Showing papers on "White noise published in 2003"

Noise spectrum estimation in adverse environments: improved minima controlled recursive averaging

Abstract: Noise spectrum estimation is a fundamental component of speech enhancement and speech recognition systems. We present an improved minima controlled recursive averaging (IMCRA) approach, for noise estimation in adverse environments involving nonstationary noise, weak speech components, and low input signal-to-noise ratio (SNR). The noise estimate is obtained by averaging past spectral power values, using a time-varying frequency-dependent smoothing parameter that is adjusted by the signal presence probability. The speech presence probability is controlled by the minima values of a smoothed periodogram. The proposed procedure comprises two iterations of smoothing and minimum tracking. The first iteration provides a rough voice activity detection in each frequency band. Then, smoothing in the second iteration excludes relatively strong speech components, which makes the minimum tracking during speech activity robust. We show that in nonstationary noise environments and under low SNR conditions, the IMCRA approach is very effective. In particular, compared to a competitive method, it obtains a lower estimation error, and when integrated into a speech enhancement system achieves improved speech quality and lower residual noise.

The effect of coloured noise on the uncertainties of rates estimated from geodetic time series

Abstract: Until recently, it was typically assumed that only white noise was present in geodetic time series. However, several data sets have now provided evidence for the presence of power-law noise. The uncertainty of any rates estimated from such data sets is dependent on the error model assumed for the data. Here a general form for the covariance matrix for any power-law noise model is introduced and simple equations that relate the rate uncertainty to the noise amplitude, sampling frequency and length of the time series are empirically derived. In addition, equations to analyse data sets and obtain a rate uncertainty when computational speed is at a premium are provided. These equations are tested against previously published geodetic data sets.

A generalized subspace approach for enhancing speech corrupted by colored noise

Abstract: A generalized subspace approach is proposed for enhancement of speech corrupted by colored noise. A nonunitary transform, based on the simultaneous diagonalization of the clean speech and noise covariance matrices, is used to project the noisy signal onto a signal-plus-noise subspace and a noise subspace. The clean signal is estimated by nulling the signal components in the noise subspace and retaining the components in the signal subspace. The applied transform has built-in prewhitening and can therefore be used in general for colored noise. The proposed approach is shown to be a generalization of the approach proposed by Y. Ephraim and H.L. Van Trees (see ibid., vol.3, p.251-66, 1995) for white noise. Two estimators are derived based on the nonunitary transform, one based on time-domain constraints and one based on spectral domain constraints. Objective and subjective measures demonstrate improvements over other subspace-based methods when tested with TIMIT sentences corrupted with speech-shaped noise and multi-talker babble.

A general fractional white noise theory and applications to finance

Abstract: We present a new framework for fractional Brownian motion in which processes with all indices can be considered under the same probability measure. Our results extend recent contributions by Hu, Oksendal, Duncan, Pasik-Duncan, and others. As an application we develop option pricing in a fractional Black-Scholesmarket with a noise process driven by a sum of fractional Brownian motions with various Hurst indices.

Systematic Strategies for Stochastic Mode Reduction in Climate

Abstract: A systematic strategy for stochastic mode reduction is applied here to three prototype ‘‘toy’’ models with nonlinear behavior mimicking several features of low-frequency variability in the extratropical atmosphere. Two of the models involve explicit stable periodic orbits and multiple equilibria in the projected nonlinear climate dynamics. The systematic strategy has two steps: stochastic consistency and stochastic mode elimination. Both aspects of the mode reduction strategy are tested in an a priori fashion in the paper. In all three models the stochastic mode elimination procedure applies in a quantitative fashion for moderately large values of « 0.5 or even « 1, where the parameter « roughly measures the ratio of correlation times of unresolved variables to resolved climate variables, even though the procedure is only justified mathematically for « K 1. The results developed here provide some new perspectives on both the role of stable nonlinear structures in projected nonlinear climate dynamics and the regression fitting strategies for stochastic climate modeling. In one example, a deterministic system with 102 degrees of freedom has an explicit stable periodic orbit for the projected climate dynamics in two variables; however, the complete deterministic system has instead a probability density function with two large isolated peaks on the ‘‘ghost’’ of this periodic orbit, and correlation functions that only weakly ‘‘shadow’’ this periodic orbit. Furthermore, all of these features are predicted in a quantitative fashion by the reduced stochastic model in two variables derived from the systematic theory; this reduced model has multiplicative noise and augmented nonlinearity. In a second deterministic model with 101 degrees of freedom, it is established that stable multiple equilibria in the projected climate dynamics can be either relevant or completely irrelevant in the actual dynamics for the climate variable depending on the strength of nonlinearity and the coupling to the unresolved variables. Furthermore, all this behavior is predicted in a quantitative fashion by a reduced nonlinear stochastic model for a single climate variable with additive noise, which is derived from the systematic mode reduction procedure. Finally, the systematic mode reduction strategy is applied in an idealized context to the stochastic modeling of the effect of mountain torque on the angular momentum budget. Surprisingly, the strategy yields a nonlinear stochastic equation for the large-scale fluctuations, and numerical simulations confirm significantly improved predicted correlation functions from this model compared with a standard linear model with damping and white noise forcing.

Modeling and analysis of high-speed links

Abstract: Very low bit error rate (BER) requirements for the operation of a high-speed link system require a very precise analysis of the link performance in order to prevent unrealistic specifications on both IC design and communication algorithm development. This paper presents the analysis of the noise and distortion sources in a high-speed link system, and their impact on the choice and effectiveness of different communication techniques. Phase-locked loop and clock-and-data recovery loop modeling is also described. It is shown that the most dominant noise and distortion sources are colored and bounded, as opposed to standard unbounded Gaussian white noise assumptions, which yield large errors in the estimation of the link performance and comparison of different signaling techniques. With very low BER requirements, shape of probability distribution of noise and distortion sources and their correlations, are much more important than just their total power, which contrasts the standard analysis in communication systems.

Blind estimation of reverberation time.

Abstract: The reverberation time (RT) is an important parameter for characterizing the quality of an auditory space. Sounds in reverberant environments are subject to coloration. This affects speech intelligibility and sound localization. Many state-of-the-art audio signal processing algorithms, for example in hearing-aids and telephony, are expected to have the ability to characterize the listening environment, and turn on an appropriate processing strategy accordingly. Thus, a method for characterization of room RT based on passively received microphone signals represents an important enabling technology. Current RT estimators, such as Schroeder’s method, depend on a controlled sound source, and thus cannot produce an online, blind RT estimate. Here, a method for estimating RT without prior knowledge of sound sources or room geometry is presented. The diffusive tail of reverberation was modeled as an exponentially damped Gaussian white noise process. The time-constant of the decay, which provided a measure of the RT, was estimated using a maximum-likelihood procedure. The estimates were obtained continuously, and an order-statistics filter was used to extract the most likely RT from the accumulated estimates. The procedure was illustrated for connected speech. Results obtained for simulated and real room data are in good agreement with the real RT values.

Stability analysis and synthesis for scalar linear systems with a quantized feedback

Abstract: It is well known that a linear system controlled by a quantized feedback may exhibit the wild dynamic behavior which is typical of a nonlinear system. In the classical literature devoted to control with quantized feedback, the flow of information in the feedback was not considered as a critical parameter. Consequently, in that case, it was natural in the control synthesis to simply choose the quantized feedback approximating the one provided by the classical methods, and to model the quantization error as an additive white noise. On the other hand, if the flow of information has to be limited, for instance, because of the use of a transmission channel with limited capacity, some specific considerations are in order. The aim of this paper is to obtain a detailed analysis of linear scalar systems with a stabilizing quantized feedback control. First, a general framework based on a sort of Lyapunov approach encompassing known stabilization techniques is proposed. In this case, a rather complete analysis can be obtained through a nice geometric characterization of asymptotically stable closed-loop maps. In particular, a general tradeoff relation between the number of quantization intervals, quantifying the information flow, and the convergence time is established. Then, an alternative stabilization method, based on the chaotic behavior of piecewise affine maps is proposed. Finally, the performances of all these methods are compared.

The Stochastic Nonlinear Schrödinger Equation in H 1

Abstract: We investigate the local and global existence of solutions in the energy space H 1(R n ) for stochastic nonlinear Schrodinger equations with either additive or multiplicative noise. The noise is assumed to be white in time and correlated in the space variables.

Correlated noise in a logistic growth model.

Abstract: The logistic differential equation is used to analyze cancer cell population, in the presence of a correlated Gaussian white noise. We study the steady state properties of tumor cell growth and discuss the effects of the correlated noise. It is found that the degree of correlation of the noise can cause tumor cell extinction.

A comparative study for orthogonal subspace projection and constrained energy minimization

Abstract: We conduct a comparative study and investigate the relationship between two well-known techniques in hyperspectral image detection and classification: orthogonal subspace projection (OSP) and constrained energy minimization. It is shown that they are closely related and essentially equivalent provided that the noise is white with large SNR. Based on this relationship, the performance of OSP can be improved via data-whitening and noise-whitening processes.

What causes a Neuron to spike

Abstract: The computation performed by a neuron can be formulated as a combination of dimensional reduction in stimulus space and the nonlinearity inherent in a spiking output. White noise stimulus and reverse correlation (the spike-triggered average and spike-triggered covariance) are often used in experimental neuroscience to "ask" neurons which dimensions in stimulus space they are sensitive to and to characterize the nonlinearity of the response. In this article, we apply reverse correlation to the simplest model neuron with temporal dynamics--the leaky integrate-and-fire model--and find that for even this simple case, standard techniques do not recover the known neural computation. To overcome this, we develop novel reverse-correlation techniques by selectively analyzing only "isolated" spikes and taking explicit account of the extended silences that precede these isolated spikes. We discuss the implications of our methods to the characterization of neural adaptation. Although these methods are developed in the context of the leaky integrate-and-fire model, our findings are relevant for the analysis of spike trains from real neurons.

A method for modifying the image quality parameters of digital radiographic images.

Abstract: A new computer simulation approach is presented that is capable of modeling several varieties of digital radiographic systems by their image quality characteristics. In this approach, the resolution and noise characteristics of ideal supersampled input images are modified according to input modulation transfer functions (MTFs) and noise power spectra (NPS). The modification process is separated into two routines-one for modification of the resolution and another for modification of the noise characteristics of the input image. The resolution modification routine blurs the input image by applying a frequency filter described by the input MTF. The resulting blurred image is then reduced to its final size to account for the sampling process of the digital system. The noise modification routine creates colored noise by filtering the frequency components of a white noise spectrum according to the input noise power. This noise is then applied to the image by a moving region of interest to account for variations in noise due to differences in attenuation. In order to evaluate the efficacy of the modification routines, additional routines were developed to assess the resolution and noise of digital images. The MTFs measured from the output images of the resolution modification routine were within 3% of the input MTF The NPS measured from the output images of the noise modification routine were within 2% of the input NPS. The findings indicate that the developed modification routines provide a good means of simulating the resolution and noise characteristics of digital radiographic systems for optimization or processing purposes.

Analytic expressions for rate and CV of a type I Neuron driven by white Gaussian noise

Abstract: We study the one-dimensional normal form of a saddle-node system under the influence of additive gaussian white noise and a static "bias current" input parameter, a model that can be looked upon as the simplest version of a type I neuron with stochastic input. This is in contrast with the numerous studies devoted to the noise-driven leaky integrate-and-fire neuron. We focus on the firing rate and coefficient of variation (CV) of the interspike interval density, for which scaling relations with respect to the input parameter and noise intensity are derived. Quadrature formulas for rate and CV are numerically evaluated and compared to numerical simulations of the system and to various approximation formulas obtained in different limiting cases of the model. We also show that caution must be used to extend these results to the Θ neuron model with multiplicative gaussian white noise. The correspondence between the first passage time statistics for the saddle-node model and the Θ neuron model is obtained only in the Stratonovich interpretation of the stochastic Θ neuron model, while previous results have focused only on the Ito interpretation. The correct Stratonovich interpretation yields CVs that are still relatively high, although smaller than in the Ito interpretation; it also produces certain qualitative differences, especially at larger noise intensities. Our analysis provides useful relations for assessing the distance to threshold and the level of synaptic noise in real type I neurons from their firing statistics. We also briefly discuss the effect of finite boundaries (finite values of threshold and reset) on the firing statistics.

Extension of the signal subspace speech enhancement approach to colored noise

Abstract: The signal subspace approach for speech enhancement is extended to colored-noise processes. Explicit forms for the linear time-domain- and spectral-domain-constrained estimators are presented. These estimators minimize the average signal distortion power for given constraints on the residual noise power in the time and spectral domains, respectively. Equivalent implementations of the two estimators using the whitening approach are described.

Point source detection using the Spherical Mexican Hat Wavelet on simulated all-sky Planck maps

Abstract: We present an estimation of the point source (PS) catalogue that could be extracted from the forthcoming ESA Planck mission data. We have applied the Spherical Mexican Hat Wavelet (SMHW) to simulated all-sky maps that include CMB, Galactic emission (thermal dust, free-free and synchrotron), thermal Sunyaev-Zel’dovich effect and PS emission, as well as instrumental white noise . This work is an extension of the one presented in Vielva et al. (2001a). We have developed an algorithm focused on a fast local optimal scale determination, that is crucial to achieve a PS catalogue with a large number of detections and a low flux limit. An important effort has been also done to reduce the CPU time processor for spherical harmonic transformation, in order to perform the PS detection in a reasonable time. The presented algorithm is able to provide a PS catalogue above fluxes: 0.48 Jy (857 GHz), 0.49 Jy (545 GHz), 0.18 Jy (353 GHz), 0.12 Jy (217 GHz), 0.13 Jy (143 GHz), 0.16 Jy (100 GHz HFI), 0.19 Jy (100 GHz LFI), 0.24 Jy (70 GHz), 0.25 Jy (44 GHz) and 0.23 Jy (30 GHz). We detect around 27700 PS at the highest frequency Planck channel and 2900 at the 30 GHz one. The completeness level are: 70% (857 GHz), 75% (545 GHz), 70% (353 GHz), 80% (217 GHz), 90% (143 GHz), 85% (100 GHz HFI), 80% (100 GHz LFI), 80% (70 GHz), 85% (44 GHz) and 80% (30 GHz). In addition, we can find several PS at different channels, allowing the study of the spectral behaviour and the physical processes acting on them. We also present the basic procedure to apply the method in maps convolved with asymmetric beams. The algorithm takes � 72 hours for the most CPU time demanding channel (857 GHz) in a Compaq HPC320 (Alpha EV68 1 GHz processor) and requires 4 GB of RAM memory; the CPU time goes as O(NRoNpix 3/2 log(Npix)), where Npix is the number of pixels in the map and NRo is the number of optimal scales needed.

Performance of quadratic time-frequency distributions as instantaneous frequency estimators

Abstract: General performance analysis of the shift covariant class of quadratic time-frequency distributions (TFDs) as instantaneous frequency (IF) estimators, for an arbitrary frequency-modulated (FM) signal, is presented. Expressions for the estimation bias and variance are derived. This class of distributions behaves as an unbiased estimator in the case of monocomponent signals with a linear IF. However, when the IF is not a linear function of time, then the estimate is biased. Cases of white stationary and white nonstationary additive noises are considered. The well-known results for the Wigner distribution (WD) and linear FM signal, and the spectrogram of signals whose IF may be considered as a constant within the lag window, are presented as special cases. In addition, we have derived the variance expression for the spectrogram of a linear FM signal that is quite simple but highly signal dependent. This signal is considered in the cases of other commonly used distributions, such as the Born-Jordan and the Choi-Williams distributions. It has been shown that the reduced interference distributions outperform the WD but only in the case when the IF is constant or its variations are small. Analysis is extended to the IF estimation of signal components in the case of multicomponent signals. All theoretical results are statistically confirmed.

Lévy-Driven Langevin Systems: Targeted Stochasticity

Abstract: Langevin dynamics driven by random Wiener noise (“white noise”), and the resulting Fokker–Planck equation and Boltzmann equilibria are fundamental to the understanding of transport and relaxation. However, there is experimental and theoretical evidence that the use of the Gaussian Wiener noise as an underlying source of randomness in continuous time systems may not always be appropriate or justified. Rather, models incorporating general Levy noises, should be adopted. In this work we study Langevin systems driven by general Levy, rather than Wiener, noises. Various issues are addressed, including: (i) the evolution of the probability density function of the system's state; (ii) the system's steady state behavior; and, (iii) the attainability of equilibria of the Boltzmann type. Moreover, the issue of reverse engineering is introduced and investigated. Namely: how to design a Langevin system, subject to a given Levy noise, that would yield a pre-specified “target” steady state behavior. Results are complemented with a multitude of examples of Levy driven Langevin systems.

Acoustic Source Localization and Beamforming: Theory and Practice

Abstract: We consider the theoretical and practical aspects of locating acoustic sources using an array of microphones. A maximum-likelihood (ML) direct localization is obtained when the sound source is near the array, while in the far-field case, we demonstrate the localization via the cross bearing from several widely separated arrays. In the case of multiple sources, an alternating projection procedure is applied to determine the ML estimate of the DOAs from the observed data. The ML estimator is shown to be effective in locating sound sources of various types, for example, vehicle, music, and even white noise. From the theoretical Cramer-Rao bound analysis, we find that better source location estimates can be obtained for high-frequency signals than low-frequency signals. In addition, large range estimation error results when the source signal is unknown, but such unknown parameter does not have much impact on angle estimation. Much experimentally measured acoustic data was used to verify the proposed algorithms.

Spatial Tuning to Virtual Sounds in the Inferior Colliculus of the Guinea Pig

Abstract: How do neurons in the inferior colliculus (IC) encode the spatial location of sound? We have addressed this question using a virtual auditory environment. For this purpose, the individual head-related transfer functions (HRTFs) of 18 guinea pigs were measured under free-field conditions for 122 locations covering the upper hemisphere. From 257 neurons, 94% responded to the short (50-ms) white noise stimulus at 70 dB sound pressure level (SPL). Out of these neurons, 80% were spatially tuned with a receptive field that is smaller than a hemifield (at 70 dB). The remainder responded omnidirectionally or showed fractured receptive fields. The majority of the neurons preferred directions in the contralateral hemisphere. However, preference for front or rear positions and high elevations occurred frequently. For stimulation at 70 dB SPL, the average diameter of the receptive fields, based on half-maximal response, was less than a quarter of the upper hemisphere. Neurons that preferred frontal directions responded weakly or showed no response to posterior directions and vice versa. Hence, front/back discrimination is present at the single-neuron level in the IC. When nonindividual HRTFs were used to create the stimuli, the spatial receptive fields of most neurons became larger, split into several parts, changed position, or the response became omnidirectional. Variation of absolute sound intensity had little effect on the preferred directions of the neurons over a range of 20 to 40 dB above threshold. With increasing intensity, most receptive fields remained constant or expanded. Furthermore, we tested the influence of binaural decorrelation and stimulus bandwidth on spatial tuning. The vast majority of neurons with a low characteristic frequency (<2.5 kHz) lost spatial tuning under stimulation with binaurally uncorrelated noise, whereas high-frequency units were mostly unaffected. Most neurons that showed spatial tuning under broadband stimulation (white noise and 1 octave wide noise) turned omnidirectional when stimulated with 1/3 octave wide noise.

1/f Noise outperforms white noise in sensitizing baroreflex function in the human brain

Abstract: We show that externally added $1/f$ noise more effectively sensitizes the baroreflex centers in the human brain than white noise. We examined the compensatory heart rate response to a weak periodic signal introduced via venous blood pressure receptors while adding $1/f$ or white noise with the same variance to the brain stem through bilateral cutaneous stimulation of the vestibular afferents. In both cases, this noisy galvanic vestibular stimulation optimized covariance between the weak input signals and the heart rate responses. However, the optimal level with $1/f$ noise was significantly lower than with white noise, suggesting a functional benefit of $1/f$ noise for neuronal information transfer in the brain.

Chernoff bounds on pairwise error probabilities of space-time codes

Abstract: We derive Chernoff bounds on pairwise error probabilities of coherent and noncoherent space-time signaling schemes. First, general Chernoff bound expressions are derived for a correlated Ricean fading channel and correlated additive Gaussian noise. Then, we specialize the obtained results to the cases of space-time-separable noise, white noise, and uncorrelated fading. We derive approximate Chernoff bounds for high and low signal-to-noise ratios (SNRs) and propose optimal signaling schemes. We also compute the optimal number of transmitter antennas for noncoherent signaling with unitary mutually orthogonal space-time codes.

Simulation studies of GPS radio occultation measurements

Abstract: [1] The atmospheric propagation of GPS signals under multipath conditions and their detection are simulated. Using the multiple phase screen method, C/A-code modulated L1 signals are propagated through a spherically symmetric refractivity field derived from a high-resolution radio sonde observation. The propagated signals are tracked by a GPS receiver implemented in software and converted to refractivity profiles by the canonical transform technique and the Abel inversion. Ignoring noise and assuming an ideal receiver tracking behavior, the true refractivity profile is reproduced to better than 0.1% at altitudes above 2 km. The nonideal case is simulated by adding between 14 and 24 dB of Gaussian white noise to the signal and tracking the signal with a receiver operating at 50 and 200 Hz sampling frequency using two different carrier phase detectors. In the upper troposphere and stratosphere the fractional refractivity retrieval error is below 0.3% for 50 Hz sampling and below 0.15% for 200 Hz sampling. In the midtroposphere down to altitudes of about 2 km, phase-locked loop tracking induces negative fractional refractivity biases on the order of −1 to −2% at 50 Hz sampling frequency. Modifications to the receiver tracking algorithm significantly improve the retrieval results. In particular, replacing the carrier loop's two-quadrant phase extractor with a four-quadrant discriminator reduces the refractivity biases by a factor of 5; increasing the sampling frequency from 50 to 200 Hz gains another factor of 2.

Orthogonal, exactly periodic subspace decomposition

Abstract: The detection and estimation of machine vibration multiperiodic signals of unknown periods in white Gaussian noise is investigated. New estimates for the subsignals (signals making up the received signal) and their periods are derived using an orthogonal subspace decomposition approach. The concept of exactly periodic signals is introduced. This in turn simplifies and enhances the understanding of periodic signals.

Robust steady-state filtering for systems with deterministic and stochastic uncertainties

Abstract: For uncertain systems containing both deterministic and stochastic uncertainties, we consider two problems of optimal filtering. The first is the design of a linear time-invariant filter that minimizes an upper bound on the mean energy gain between the noise affecting the system and the estimation error. The second is the design of a linear time-invariant filter that minimizes an upper bound on the asymptotic mean square estimation error when the plant is driven by a white noise. We present filtering algorithms that solve each of these problems, with the filter parameters determined via convex optimization based on linear matrix inequalities. We demonstrate the performance of these robust algorithms on a numerical example consisting of the design of equalizers for a communication channel.

Noise-assisted preparation of entangled atoms

Abstract: We discuss the generation of entangled states of two two-level atoms inside an optical cavity. The cavity mode is supposed to be coupled to a white noise with adjustable intensity. We describe how the entanglement between the atoms arise in such a situation. The entanglement is maximized for intermediate values of the noise intensity, while it is a monotonic function of the atomic decay rate. This resembles the phenomenon of stochastic resonance and sheds more light on the idea to exploit the white noise in quantum-information processing.

Statistics of extremal intensities for Gaussian interfaces.

Abstract: The extremal Fourier intensities are studied for stationary Edwards-Wilkinson -type, Gaussian, interfaces with power-law dispersion. We calculate the probability distribution of the maximal intensity and find that, generically, it does not coincide with the distribution of the integrated power spectrum (i.e., roughness of the surface), nor does it obey any of the known extreme statistics limit distributions. The Fisher-Tippett-Gumbel limit distribution is, however, recovered in three cases; (i) in the nondispersive (white noise) limit, (ii) for high dimensions, and (iii) when only short-wavelength modes are kept. In the last two cases the limit distribution emerges in nonconventional scenarios.

Exact stationary probability density functions for non-linear systems under Poisson white noise excitation

Abstract: The paper presents exact stationary probability density functions for systems under Poisson white noise excitation Two different solution methods are outlined In the first one, a class of non-linear systems is determined whose state vector is a memoryless transformation of the state vector of a linear system The second method considers the generalized Fokker–Planck (Kolmogorov-forward) equation Non-linear system functions are identified such that the stationary solution of the system admits a prescribed stationary probability density function Both methods make use of the stochastic integro-differential equations approach This approach seems to have some computational advantages for the determination of exact stationary probability density functions when compared to the stochastic differential equations approach