White Noise Source Research Articles

RealSinger: Ultra-realistic singing voice generation via stochastic differential equations

Synthesizing high-quality singing voice from music score is a challenging problem in music generation and has many practical applications. Samples generated by existing singing voice synthesis (SVS) systems can roughly reflect the lyrics, pitch and duration in a given score, but they fail to contain necessary details. In this paper, based on stochastic differential equations (SDE) we propose RealSinger to generate 22.05kHz ultra-realistic singing voice conditioned on a music score. Our RealSinger learns to find the stochastic process path from a source of white noise to the target singing voice manifold under the conditional music score, allowing to sing the music score while maintaining the local voice details of the target singer. During training, our model learns to accurately predict the direction of movement in the ambient Euclidean space onto the low-dimensional singing voice manifold. RealSinger’s framework is very flexible. It can either generate intermediate feature representations of the singing voice, such as mel-spectrogram, or directly generate the final waveform, as in the end-to-end style which rectify defects and accumulation errors introduced by two-stage connected singing synthesis systems. An extensive subjective and objective test on benchmark datasets shows significant gains in perceptual quality using RealSinger. The mean opinion scores (MOS) obtained with RealSinger are closer to those of the human singer’s original high-fidelity singing voice than to those obtained with any state-of-the-art method. Audio samples are available at https://realsinger.github.io/.

1/f Noise Mitigation in an Opto-Mechanical Sensor with a Fabry-Pérot Interferometer.

Low-frequency and 1/f noise are common measurement limitations that arise in a variety of physical processes. Mitigation methods for these noises are dependent on their source. Here, we present a method for removing 1/f noise of optical origin using a micro-cavity Fabry-Pérot (FP) interferometer. A mechanical modulation of the FP cavity length was applied to a previously studied opto-mechanical sensor. It effectively mimics an up-conversion of the laser frequency, shifting signals to a region where lower white-noise sources dominate and 1/f noise is not present. Demodulation of this signal shifts the results back to the desired frequency range of observation with the reduced noise floor of the higher frequencies. This method was found to improve sensitivities by nearly two orders of magnitude at 1 Hz and eliminated 1/f noise in the range from 1 Hz to 4 kHz. A mathematical model for low-finesse FP cavities is presented to support these results. This study suggests a relatively simple and efficient method for 1/f noise suppression and improving the device sensitivity of systems with an FP interferometer readout.

Multilayered noise model for transport in complex environments.

Transport in complex fluidic environments often exhibits transient subdiffusive dynamics accompanied by non-Gaussian probability density profiles featuring a nonmonotonic non-Gaussian parameter. Such properties cannot be adequately explained by the original theory of Brownian motion. Based on an extension of kinetic theory, this study introduces a chain of hierarchically coupled random walks approach that effectively captures all these intriguing characteristics. If the environment consists of a series of independent white noise sources, then the problem can be expressed as a system of hierarchically coupled Ornstein-Uhlenbech equations. Due to the linearity of the system, the most essential transport properties have a closed analytical form.

Influence of Auditory Information on Postural Control During Different Gait Tasks in the Elderly.

Hearing loss is frequently associated with reduced postural control. This is possibly not only related to simultaneous pathophysiological changes within the hearing and vestibular system. The auditory input itself could provide helpful information for maintaining postural control. Previous studies of our group already showed that continuous or interrupted white noise can significantly improve postural control during gait conditions in young healthy individuals. The present study aimed at investigating if those effects are also active in the elderly. Elderly volunteers (mean age 67 years) without any history of disorders to influence gait performance successfully completed 5 walking tasks under 4 different acoustic conditions. Angular sway velocity was measured close to the center of gravity with the Vertiguard® system. Significant changes in body sway velocity were found in 4 of 5 investigated tasks. Only "walking with turning head in rhythm" was not associated with any change in the acoustic input. The sway increased by 8.9% during "walking with open eyes" in the pitch direction and by 11.5% during "tandem walking" in the roll direction if ear protection was applied. The sway was reduced by 9.1% during "walking over barriers" in the pitch direction and by 16.7% in the roll direction during "walking with closed eyes" if a stationary source of continuous white noise was presented. The data of the present study indicate that auditory information could significantly alter postural control during walking in the elderly. Continuous white noise seems to be helpful for maintaining balance in different walking tasks.

Convergence rates of stationary and non-stationary asymptotical regularization methods for statistical inverse problems in Banach spaces

We investigate stationary and non-stationary asymptotical regularization methods for statistical inverse problems in Banach spaces. The mean-squared errors (MSE) of both methods are estimated without the conventional assumption of the commutativity between the solution variance and the noise variance. Moreover, the a priori smoothness of solution is characterized in terms of real interpolation, which is strictly weaker than the classical settings. The sufficient and necessary conditions of optimal convergence rates of MSE are proven. Our results extend theoretical findings in Hilbert settings given in the recent paper by Lu et al. [SIAM/ASA J. Uncertain., 9 (2021), pp. 1488-1525]. Two examples of integral equations with white noise and inverse source problems in elliptic partial differential equations are demonstrated to show the usefulness of our theoretical results.

Noise influence on recurrent neural network with nonlinear neurons

The purpose of this study is to establish the features of noise propagation and accumulation in a recurrent neural network using a simplified echo network as an example. In this work, we studied the influence of activation function of artificial neurons and the connection matrices between them. Methods. We have considered white Gaussian noise sources. We used additive, multiplicative and mixed noise depending on how the noise is introduced into artificial neurons. The noise impact was estimated using the dispersion (variance) of the output signal. Results. It is shown that the activation function plays a significant role in noise accumulation. Two nonlinear activation functions have been considered: the hyperbolic tangent and the sigmoid function with range form 0 to 1. It is shown that some types of noise are suppressed in the case of the second function. As a result of considering the influence of coupling matrices, it was found that diagonal coupling matrices with a large blurring coefficient lead to less noise accumulation in the echo network reservoir with an increase in the reservoir memory influence. Conclusion. It is shown that activation functions of the form of sigmoid with range from 0 to 1 are suitable for suppressing multiplicative and mixed noise. The accumulation of noise in the reservoir was considered for three types of coupling matrices inside the reservoir: a uniform matrix, a band matrix with a small blurring coefficient, and a band matrix with a large blurring coefficient. It has been found that the band matrix echo networks with a high blurring coefficient accumulates the least noise. This holds for both additive and multiplicative noise.

Multistability near the boundary of noise-induced synchronization in ensembles of uncoupled chaotic systems

The aim of this work is to study the possibility of the existence of multistability near the boundary of noise-induced synchronization in chaotic continuous and discrete systems. Ensembles of uncoupled Lorenz systems and logistic maps being under influence of a common source of white noise have been chosen as an object under study. Methods. The noise-induced synchronization regime detection has been performed by means of direct comparison of the system states being under influence of the common noise source and by calculation of the synchronization error. To determine the presence of multistability near the boundary of this regime, the multistability measure has been calculated and its dependence on the noise intensity has been obtained. In addition, for fixed moments of time, the basins of attraction of the synchronous and asynchronous regimes have been received for one of the systems driven by noise for fixed initial conditions of the other system. The result of the work is a proof of the presence of multistability near the boundary of noise-induced synchronization. Conclusion. It is shown that the regime of intermittent noise-induced synchronization, as well as the regime of intermittent generalized synchronization, is characterized by multistability, which manifests itself in this case as the existence in the same time interval of the synchronous behavior in one pair of systems being under influence of a common noise source, whereas in the other pair the asynchronous behavior is observed. The found effect is typical for both flow systems and discrete maps being under influence of a common noise source. It can find an application in the information and telecommunication systems for improvement the methods for secure information transmission based on the phenomenon of chaotic synchronization.

Mechanical models as ground truth for vowel resonance analysis

It has long been established that LPC analysis results in formant estimates that are not accurate representations of the resonances; they are biased towards the nearest harmonic, and this bias worsens as F0 rises to 200 Hz or more. Manual measurement of formants with the reassigned spectrogram (RS) has been shown to be more accurate, but the ground truth is needed in order to test automatic measurement methods. Here, “vocal tract” models were 3D-printed to allow resonances to be excited replicably. Using the principle of acoustic reciprocity, source signals were played over an external loudspeaker, and the output filtered by the model was recorded via a microphone located in the model’s “glottis.” A white noise source signal was used to determine the resonances. Sawtooth and impulse train source signals (F0s 83–400 Hz) were filtered by the physical model and then analyzed with both LPC and RS. LPC formants were biased towards the nearest harmonic, resulting in errors from 10 Hz at low F0 to 250 at 300 Hz. RS errors ranged from 0 to 20 Hz and were not correlated with F0. These results indicate physical models are useful for creating known resonances for validating accuracy in our measurements.

A general framework for SPDE-based stationary random fields

This paper presents theoretical advances in the application of the Stochastic Partial Differential Equation (SPDE) approach in geostatistics. We show a general approach to construct stationary models related to a wide class of linear SPDEs, with applications to spatio-temporal models having non-trivial properties. Within the framework of Generalized Random Fields, a criterion for existence and uniqueness of stationary solutions for this class of SPDEs is proposed and proven. Their covariance are then obtained through their spectral measure. We present a result relating the covariance of the solution in the case of a White Noise source term with the covariance in a generic case through convolution. Then, we obtain a variety of SPDE-based stationary random fields. In particular, well-known results regarding the Matérn Model and Markovian models are recovered. A new relationship between the Stein model and a particular SPDE is obtained. New spatio-temporal models obtained from evolution SPDEs of arbitrary temporal derivative order are then obtained, for which properties of separability and symmetry can be controlled. We also obtain results concerning stationary solutions for physically inspired models, such as solutions to the heat equation, the advection-diffusion equation, some Langevin’s equations and the wave equation.

Kovacs Memory Effect with an Optically Levitated Nanoparticle.

The understanding of the dynamics of nonequilibrium cooling and heating processes at the nanoscale is still an open problem. These processes can follow surprising relaxation paths due to, e.g., memory effects, which significantly alter the expected equilibration routes. The Kovacs effect can take place when a thermalization process is suddenly interrupted by a change of the bath temperature, leading to a nonmonotonic evolution of the energy of the system. Here, we demonstrate that the Kovacs effect can be observed in the thermalization of the center of mass motion of a levitated nanoparticle. The temperature is controlled during the experiment through an external source of white Gaussian noise that mimics an effective thermal bath at a temperature that can be changed faster than any relaxation time of the system. We describe our experiments in terms of the dynamics of a Brownian particle in a harmonic trap without any fitting parameter, suggesting that the Kovacs effect can appear in a large variety of systems.

Interspike interval correlations in neuron models with adaptation and correlated noise.

The generation of neural action potentials (spikes) is random but nevertheless may result in a rich statistical structure of the spike sequence. In particular, contrary to the popular renewal assumption of theoreticians, the intervals between adjacent spikes are often correlated. Experimentally, different patterns of interspike-interval correlations have been observed and computational studies have identified spike-frequency adaptation and correlated noise as the two main mechanisms that can lead to such correlations. Analytical studies have focused on the single cases of either correlated (colored) noise or adaptation currents in combination with uncorrelated (white) noise. For low-pass filtered noise or adaptation, the serial correlation coefficient can be approximated as a single geometric sequence of the lag between the intervals, providing an explanation for some of the experimentally observed patterns. Here we address the problem of interval correlations for a widely used class of models, multidimensional integrate-and-fire neurons subject to a combination of colored and white noise sources and a spike-triggered adaptation current. Assuming weak noise, we derive a simple formula for the serial correlation coefficient, a sum of two geometric sequences, which accounts for a large class of correlation patterns. The theory is confirmed by means of numerical simulations in a number of special cases including the leaky, quadratic, and generalized integrate-and-fire models with colored noise and spike-frequency adaptation. Furthermore we study the case in which the adaptation current and the colored noise share the same time scale, corresponding to a slow stochastic population of adaptation channels; we demonstrate that our theory can account for a nonmonotonic dependence of the correlation coefficient on the channel's time scale. Another application of the theory is a neuron driven by network-noise-like fluctuations (green noise). We also discuss the range of validity of our weak-noise theory and show that by changing the relative strength of white and colored noise sources, we can change the sign of the correlation coefficient. Finally, we apply our theory to a conductance-based model which demonstrates its broad applicability.

Trapping enhanced by noise in nonhyperbolic and hyperbolic chaotic scattering

The noise-enhanced trapping is a surprising phenomenon that has already been studied in chaotic scattering problems where the noise affects the physical variables but not the parameters of the system. Following this research, in this work we provide strong numerical evidence to show that an additional mechanism that enhances the trapping arises when the noise influences the energy of the system. For this purpose, we have included a source of Gaussian white noise in the HȨnon-Heiles system, which is a paradigmatic example of open Hamiltonian system. For a particular value of the noise intensity, some trajectories decrease their energy due to the stochastic fluctuations. This drop in energy allows the particles to spend very long transients in the scattering region, increasing their average escape times. This result, together with the previously studied mechanisms, points out the generality of the noise-enhanced trapping in chaotic scattering problems.

Asymptotic behavior of the time-dependent divergence exponent.

The divergence rate method, which is used to determine the maximum Lyapunov exponent out of time series, is based on the evaluation of the time-dependent divergence exponent. For chaotic systems and in the small time regime, this exponent grows linearly in time. The asymptotic regime is instead characterized by a time-independent behavior due to the system eventually losing its memory of the starting conditions. The amplitude of this "plateau"-like divergence exponent depends both on the choice of the embedding dimension and lag and on the maximum distance of nearby starting trajectories in a way that is characteristic of the underlying dynamical system. In this paper, upon introducing the basic mathematical tools, we address the plateau evaluation for two classes of time series, those generated by a white noise source and those generated by a finite-dimensional chaotic system. The different behavior provides a novel tool to distinguish purely stochastic sources from deterministic ones, as well as to provide a precise estimate of the correlation dimension in the latter case. The method is also sensitive to correlated noise sources.

Helmholtz in the kitchen: a frying pan as a volume resonator

Helmholtz resonators are an interesting, widespread phenomenon, which can spark students’ interest in acoustics and more generally in applying physics to the phenomena of everyday life. Using a smartphone as an experimental tool to measure and analyze acoustic data, this work presents an investigation of the sizzling noise of something frying in a pan, and also of the change of this sound when the lid of the pan is opened and closed. We adapt the general resonance frequency result of the Helmholtz resonator (1) to the case of a real lid-pan system (2) and to a better controlled case using an artificial lid with a rectangular opening and a white noise source (also provided by a smartphone) inside the pan. Experimental spectra obtained for both cases show satisfactory agreement with the theoretical prediction. We conclude with a discussion of the limitations and perspectives of the experiment.

Determination of Natural Frequencies of Pipes Using White Noise for Magnetostrictive Longitudinal Guided-Wave Nondestructive Testing

Magnetostrictive guided waves are widely used in nondestructive testing and structural health monitoring of pipes to ensure their integrity. These guided waves are mechanical waves, and if the natural frequencies of the pipe are used as excitation frequencies, the mechanical vibration amplitude can be enhanced, which will then improve the amplitude of the guided waves. Comparison of the various methods to determine the natural frequencies of pipes shows that the white noise signals remain relatively smooth in both time and frequency domains. White noise has a wide bandwidth and uniform energy distribution. It does not require high energy within a short time period, so it is easy to generate. In this article, white noise is used to determine the natural frequencies of pipes. Comparison of the white noise spectra produced by analog and digital circuits shows that the energy spectrum of white noise produced by the analog circuit is high and uniform, so the analog circuit is used as the white noise source and this noise is loaded onto a magnetostrictive sensor. The detected signal spectrum is then analyzed and the frequencies with high power density spectra are determined to be the natural frequencies. The natural frequencies of the pipeline detected using white noise are compared with the results of modal analysis. Simulation results and experimental results demonstrate that the use of white noise allows the natural frequencies of pipes to be determined quickly and accurately. These natural frequencies can be used in magnetostrictive guided-wave nondestructive testing.

15 kW polarization-maintained Yb-doped amplifier with 13 GHz linewidth by suppressing the self-pulsing and stimulated Brillouin scattering

In this work, we study the characteristics of self-pulsing in a polarization-maintained fiber amplifier operated with different linewidths based on white noise source phase modulation. It indicates that the self-pulsing is almost simultaneous with the stimulated Brillouin scattering process, and its threshold is increasing near-linearly with the linewidth. By optimizing the laser structure, the threshold of self-pulsing increases by a factor of 1.5. We demonstrate a high-power linear polarization and all-fiberized amplifier with narrow linewidth and near-diffraction-limited beam quality. The output power scales to 1.5 kW with the pumping efficiency of 83%. The full width at half-maximum linewidth was measured to be 13 GHz. The polarization extinction ratio was larger than 13 dB. The beam quality M2 was about 1.14 at the maximum laser power.

Practical Prediction of CFO-Made OFDM Symbol Distortion

The Carrier Frequency Offset (CFO) is considered to be a major drawback of the Orthogonal Frequency-Division Multiplexing (OFDM) signal. So, in many practical situations, specifically with LTE-Advanced downlink introducing carrier aggregation, estimation of the CFO-induced OFDM symbol phase deviation, is of interest. However, this demands complex test equipment, such as e.g. a Vector Signal Analyzer (VSA), which might not be always and everywhere available. Therefore, we applied the link abstraction principle on the Bit Error Rate (BER) that is considered to be determined just by the CFO-caused phase deviation, i.e. as if the channel was noiseless and time-dispersion-free (so that evident bit errors occur just due to the actual CFO). Furthermore, as the CFO-caused squared phase deviation is linear with the instantaneous (per-OFDM-symbol) Peak-to-Average Power Ratio (PAPR), which is related to the Error Vector Magnitude (EVM) and so with BER, we develop a simple model for analytical BER-based estimating of CFO. In this sense, we considered the easy-to-measure BER degradation as resulting just from the according additive white Gaussian noise (AWGN) source, which abstracts the CFO distortion. The proposed analytical model is validated by according Monte-Carlo simulations.

Improving AoA Localization Accuracy in Wireless Acoustic Sensor Networks with Angular Probability Density Functions.

Advances in energy efficient electronic components create new opportunities for wireless acoustic sensor networks. Such sensors can be deployed to localize unwanted and unexpected sound events in surveillance applications, home assisted living, etc. This research focused on a wireless acoustic sensor network with low-profile low-power linear MEMS microphone arrays, enabling the retrieval of angular information of sound events. The angular information was wirelessly transmitted to a central server, which estimated the location of the sound event. Common angle-of-arrival localization approaches use triangulation, however this article presents a way of using angular probability density functions combined with a matching algorithm to localize sound events. First, two computationally efficient delay-based angle-of-arrival calculation methods were investigated. The matching algorithm is described and compared to a common triangulation approach. The two localization algorithms were experimentally evaluated in a m by m room, localizing white noise and vocal sounds. The results demonstrate the superior accuracy of the proposed matching algorithm over a common triangulation approach. When localizing a white noise source, an accuracy improvement of up to 114% was achieved.

An Analysis of Deterministic Chaos as an Entropy Source for Random Number Generators.

This paper presents an analytical study on the use of deterministic chaos as an entropy source for the generation of random numbers. The chaotic signal generated by a phase-locked loop (PLL) device is investigated using numerical simulations. Depending on the system parameters, the chaos originating from the PLL device can be either bounded or unbounded in the phase direction. Bounded and unbounded chaos differs in terms of the flatness of the power spectrum associated with the chaotic signal. Random bits are generated by regular sampling of the signal from bounded and unbounded chaos. A white Gaussian noise source is also sampled regularly to generate random bits. By varying the sampling frequency, and based on the autocorrelation and the approximate entropy analysis of the resulting bit sequences, a comparison is made between bounded chaos, unbounded chaos and Gaussian white noise as an entropy source for random number generators.

Identification of suitable embedding dimensions and lags for time series generated by chaotic, finite-dimensional systems

In the field of nonlinear dynamics, many methods have been proposed to tackle the issue of optimally setting embedding dimension and lag in order to analyze sampled scalar signals. However, intrinsic statistical uncertainties due to the finiteness of input sequences severely hinder a general solution to the problem. A more achievable approach consists of assessing sets of dimension and lag pairs that are equivalently suitable to embed a time series. Here we present a method to identify these sets of embedding pairs, under the hypothesis that the time series of interest is generated by a chaotic, finite-dimensional dynamical system. We first introduce a ``distance gauge transformation'' based on the analytical forms of correlation integrals corresponding to a Gaussian white noise source. We show that in this new distance gauge, correlation integrals generated by chaotic, finite-dimensional systems are characterized by distinctive features, whose absence is a marker of the unsuitability of the underlying embedding choice. By means of a new estimator of the correlation dimension that relies on the new distance gauge, sets of suitable embedding pairs are finally identified by looking at the uniformity of the estimation. The method is completely automatic and was successfully tested on both synthetic and experimental time series. It also provides a tool to estimate the redundance and irrelevance timescales of the system that underlie the time series as well as a lower constraint to the sampling rate. The method is suitable for applications in research fields where a chaotic behavior has to be identified, such as neuroscience, geophysics, and economics.