the approximation worsened continuously. Predictions to ramp-and-hold stimuli were computed, as well as responses to random stimulation. Limiting the upper cutoff frequency did not diminish the value of the techniques applied.

Simulation of post-synaptic activities in hippocampal cells during theta rhythm

Three types of discharge patterns can be recorded from hippocampal cells during theta (θ) rhythm. The Type 1 discharges are in rhythmic bursts phase-locked with θ; the Type 2 pattern, although non-rhythmic shows a phase relationship with θ; and the Type 3 activity is non-rhythmic and unrelated with θ. Furthermore, depending on the presence or absence of θ and on other undetermined factors, units with Type 1 activity may become non-rhythmic or vice-versa. These patterns may derive from the relative amounts of rhythmic versus non-rhythmic inputs received by each cell. This possibility was tested through computer simulation of a hypothetical neuron receiving random and rhythmic inputs. The inputs produced membrane potential (MP) variations simulated as a band-limited gaussian white noise (WN) and a sinewave, respectively, which were summated by the cell. Spikes were triggered when a MP threshold was reached. The simulated neuron exhibited the three types of discharge patterns by changing the sinewave to WN ratio. Ratios of 0.4 and 0.1 generated Types 1 and 2 behavior, respectively, and lower ratios Type 3. Statistical methods, based on autocorrelations and averages, were used to assess rhythmicities and relationships between spikes and EEC or the simulated MP. The simulation supports the tested hypothesis, provides a good description of the possible mechanisms involved and is predictive, indicating that most hippocampal cells, rhythmic or not might show periodic MP oscillations phase-locked with θ.