Combination Of White Noise Research Articles

The effects of white noise and swaddling methods on orogastric tube insertion-related pain in preterm infants: A randomized controlled trial.

This study aims to investigate the effects of the white noise, swaddling and white noise + swaddling methods on pain and physiological parameters associated with orogastric tube insertion procedure. This was a randomized controlled trial. A total of 132 preterm infants were randomly assigned to four groups as white noise group (n = 33), swaddling group (n = 33), white noise + swaddling group (n = 33) and control group (n = 33). Interventions were initiated 5 min before the orogastric tube insertion procedure and continued during and up to 5 min after the procedure. White noise intervention alone did not have a significant effect on reducing pain associated with orogastric tube insertion (p > 0.05). Compared with the control group, the preterm infants in the swaddling group experienced 0.587 times less pain, and those in the white noise + swaddling group experienced 0.473 times less pain. Findings indicate the swaddling and the combination of white noise + swaddling may be a useful intervention in reducing the invasive pain experienced by preterm infants during and after orogastric tube insertion and in improving the physiological parameters associated with pain.

A new approach considering temporal correlations for GPS campaign time series

GPS campaign-mode surveys are periodically collected measurements and their time series has a considerable percentage of data gaps unlike continuous time series. Studying error characteristics of a time series is imperative to compute reliable parameter uncertainties. The power-law process can best describe the background noise for a GPS continuous time series and may be introduced into the analysis through well-known methods. However, the power-law process cannot be applied successfully over GPS campaign time series due to the constraints mentioned above. Here we demonstrate a new approach enabling one to project the stochastic properties of campaign time series into the stochastic domain of the permanent stations of International GNSS Service (IGS) network. The stochastic domain, the combination of white noise (WN) and flicker noise (FN), was obtained from the power spectrum of a continuous time series consisting of truncated daily RINEX observations. We implemented it in the Python3 environment as an open-source package called GPS/GNSS campaign time series analysis (GCTS v1.0). The analysis showed that the velocity uncertainties may be, on average, underestimated by a factor of 2 when assuming the WN-only noise model using campaign data from the UNAVCO data archive collected in San Bernardino and its vicinity. Moreover, to reveal the progress of the new approach, we modelled buried screw dislocations of the San Jacinto, the San Andreas, and parallel faults in their vicinity in elastic half-space. When using the new approach with the combination of WN and FN instead of the WN-only model, we achieved a significant improvement of 15% on average in the chi-square value. Our outcomes showed that the noise process should be considered even for campaign time series. The proposed approach facilitates the analysis of GPS campaign time series even if they include considerable data gaps.

A Hybrid LSTM-ResNet Deep Neural Network for Noise Reduction and Classification of V-Band Receiver Signals

Noise reduction is one of the most important process used for signal processing in communication systems. The signal-to-noise ratio (SNR) is a key parameter to consider for minimizing the bit error rate (BER). The inherent noise found in millimeter-wave systems is mainly a combination of white noise and phase noise. Increasing the SNR in wireless data transfer systems can lead to reliability and performance improvements. To address this issue, we propose to use a recurrent neural network (RNN) with a long short-term memory (LSTM) autoencoder architecture to achieve signal noise reduction. This design is based on a composite LSTM autoencoder with a single encoder layer and two decoder layers. A V-band receiver test bench is designed and fabricated to provide a high-speed wireless communication system. Constellation diagrams display the output signals measured for various random sequences of PSK and QAM modulated signals. The LSTM autoencoder is trained in real time using various noisy signals. The trained system is then used to reduce noise levels in the tested signals. The SNR of the designed receiver is of the order of 11.8dB, and it increases to 13.66dB using the three-level LSTM autoencoder. Consequently, the proposed algorithm reduces the bit error rate from 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−8</sup> to 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−11</sup> . The performance of the proposed algorithm is comparable to other noise reduction strategies. Augmented denoised signals are fed into a ResNet-152 deep convolutional network to perform the final classification. The demodulation types are classified with an accuracy of 99.93%. This is confirmed by experimental measurements.

On the application of Monte Carlo singular spectrum analysis to GPS position time series

Singular spectrum analysis (SSA) has recently been applied to various geodetic time series studies. As a data-adaptive method, SSA is capable of extracting signals with non-constant phase and amplitudes. Although SSA is a competent method in the presence of white noise, the contribution of colored noise, having semi-periodic behavior, degrades its performance. Parts of colored noise can be absorbed in the SSA eigenmodes, which specifies signals and hence resulting in spurious modulation or losing significant signals. Signals and colored noise are thus to be discriminated in the signal identification procedure. Monte Carlo SSA (MCSSA) in its original formulation, providing a significance test against the AR(1) noise null hypothesis, can be misinterpreted when other colored noise structures contribute to the series. We propose an algorithm for MCSSA that is not limited to the AR(1) noise hypothesis. It estimates the noise model parameters using LS-VCE and generates the surrogate data using the Cholesky decomposition. The algorithm is adapted to GPS position time series where the underlying noise is a combination of white noise and flicker noise. GPS position time series, postulated real situation, are first simulated to include annual and semiannual signals plus white and flicker noise. The results indicate that MCSSA can extract the annual and semiannual signals with 2.11 and 1.25 mm amplitudes (the global mean values) from 20-year-long time series, with 95% confidence level, if flicker noise is less than 17 and 13 $$ {\text{mm/year}}^{1/4} $$ , respectively. The longer the time series or the stronger the signals are, the higher these thresholds will be. This conclusion is also verified when applying MCSSA to the up component of GPS position time series of 347 JPL stations.

A comprehensive study of the 2016 Mw 6.0 Italy earthquake based on high-rate (10 Hz) GPS data

The 2016 Mw 6.0 Italy earthquake is successfully recorded by the near-field 10 Hz GPS and 200 Hz Strong Motion (SM) stations, providing valuable data for this study. A comprehensive study of this earthquake is carried out based on GPS data, which contains coseismic deformations analysis, noise analysis, seismic wave picking, and magnitude determination. The noise of most GPS-derived displacement waveforms can be described as a combination of white noise, flicker noise, and random walk noise after the earthquake occurrence, and the spectral indices vary significantly for most stations, implying that the seismic signals have affected the noise characteristic of GPS-derived displacement waveforms. S-transform is employed to assess the GPS capability to detect the seismic arrival time. The SM station AMT and the GPS station AMAT are in good agreement in seismic wave picking, and the difference is only 1.2 s in the north component, suggesting that the outcome of seismic wave picking using GPS data is reliable. Then, a classic empirical formula is employed to determine the moment magnitude. A robust moment magnitude (Mw 5.90) can be estimated by the nine GPS stations with about 23.9 s. If four GPS stations near the epicenter is chosen to determine the magnitude, it only take 13.0 s to retrieve a reliable preliminary (Mw 5.82) magnitude, which is 5.4 s ahead of nine stations. In addition, Cross Wavelet Transform (XWT) is adopted to measuring the correlation and phase relationship between GPS and SM records. The result of XWT analysis indicates 10 Hz GPS is capable of capturing reliable and accurate coseismic dynamic deformations, as evidenced by the XWT-based semblance being close to 1 between GPS and SM records. The above results confirm the capability of 10 Hz GPS to capture coseismic dynamic deformations, detect seismic arrival time, and determine earthquake magnitude. Moreover, rapid magnitude determination based on 10 Hz GPS data can be regarded as an important supplement to Earthquake Early Warning (EEW).

Effect of removing the common mode errors on linear regression analysis of noise amplitudes in position time series of a regional GPS network & a case study of GPS stations in Southern California

The analysis of the correlations between the noise in different components of GPS stations has positive significance to those trying to obtain more accurate uncertainty of velocity with respect to station motion. Previous research into noise in GPS position time series focused mainly on single component evaluation, which affects the acquisition of precise station positions, the velocity field, and its uncertainty. In this study, before and after removing the common-mode error (CME), we performed one-dimensional linear regression analysis of the noise amplitude vectors in different components of 126 GPS stations with a combination of white noise, flicker noise, and random walking noise in Southern California. The results show that, on the one hand, there are above-moderate degrees of correlation between the white noise amplitude vectors in all components of the stations before and after removal of the CME, while the correlations between flicker noise amplitude vectors in horizontal and vertical components are enhanced from un-correlated to moderately correlated by removing the CME. On the other hand, the significance tests show that, all of the obtained linear regression equations, which represent a unique function of the noise amplitude in any two components, are of practical value after removing the CME. According to the noise amplitude estimates in two components and the linear regression equations, more accurate noise amplitudes can be acquired in the two components.

Above the Noise: The Search for Periodicities in the Inner Heliosphere

Remote sensing of coronal and heliospheric periodicities can provide vital insight into the local conditions and dynamics of the solar atmosphere. We seek to trace long (one hour or longer) periodic oscillatory signatures (previously identified above the limb in the corona by, e.g., Telloni et al. in Astrophys. J.767, 138, 2013) from their origin at the solar surface out into the heliosphere. To do this, we combined on-disk measurements taken by the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO) and concurrent extreme ultra-violet (EUV) and coronagraph data from one of the Solar Terrestrial Relations Observatory (STEREO) spacecraft to study the evolution of two active regions in the vicinity of an equatorial coronal hole over several days in early 2011. Fourier and wavelet analysis of signals were performed. Applying white-noise-based confidence levels to the power spectra associated with detrended intensity time series yields detections of oscillatory signatures with periods from 6 – 13 hours in both AIA and STEREO data. As was found by Telloni et al. (2013), these signatures are aligned with local magnetic structures. However, typical spectral power densities all vary substantially as a function of period, indicating spectra dominated by red (rather than white) noise. Contrary to the white-noise-based results, applying global confidence levels based on a generic background-noise model (allowing a combination of white noise, red noise, and transients following Auchère et al. in Astrophys. J.825, 110, 2016) without detrending the time series uncovers only sporadic, spatially uncorrelated evidence of periodic signatures in either instrument. Automating this method to individual pixels in the STEREO/COR coronagraph field of view is non-trivial. Efforts to identify and implement a more robust automatic background noise model fitting procedure are needed.

Non-negative least-squares variance component estimation with application to GPS time series

The problem of negative variance components is probable to occur in many geodetic applications. This problem can be avoided if non-negativity constraints on variance components (VCs) are introduced to the stochastic model. Based on the standard non-negative least-squares (NNLS) theory, this contribution presents the method of non-negative least-squares variance component estimation (NNLS-VCE). The method is easy to understand, simple to implement, and efficient in practice. The NNLS-VCE is then applied to the coordinate time series of the permanent GPS stations to simultaneously estimate the amplitudes of different noise components such as white noise, flicker noise, and random walk noise. If a noise model is unlikely to be present, its amplitude is automatically estimated to be zero. The results obtained from 350 GPS permanent stations indicate that the noise characteristics of the GPS time series are well described by combination of white noise and flicker noise. This indicates that all time series contain positive noise amplitudes for white and flicker noise. In addition, around two-thirds of the series consist of random walk noise, of which its average amplitude is the (small) value of 0.16, 0.13, and 0.45 \(\text{ mm/year }^{1/2}\) for the north, east, and up components, respectively. Also, about half of the positive estimated amplitudes of random walk noise are statistically significant, indicating that one-third of the total time series have significant random walk noise.

Velocity Field Derived from Taiwan Continuous GPS Array (2007 - 2013)

Data were collected from 281 Taiwan continuous Global Positioning System (cGPS) Array sites from 2007-2013 and processed with GAMIT/GLOBK software. Power spectral density stacking from cGPS position time series in Taiwan found the spectral index as -0.72, -0.77, and -0.57 for the E, N, U components, respectively. This indicates the cGPS data errors can be described as a combination of white noise and flicker noise. The common-mode errors are removed by stacking data from 50 cGPS sites with data periods greater than 5 years. By removing the common-mode errors the GPS data precision is further improved to 2.3, 1.9, and 6.9 mm in the E, N, U components, respectively. After strict data quality control, time series analysis and noise analysis, we derive a new Taiwan velocity field using cGPS data from 2007-2013. The general pattern of the newly derived 2007-2013 velocity field is quite similar to that from previous studies, but the station density is much larger and spatial coverage better. About 80 mm yr^(-1) plate convergence rate is observed, half of the rate is accommodated on the fold and thrust belt of western Taiwan and another half is taken up in the Longitudinal Valley and Coastal Range in eastern Taiwan. The velocities in western Taiwan generally show a fan-shaped pattern, consistent with the maximum compression tectonic stress direction. In northern Taiwan the velocity vectors reveal clockwise rotation, indicating the on-going extensional deformation related to the back-arc extension of the Okinawa Trough. In southern Taiwan, the horizontal velocity increases from about 40 mm yr^(-1) in the Chia-Nan area to 55 mm yr^(-1) in the Kao-Ping area with a counterclockwise rotation.

Fundamental sensitivity limit imposed by dark 1/f noise in the low optical signal detection regime

The impact of dark 1/f noise on fundamental signal sensitivity in direct low optical signal detection is an understudied issue. In this theoretical manuscript, we study the limitations of an idealized detector with a combination of white noise and 1/f noise, operating in detector dark noise limited mode. In contrast to white noise limited detection schemes, for which there is no fundamental minimum signal sensitivity limit, we find that the 1/f noise characteristics, including the noise exponent factor and the relative amplitudes of white and 1/f noise, set a fundamental limit on the minimum signal that such a detector can detect.

Assessment of noise in GPS coordinate time series: Methodology and results

We propose a methodology to assess the noise characteristics in time series of position estimates for permanent Global Positioning System (GPS) stations. Least squares variance component estimation (LS‐VCE) is adopted to cope with any type of noise in the data. LS‐VCE inherently provides the precision of (co)variance estimators. One can also apply statistical hypothesis testing in conjunction with LS‐VCE. Using the w‐test statistic, a combination of white noise and flicker noise turns out in general to best characterize the noise in all three position components. An interpretation for the colored noise of the series is given. Unmodelled periodic effects in the data will be captured by a set of harmonic functions for which we rely on the least squares harmonic estimation (LS‐HE) method and parameter significance testing developed in the same framework as LS‐VCE. Having included harmonic functions into the model, practically only white noise can be shown to remain in the data. Remaining time correlation, present only at very high frequencies (spanning a few days only), is expressed as a first‐order autoregressive noise process. It can be caused by common and well‐known sources of errors like atmospheric effects as well as satellite orbit errors. The autoregressive noise should be included in the stochastic model to avoid the overestimation (upward bias) of power law noise. The results confirm the presence of annual and semiannual signals in the series. We observed also significant periodic patterns with periods of 350 days and its fractions 350/n, n = 2, …, 8 that resemble the repeat time of the GPS constellation. Neglecting these harmonic signals in the functional model can seriously overestimate the rate uncertainty.

Distribution of Increases in Residual Log Likelihood for Nested Spatial Models

Here we review nested relationships between models in the Matérn family of spatial models. The problem of comparing nested statistical models is straightforward in regular parametric problems via the likelihood ratio statistics and its asymptotic distribution. Here we examine the distribution of increments in residual log likelihood between nested spatial models when the null hypothesis is that the spatial structure is a convex combination of white noise and the de Wijs process, also known by its logarithmic covariance function. This study is carried out by simulation of spatial processes and the important aspects of this work include how to simulate a spatial process of order 0, the lack of strong bias in the estimates of variance components, and the validity of the usual asymptotic results for nested spatial models examined here.

Error analysis of continuous GPS position time series

A total of 954 continuous GPS position time series from 414 individual sites in nine different GPS solutions were analyzed for noise content using maximum likelihood estimation (MLE). The lengths of the series varied from around 16 months to over 10 years. MLE was used to analyze the data in two ways. In the first analysis the noise was assumed to be white noise only, a combination of white noise plus flicker noise, or a combination of white noise plus random walk noise. For the second analysis the spectral index and amplitude of the power law noise were estimated simultaneously with the white noise. In solutions where the sites were globally distributed, the noise can be best described by a combination of white noise plus flicker noise. Both noise components show latitude dependence in their amplitudes (higher at equatorial sites) together with a bias to larger values in the Southern Hemisphere. In the regional solutions, where a spatially correlated (common mode) signal has been removed, the noise is significantly lower. The spectral index of the power law in regional solutions is more varied than in the global solutions and probably reflects a mixture of local effects. A significant reduction in noise can be seen since the first continuous GPS networks began recording in the early 1990s. A comparison of the noise amplitudes to the different monument types in the Southern California Integrated GPS Network suggests that the deep drill braced monument is preferred for maximum stability.

Noise in GPS coordinate time series

We assess the noise characteristics in time series of daily position estimates for 23 globally distributed Global Positioning System (GPS) stations with 3 years of data, using spectral analysis and Maximum Likelihood Estimation. A combination of white noise and flicker noise appears to be the best model for the noise characteristics of all three position components. Both white and flicker noise amplitudes are smallest in the north component and largest in the vertical component. The white noise part of the vertical component is higher for tropical stations (±23° latitude) compared to midlatitude stations. Velocity error in a GPS coordinate time series may be underestimated by factors of 5–11 if a pure white noise model is assumed.

White noise analysis of a chromatic type horizontal cell in the Xenopus retina.

The dynamics of color-coded signal transmission in the light-adapted Xenopus retina were studied by a combination of white noise (Wiener) analysis and simultaneous recordings from two types of horizontal cells: chromatic-type horizontal cells (C-HCs) are hyperpolarized by blue light and depolarized by red light, whereas luminosity-type horizontal cells (L-HCs) are hyperpolarized by all wave-lengths. The retina was stimulated by two superimposed fields of red and blue light modulated by two independent white noise signals, and the resulting intracellular responses were decomposed into red and blue components (first-order kernels). The first-order kernels predict the intracellular responses with a small degree of error (3.5-9.5% in terms of mean square error) under conditions where modulated responses exceeded 30 mV in amplitude peak-to-peak, thus demonstrating that both red and blue modulation responses are linear. Moreover, there is little or no interaction between the red- and blue-evoked responses; i.e., nearly identical first-order kernels were obtained for one color whether the other color was modulated or not. In C-HCs (but not L-HCs), there were consistent differences in the dynamics of the red and blue responses. In the C-HC, the cutoff frequency of the red response was higher than for the blue (approximately 12 vs 5 Hz), and the red kernel was more bandpass than the blue. In the L-HC, kernel waveform and cutoff frequencies were similar for both colors (approximately 12 Hz or greater), and the time-to-peak of the L-HC kernel was always shorter than either the red or blue C-HC kernel. These results have implications for the mechanisms underlying color coding in the distal retina, and they further suggest that nonlinear phenomena, such as voltage-dependent conductances in HCs, do not contribute to the generation of modulation responses under the experimental conditions used here.

?Escape? of a periodically driven particle from a metastable state in a noisy system

We consider the statistical properties of the escape time of a particle initially sitting in a potential well subject to a combination of white noise and a periodic forcing term. As one finds in the case of the much-studied bistable potential, different kinds of resonant effects can occur, as measured by the survival probability and the average residence time. When this time is considered as a function of the noise strength, then we show that for small amplitudes of the forcing term there are no resonant effects, while for large amplitudes such effects can appear. We also show that a resonant phenomenon is possible in terms of the amplitude of a periodic forcing term.