Showing papers on "White noise published in 2020"

DiffWave: A Versatile Diffusion Model for Audio Synthesis

Abstract: In this work, we propose DiffWave, a versatile diffusion probabilistic model for conditional and unconditional waveform generation. The model is non-autoregressive, and converts the white noise signal into structured waveform through a Markov chain with a constant number of steps at synthesis. It is efficiently trained by optimizing a variant of variational bound on the data likelihood. DiffWave produces high-fidelity audios in different waveform generation tasks, including neural vocoding conditioned on mel spectrogram, class-conditional generation, and unconditional generation. We demonstrate that DiffWave matches a strong WaveNet vocoder in terms of speech quality (MOS: 4.44 versus 4.43), while synthesizing orders of magnitude faster. In particular, it significantly outperforms autoregressive and GAN-based waveform models in the challenging unconditional generation task in terms of audio quality and sample diversity from various automatic and human evaluations.

Finite-Horizon $H_{\infty}$ State Estimation for Periodic Neural Networks Over Fading Channels

Abstract: The problem of finite-horizon $H_{\infty}$ state estimator design for periodic neural networks over multiple fading channels is studied in this paper. To characterize the measurement signals transmitted through different channels experiencing channel fading, a multiple fading channels model is considered. For investigating the situation of correlated fading channels, a set of correlated random variables is introduced. Specifically, the channel coefficients are described by white noise processes and are assumed to be correlated. Two sufficient criteria are provided, by utilizing a stochastic analysis approach, to guarantee that the estimation error system is stochastically stable and achieves the prescribed $H_{\infty}$ performance. Then, the parameters of the estimator are derived by solving recursive linear matrix inequalities. Finally, some simulation results are shown to illustrate the effectiveness of the proposed method.

Testing for calibration systematics in the EDGES low-band data using Bayesian model selection

Abstract: Cosmic Dawn, when the first stars and proto-galaxies began to form, is commonly expected to be accompanied by an absorption signature at radio frequencies. This feature arises as Lyman-$\alpha$ photons emitted by these first luminous objects couple the 21 cm excitation temperature of intergalactic hydrogen gas to its kinetic temperature, driving it into absorption relative to the CMB. The detailed properties of this absorption profile encode powerful information about the physics of Cosmic Dawn. Recently, Bowman et al. analysed data from the EDGES low-band radio antenna and found an unexpectedly deep absorption profile centred at 78 MHz, which could be a detection of this signature. Their specific analysis fit their measurements using a polynomial foreground model, a flattened Gaussian absorption profile and a white noise model; we argue that a more accurate model, that includes a detailed noise model and accounting for the effects of plausible calibration errors, is essential for describing the EDGES data set. We perform a Bayesian evidence-based comparison of models of the EDGES low-band data set and find that those incorporating these additional components are decisively preferred. The subset of the best fitting models of the data that include a global signal favour an amplitude consistent with standard cosmological assumptions (A < 209 mK). However, there is not strong evidence to favour models of the data including a global 21 cm signal over those without one. Ultimately, we find that the derivation of robust constraints on astrophysics from the data is limited by the presence of systematics.

Systematic convergence of nonlinear stochastic estimators on the Special Orthogonal Group SO(3)

Abstract: This paper introduces two novel nonlinear stochastic attitude estimators developed on the Special Orthogonal Group \mathbb{SO}\left(3\right) with the tracking error of the normalized Euclidean distance meeting predefined transient and steady-state characteristics. The tracking error is confined to initially start within a predetermined large set such that the transient performance is guaranteed to obey dynamically reducing boundaries and decrease smoothly and asymptotically to the origin in probability from almost any initial condition. The proposed estimators produce accurate attitude estimates with remarkable convergence properties using measurements obtained from low-cost inertial measurement units. Unit-quaternion representation of the proposed filters are presented. The estimators proposed in continuous form are complemented by their discrete versions for the implementation purposes. The simulation results illustrate the effectiveness and robustness of the proposed estimators against uncertain measurements and large initialization error, whether in continuous or discrete form. Keywods: Attitude estimates, transient, steady-state error, nonlinear filter, special orthogonal group, SO(3), stochastic system, stochastic differential equations, Ito, Stratonovich, asymptotic stability, Wong-Zakai, inertial measurment unit, IMU, prescribed performance function, Euler Angles, roll, bitch, yaw, color noise, white noise, Nonlinear attitude filter, Nonlinear attitude observer, Orientation, nonlinear stochastic attitude filter on SO(3), unit-quaternion based nonlinear stochastic attitude filter, discrete stochastic attitude filter.

Strong approximation of monotone stochastic partial differential equations driven by white noise

Abstract: We establish an optimal strong convergence rate of a fully discrete numerical scheme for second order parabolic stochastic partial differential equations with monotone drifts, including the stochastic Allen-Cahn equation, driven by an additive space-time white noise Our first step is to transform the original stochastic equation into an equivalent random equation whose solution possesses more regularity than the original one Then we use the backward Euler in time and spectral Galerkin in space to fully discretize this random equation By the monotone assumption, in combination with the factorization method and stochastic calculus in martingale-type 2 Banach spaces, we derive a uniform maximum norm estimation and a Holder-type regularity for both stochastic and random equations Finally, the strong convergence rate of the proposed fully discrete scheme under the $l_t^\infty L^2_\omega L^2_x \cap l_t^q L^q_\omega L^q_x$-norm is obtained Several numerical experiments are carried out to verify the theoretical result

Approximate Message Passing algorithms for rotationally invariant matrices.

Abstract: Approximate Message Passing (AMP) algorithms have seen widespread use across a variety of applications. However, the precise forms for their Onsager corrections and state evolutions depend on properties of the underlying random matrix ensemble, limiting the extent to which AMP algorithms derived for white noise may be applicable to data matrices that arise in practice. In this work, we study more general AMP algorithms for random matrices $W$ that satisfy orthogonal rotational invariance in law, where $W$ may have a spectral distribution that is different from the semicircle and Marcenko-Pastur laws characteristic of white noise. The Onsager corrections and state evolutions in these algorithms are defined by the free cumulants or rectangular free cumulants of the spectral distribution of $W$. Their forms were derived previously by Opper, Cakmak, and Winther using non-rigorous dynamic functional theory techniques, and we provide rigorous proofs. Our motivating application is a Bayes-AMP algorithm for Principal Components Analysis, when there is prior structure for the principal components (PCs) and possibly non-white noise. For sufficiently large signal strengths and any non-Gaussian prior distributions for the PCs, we show that this algorithm provably achieves higher estimation accuracy than the sample PCs.

Partial Discharge Signal Denoising Based on Singular Value Decomposition and Empirical Wavelet Transform

Abstract: Online partial discharge (PD) monitoring is an important means to detect insulation deterioration. However, it is difficult to extract the PD signal due to various interferences in the field. Noisy PD signal is used to judge the status of insulation, which would affect the conclusion; therefore, denoising PD signal is a major task in online PD monitoring. Common methods for PD denoising include the empirical mode decomposition (EMD) and wavelet transform; however, the denoising results are highly dependent on the modal aliasing, the selection of mother wavelets, and decomposition levels. This article proposes a method to solve these problems. This method uses traditionally singular value transform [singular value decomposition (SVD)] to reconstruct narrowband interference and remove it. Next, the empirical wavelet transform (EWT) is carried out for the PD signal that has residual white noise. Then, the noisy signal is decomposed into several modes corresponding to each spectrum segment. The $3~\sigma $ principle is used to denoise the modes with large kurtosis, and the modes are combined into a reference signal. The start-end positions of PD signal are then obtained from the reference signal. Finally, the PD signal is obtained by time-domain denoising. The results from both simulated and actual field detection signals show the excellent performance of this method.

Analysis of White Noise on Power Frequency Estimation by DFT-Based Frequency Shifting and Filtering Algorithm

Abstract: The frequency shifting and filtering (FSF) algorithm, a variant of DFT, has the merit of high efficiency for frequency analysis thanks to its simple implementation in the time domain. However, the inevitable white noise injected by various factors leads to inaccurate frequency estimation in practical measurement. This article investigates the influence of a stationary white noise on FSF-based frequency estimation of the power system. The variance expression of the frequency estimator is derived theoretically and compared to its unbiased Cramer–Rao lower bound (CRLB). The obtained results are validated by several computer simulations.

Renormalizing the Kardar–Parisi–Zhang Equation in $$d\ge 3$$ in Weak Disorder

Abstract: We study Kardar–Parisi–Zhang equation in spatial dimension 3 or larger driven by a Gaussian space–time white noise with a small convolution in space. When the noise intensity is small, it is known that the solutions converge to a random limit as the smoothing parameter is turned off. We identify this limit, in the case of general initial conditions ranging from flat to droplet. We provide strong approximations of the solution which obey exactly the limit law. We prove that this limit has sub-Gaussian lower tails, implying existence of all negative (and positive) moments.

Convergence of transport noise to Ornstein–Uhlenbeck for 2D Euler equations under the enstrophy measure

Abstract: We consider the vorticity form of the 2D Euler equations which is perturbed by a suitable transport type noise and has white noise initial condition. It is shown that stationary solutions of this equation converge to the unique stationary solution of the 2D Navier–Stokes equation driven by the space-time white noise.

Weak SINDy: Galerkin-Based Data-Driven Model Selection

Abstract: We present a weak formulation and discretization of the system discovery problem from noisy measurement data. This method of learning differential equations from data fits into a new class of algorithms that replace pointwise derivative approximations with linear transformations and a variance reduction technique. Our approach improves on the standard SINDy algorithm by orders of magnitude. We first show that in the noise-free regime, this so-called Weak SINDy (WSINDy) framework is capable of recovering the dynamic coefficients to very high accuracy, with the number of significant digits equal to the tolerance of the data simulation scheme. Next we show that the weak form naturally accounts for white noise by identifying the correct nonlinearities with coefficient error scaling favorably with the signal-to-noise ratio while significantly reducing the size of linear systems in the algorithm. In doing so, we combine the ease of implementation of the SINDy algorithm with the natural noise-reduction of integration to arrive at a more robust and user-friendly method of sparse recovery that correctly identifies systems in both small-noise and large-noise regimes.

A Denoising Algorithm for Partial Discharge Measurement Based on the Combination of Wavelet Threshold and Total Variation Theory

Abstract: In electrical engineering, partial discharge (PD) measurement is frequently employed to detect insulation defects and judge insulation conditions of high-voltage electrical apparatus. However, it is easily corrupted by white noises in the field. In this article, a joint algorithm is proposed, in which the wavelet threshold and total variation (TV) denoising methods are combined by the convex optimization theory to denoise ultrahigh frequency (UHF) PD signals corrupted by white noises. Since the two respective methods are incorporated into the joint algorithm, it is with high potential to reduce oscillation error introduced by the wavelet threshold method and eliminate stair error introduced by the TV denoising method. In order to validate the effect of the proposed algorithm, a numerical simulation is carried out to compare it with several existing methods. Indicators of their performance are computed, and the results verify that the proposed algorithm outperforms all the other methods.

Wavelet entropy-based evaluation of intrinsic predictability of time series.

Abstract: Intrinsic predictability is imperative to quantify inherent information contained in a time series and assists in evaluating the performance of different forecasting methods to get the best possible prediction. Model forecasting performance is the measure of the probability of success. Nevertheless, model performance or the model does not provide understanding for improvement in prediction. Intuitively, intrinsic predictability delivers the highest level of predictability for a time series and informative in unfolding whether the system is unpredictable or the chosen model is a poor choice. We introduce a novel measure, the Wavelet Entropy Energy Measure (WEEM), based on wavelet transformation and information entropy for quantification of intrinsic predictability of time series. To investigate the efficiency and reliability of the proposed measure, model forecast performance was evaluated via a wavelet networks approach. The proposed measure uses the wavelet energy distribution of a time series at different scales and compares it with the wavelet energy distribution of white noise to quantify a time series as deterministic or random. We test the WEEM using a wide variety of time series ranging from deterministic, non-stationary, and ones contaminated with white noise with different noise-signal ratios. Furthermore, a relationship is developed between the WEEM and Nash-Sutcliffe Efficiency, one of the widely known measures of forecast performance. The reliability of WEEM is demonstrated by exploring the relationship to logistic map and real-world data.

Identification and Estimation in Non-Fundamental Structural VARMA Models

Abstract: The basic assumption of a structural vector autoregressive moving-average (SVARMA) model is that it is driven by a white noise whose components are uncorrelated or independent and can be interpreted as economic shocks, called “structural” shocks. When the errors are Gaussian, independence is equivalent to non-correlation and these models face two identification issues. The first identification problem is “static” and is due to the fact that there is an infinite number of linear transformations of a given random vector making its components uncorrelated. The second identification problem is “dynamic” and is a consequence of the fact that, even if a SVARMA admits a non invertible moving average (MA) matrix polynomial, it may feature the same second-order dynamic properties as a VARMA process in which the MA matrix polynomials are invertible (the fundamental representation). The aim of this paper is to explain that these difficulties are mainly due to the Gaussian assumption, and that both identification challenges are solved in a non-Gaussian framework if the structural shocks are assumed to be instantaneously and serially independent. We develop new parametric and semi-parametric estimation methods that accommodate non-fundamentalness in the moving average dynamics. The functioning and performances of these methods are illustrated by applications conducted on both simulated and real data.

Tracking Performance Limitations of MIMO Networked Control Systems With Multiple Communication Constraints

Abstract: In this paper, the tracking performance limitation of networked control systems (NCSs) is studied. The NCSs are considered as continuous-time linear multi-input multioutput (MIMO) systems with random reference noises. The controlled plants include unstable poles and nonminimum phase (NMP) zeros. The output feedback path is affected by multiple communication constraints. We focus on some basic communication constraints, including additive white noise (AWN), quantization noise, bandwidth, as well as encoder-decoder. The system performance is evaluated with the tracking error energy, and used a two-degree-of-freedom (2DOF) controller. The explicit representation of the tracking performance is given in this paper. The results indicate the tracking performance limitations rely to internal characteristics of the plant (unstable poles and NMP zeros), reference noises [the reference noise power distribution (RNPD) and its directions], and the characteristics of communication constraints. The characteristics of communication constraints include communication noise power distribution (CNPD); quantization noise power distribution (QNPD), and their distribution directions; transform bandwidth allocation (TBA); transform encoder-decoder allocation (TEA), and their allocation directions; and NMP zeros and MP part of bandwidth. Moreover, the tracking performance limitations are also affected by the angles between the each transform NMP zero direction and RNPD direction, and these angles between each transform unstable poles direction and the direction of communication constraint distribution/allocation. In addition, for MIMO NCSs, bandwidth (there are not identical two channels) can always affect the direction of unstable poles, and the channel allocation of bandwidth and encode-decode may be used for a feasible method for the performance allocation of each channel. Finally, an instance is given for verifying the effectiveness of the theoretical outcomes.

Propagation characteristics of weak signal in feedforward Izhikevich neural networks

Abstract: The feedforward neural network is widely applied in various machine learning architectures, in which the synaptic weight between layers plays an important role in the weak signal propagation. In this paper, the five-layer Izhikevich neural networks with excitatory or excitatory–inhibition neurons are employed to study the effect of Gaussian white noise and synaptic weight between layers on the weak signal transmission characteristics of the subthreshold excitatory postsynaptic currents signal imposed on the input layer. It can be found that there is an optimum value of noise intensity (a medium noise intensity) at which the weak signal can be stably propagated in the five-layer Izhikevich neural networks. The spike timing precision (STP) under the optimal noise intensity will become maximum by increasing the synaptic weight. The noise intensity and synaptic weight corresponding to the maximum value of the STP in the excitatory–inhibition network are smaller than those in excitatory–inhibition network. For the smaller or the bigger noise intensity, however, the STP will become very small, and the weak signal cannot be transmitted from the input layer to the output layer. Furthermore, the weak signal is propagated from the input layer to the output layer and enhanced under a larger synaptic weight in the feedforward neural networks.

19.3 A 200dB FoM 4-to-5GHz Cryogenic Oscillator with an Automatic Common-Mode Resonance Calibration for Quantum Computing Applications

Abstract: Low-power, low phase noise (PN) cryogenic frequency generation is required for the control electronics of quantum computers. To avoid limiting the performance of quantum bits, the frequency noise of a PLL should be < 1.9 kHz rms [1]. However, it is challenging for RF oscillators, as the heart of frequency synthesizers to satisfy such a requirement at cryogenic temperatures (CT), since 1) white noise in nanoscale CMOS devices is limited by temperature-independent shot noise; 2) the transistor 1/f noise is much higher, resulting in the oscillator PN being dominated by the 30dB/dec region [1].

Nonlinear stochastic modeling with Langevin regression

Abstract: Many physical systems characterized by nonlinear multiscale interactions can be effectively modeled by treating unresolved degrees of freedom as random fluctuations. However, even when the microscopic governing equations and qualitative macroscopic behavior are known, it is often difficult to derive a stochastic model that is consistent with observations. This is especially true for systems such as turbulence where the perturbations do not behave like Gaussian white noise, introducing non-Markovian behavior to the dynamics. We address these challenges with a framework for identifying interpretable stochastic nonlinear dynamics from experimental data, using both forward and adjoint Fokker-Planck equations to enforce statistical consistency. If the form of the Langevin equation is unknown, a simple sparsifying procedure can provide an appropriate functional form. We demonstrate that this method can effectively learn stochastic models in two artificial examples: recovering a nonlinear Langevin equation forced by colored noise and approximating the second-order dynamics of a particle in a double-well potential with the corresponding first-order bifurcation normal form. Finally, we apply the proposed method to experimental measurements of a turbulent bluff body wake and show that the statistical behavior of the center of pressure can be described by the dynamics of the corresponding laminar flow driven by nonlinear state-dependent noise.

Invariance of white noise for KdV on the line

Abstract: We consider the Korteweg–de Vries equation with white noise initial data, posed on the whole real line, and prove the almost sure existence of solutions. Moreover, we show that the solutions obey the group property and follow a white noise law at all times, past or future. As an offshoot of our methods, we also obtain a new proof of the existence of solutions and the invariance of white noise measure in the torus setting.