Showing papers on "White noise published in 1998"

Wavelet-based statistical signal processing using hidden Markov models

Abstract: Wavelet-based statistical signal processing techniques such as denoising and detection typically model the wavelet coefficients as independent or jointly Gaussian. These models are unrealistic for many real-world signals. We develop a new framework for statistical signal processing based on wavelet-domain hidden Markov models (HMMs) that concisely models the statistical dependencies and non-Gaussian statistics encountered in real-world signals. Wavelet-domain HMMs are designed with the intrinsic properties of the wavelet transform in mind and provide powerful, yet tractable, probabilistic signal models. Efficient expectation maximization algorithms are developed for fitting the HMMs to observational signal data. The new framework is suitable for a wide range of applications, including signal estimation, detection, classification, prediction, and even synthesis. To demonstrate the utility of wavelet-domain HMMs, we develop novel algorithms for signal denoising, classification, and detection.

Channel estimation for OFDM systems based on comb-type pilot arrangement in frequency selective fading channels

Abstract: The channel estimation methods for OFDM systems based on a comb-type pilot sub-carrier arrangement are investigated. The channel estimation algorithm based on comb-type pilots is divided into pilot signal estimation and channel interpolation. The pilot signal estimation based on LS or MMSE criteria, together with channel interpolation based on piecewise-linear interpolation or piecewise second-order polynomial interpolation is studied. Owing to the MMSE estimate of the pilot signals, the inter-carrier interference and additive white Gaussian noise are reduced considerably. The computational complexity of pilot signal estimation based on MMSE criterion can be reduced by using a simplified LMMSE estimator with low-rank approximation using singular value decomposition. Phase compensators before and after interpolation are also presented to combat the phase changes of subchannel symbols arising from the frame synchronization errors. Compared to the transform-domain processing based channel estimation algorithm the MMSE estimate of pilot signals together with phase compensated linear interpolation algorithm provides a better performance and requires less computations.

Product high-order ambiguity function for multicomponent polynomial-phase signal modeling

Abstract: Parameter estimation and performance analysis issues are studied for multicomponent polynomial-phase signals (PPSs) embedded in white Gaussian noise. Identifiability issues arising with existing approaches are described first when dealing with multicomponent PPS having the same highest order phase coefficients. This situation is encountered in applications such as synthetic aperture radar imaging or propagation of polynomial phase signals through channels affected by multipath and is thus worthy of a careful analysis. A new approach is proposed based on a transformation called product high-order ambiguity function (PHAF). The use of the PHAF offers a number of advantages with respect to the high-order ambiguity function (HAF). More specifically, it removes the identifiability problem and improves noise rejection capabilities. Performance analysis is carried out using the perturbation method and verified by simulation results.

Adaptive stochastic resonance

Abstract: This paper shows how adaptive systems can learn to add an optimal amount of noise to some nonlinear feedback systems. This "stochastic resonance" (SR) effect occurs in a wide range of physical and biological systems. The noise energy can enhance the faint periodic signals or faint broadband signals that force the dynamical systems. Fuzzy and other adaptive systems can learn to induce SR based only on samples from the process. The paper derives the SR optimality conditions that any stochastic learning system should try to achieve. The adaptive system learns the SR effect as the system performs a stochastic gradient ascent on the signal-to-noise ratio. The stochastic learning scheme does not depend on a fuzzy system or any other adaptive system. Simulations test this SR learning scheme on the popular quartic-bistable dynamical system and on other dynamical systems. The driving noise types range from Gaussian white noise to impulsive noise to chaotic noise.

Fast nearly ML estimation of the parameters of real or complex single tones or resolved multiple tones

Abstract: This paper presents new computationally efficient algorithms for estimating the parameters (frequency, amplitude, and phase) of one or more real tones (sinusoids) or complex tones (cisoids) in noise from a block of N uniformly spaced samples. The first algorithm is an interpolator that uses the peak sample in the discrete Fourier spectrum (DFS) of the data and its two neighbors. We derive Cramer-Rao bounds (CRBs) for such interpolators and show that they are very close to the CRB's for the maximum likelihood (ML) estimator. The new algorithm almost reaches these bounds. A second algorithm uses the five DFS samples centered on the peak to produce estimates even closer to ML. Enhancements are presented that maintain nearly ML performance for small values of N. For multiple complex tones with frequency separations of at least 4/spl pi//N rad/sample, unbiased estimates are obtained by incorporating the new single-tone estimators into an iterative "cyclic descent" algorithm, which is a computationally cheap nonlinear optimization. Single or multiple real tones are handled in the same way. The new algorithms are immune to nonzero mean signals and (provided N is large) remain near-optimal in colored and non-Gaussian noise.

An optimal two stage identification algorithm for Hammerstein-Wiener nonlinear systems

Abstract: An optimal two stage identification algorithm is presented for Hammerstein-Wiener systems where two static nonlinear elements surround a linear block. The proposed algorithm consists of two steps: The first one is the recursive least squares and the second one is the singular value decomposition of two matrices whose dimensions are fixed and do not increase as the number of the data point increases. Moreover, the algorithm is shown to be convergent in the absence of noise and convergent with probability one in the presence of white noise.

Instantaneous frequency estimation using the Wigner distribution with varying and data-driven window length

Abstract: The estimation of the instantaneous frequency (IF) of a harmonic complex-valued signal with an additive noise using the Wigner distribution is considered. If the IF is a nonlinear function of time, the bias of the estimate depends on the window length. The optimal choice of the window length, based on the asymptotic formulae for the variance and bias, can be used in order to resolve the bias-variance tradeoff. However, the practical value of this solution is not significant because the optimal window length depends on the unknown smoothness of the IF. The goal of this paper is to develop an adaptive IF estimator with a time-varying and data-driven window length, which is able to provide quality close to what could be achieved if the smoothness of the IF were known in advance. The algorithm uses the asymptotic formula for the variance of the estimator only. Its value may be easily obtained in the case of white noise and relatively high sampling rate. Simulation shows good accuracy for the proposed adaptive algorithm.

HMM-based strategies for enhancement of speech signals embedded in nonstationary noise

Abstract: An improved hidden Markov model-based (HMM-based) speech enhancement system designed using the minimum mean square error principle is implemented and compared with a conventional spectral subtraction system. The improvements to the system are: (1) incorporation of mixture components in the HMM for noise in order to handle noise nonstationarity in a more flexible manner, (2) two efficient methods in the speech enhancement system design that make the system real-time implementable, and (3) an adaptation method to the noise type in order to accommodate a wide variety of noise expected under the enhancement system's operating environment. The results of the experiments designed to evaluate the performance of the HMM-based speech enhancement systems in comparison with spectral subtraction are reported. Three types of noise-white noise, simulated helicopter noise, and multitalker (cocktail party) noise-were used to corrupt the test speech signals. Both objective (global SNR) and subjective mean opinion score (MOS) evaluations demonstrate consistent superiority of the HMM-based enhancement systems that incorporate the innovations described in this paper over the conventional spectral subtraction method.

The stochastic wave equation in two spatial dimensions

Abstract: Keywords: stochastic wave equation ; Gaussian noise ; process solution Reference PROB-ARTICLE-1998-001View record in Web of Science Record created on 2008-12-01, modified on 2017-05-12

A parametric formulation of the generalized spectral subtraction method

Abstract: In this paper, two short-time spectral amplitude estimators of the speech signal are derived based on a parametric formulation of the original generalized spectral subtraction method. The objective is to improve the noise suppression performance of the original method while maintaining its computational simplicity. The proposed parametric formulation describes the original method and several of its modifications. Based on the formulation, the speech spectral amplitude estimator is derived and optimized by minimizing the mean-square error (MSE) of the speech spectrum. With a constraint imposed on the parameters inherent in the formulation, a second estimator is also derived and optimized. The two estimators are different from those derived in most modified spectral subtraction methods, which are predominantly nonstatistical. When tested under stationary white Gaussian noise and semistationary Jeep noise, they showed improved noise suppression results.

The modified Cramer-Rao bound in vector parameter estimation

Abstract: In this paper we extend the scalar modified Cramer-Rao bound (MCRB) to the estimation of a vector of nonrandom parameters in the presence of nuisance parameters. The resulting bound is denoted with the acronym MCRVB, where "V" stands for "vector". As with the scalar bound, the MCRVB is generally looser than the conventional CRVB, but the two bounds are shown to coincide in some situations of practical interest. The MCRVB is applied to the joint estimation of carrier frequency, phase, and symbol epoch of a linearly modulated waveform corrupted by correlated impulsive noise (encompassing white Gaussian noise as a particular case), wherein data symbols and noise power are regarded as nuisance parameters. In this situation, calculation of the conventional CRVB is infeasible, while application of the MCRVB leads to simple useful expressions with moderate analytical effort. When specialized to the case of white Gaussian noise, the MCRVB yields results already available in the literature in fragmentary form and simplified contexts.

A hybrid analytical-simulation procedure for performance evaluation in M-QAM-OFDM schemes in presence of nonlinear distortions

Abstract: Presents a hybrid analytical-simulation procedure for performance evaluation in M-ary quadrature amplitude modulation (M-QAM) orthogonal frequency-division multiplexing (OFDM) digital radio systems in the presence of nonlinear distortions caused by high-power amplifiers (HPAs). The present analysis is carried out considering an additive white Gaussian noise (AWGN) transmission channel. It is shown that, in the case of an OFDM system with a large number of subcarriers, the distortion on the received symbol caused by the amplifier can be modeled, with good approximation, as a "Gaussian nonlinear noise" added to the received symbol. This important result allows a hybrid analytical-simulation approach to solve the problem of performance evaluation. In practice, the simulation aspect is only used to estimate means and variances of the "nonlinear noise". Such estimated parameters are subsequently used to evaluate analytically the system bit-error rate (BER) using an expression, which takes into account both AWGN and "nonlinear noise" effects. The advantage of the proposed method lies in the strongly reduced computational time. In fact, an accurate estimate of the "nonlinear noise" parameters requires only few iterations when compared with a classical semianalytical approach. This is especially true when low BER values (<10/sup -4/) have to be estimated. The proposed procedure is applied to evaluate M-QAM-OFDM performance in the presence of nonlinear distortions caused by traveling-wave tube (TWT) and solid-state-power (SSP) amplifiers.

Random Processes for Image and Signal Processing

Abstract: Probability theory; random processes; canonical representation; optimal filtering; random models.

Maximum likelihood track-before-detect with fluctuating target amplitude

Abstract: An important problem in target tracking is the detection and tracking of targets in very low signal-to-noise ratio (SNR) environments. In the past, several approaches have been used, including maximum likelihood. The major novelty of this work is the incorporation of a model for fluctuating target amplitude into the maximum likelihood approach for tracking of constant velocity targets. Coupled with a realistic sensor model, this allows the exploitation of signal correlation between resolution cells in the same frame, and also from one frame to the next. The fluctuating amplitude model is a first order model to reflect the inter-frame correlation. The amplitude estimates are obtained using a Kalman filter, from which the likelihood function is derived. A numerical maximization technique avoids problems previously encountered in "velocity filtering" approaches due to mismatch between assumed and actual target velocity, at the cost of additional computation. The Cramer-Rao lower bound (CRLB) is derived for a constant, known amplitude case. Estimation errors are close to this CRLB even when the amplitude is unknown. Results show track detection performance for unknown signal amplitude is nearly the same as that obtained when the correct signal model is used.

Upper semicontinuity of attractors for small random perturbations of dynamical systems

Abstract: The relationship between random attractors and global attractors for dynamical systems is studied. If a partial differential equation is perturbed by an E-small random term and certain hypotheses are satisfied, the upper semicontinuity of the random attractors is obtalned as c goes to zero. The results are applied to the Navier-Stokes equations and a problem of reaction-diffusion type, both perturbed by an additive white noise.

An excursion set model for the distribution of dark matter and dark matter haloes

Abstract: A model of the gravitationally evolved dark matter distribution, in the Eulerian space, is developed. It is a simple extension of the excursion set model that is commonly used to estimate the mass function of collapsed dark matter haloes. In addition to describing the evolution of the dark matter itself, the model allows one to describe the evolution of the Eulerian space distribution of the haloes. It can also be used to describe density profiles, on scales larger than the virial radius, of these haloes, and to quantify the way in which matter flows in and out of Eulerian cells. When the initial Lagrangian space distribution is white noise Gaussian, the model suggests that the Inverse Gaussian distribution should provide a reasonably good approximation to the evolved Eulerian density field, in agreement with numerical simulations. Application of this model to clustering from more general Gaussian initial conditions is discussed at the end.

Modeling and estimation of FPN components in CMOS image sensors

Abstract: Fixed pattern noise (FPN) for a CCD sensor is modeled as a sample of a spatial white noise process. This model is, however, not adequate for characterizing FPN in CMOS sensors, since the redout circuitry of CMOS sensors and CCDs are very different. The paper presents a model for CMOS FPN as the sum of two components: a column and a pixel component. Each component is modeled by a first order isotropic autoregressive random process, and each component. Each component is modeled by a first order isotropic autoregressive random process, and each component is assumed to be uncorrelated with the other. The parameters of the processes characterize each component of the FPN and the correlations between neighboring pixels and neighboring columns for a batch of sensor. We show how to estimate the model parameters from a set of measurements, and report estimates for 64 X 64 passive pixel sensor (PPS) and active pixel sensor (APS) test structures implemented in a 0.35 micron CMOS process. High spatial correlations between pixel components were measured for the PPS structures, and between the column components in both PPS and APS. The APS pixel components were uncorrelated.

Method for coding an audio signal

Abstract: The invention relates to a method for coding or de-coding an audio signal combining the advantages of TNS processing and noise substitution. A time discrete audio signal is initially transformed in a frequency range in order to obtain spectral value of the temporal audio signal. A prediction of the spectral values in relation to frequency is subsequently made in order to enable spectral residual values. Areas within the spectral values encompassing spectral values with noise properties are detected . The spectral residual values are noise substituted in the noise areas, whereupon data relating to the noise areas and noise substitution are incorporated into side information pertaining to a coded audio signal.

Noise-predictive maximum likelihood (NPML) detection

Abstract: Sequence detectors for the digital magnetic recording channel that are based on noise-predictive partial-response equalization are described. Called Noise-Predictive Maximum Likelihood (NPML) detectors, they arise by imbedding a noise prediction/whitening process into the branch metric computation of a Viterbi detector. NPML detectors can be realized in a form that allows RAM table look-up implementation of the imbedded feedback. Alternatively, the noise prediction/whitening mechanism can be implemented as an infinite impulse response (IIR) filter. For a Lorentzian channel with operating points in the range 0.5

Comments on "The Cramer-Rao lower bounds for signals with constant amplitude and polynomial phase

Abstract: For original paper see IEEE Trans. Signal Processing, vol.39, p.749-52 (March 1991). Different expressions for the Cramer-Rao lower bounds (CRLBs) of constant amplitude polynomial phase signals embedded in white Gaussian noise appear in the literature. The present paper revisits the derivation of the bounds reported by Peleg and Porat (1991) and indicates that the resulting expressions depend on the interval over which the signal is defined. The proper choice of the interval is the one that centers the signal around zero and results in the minimum lower bounds.

A subspace approach to estimation of autoregressive parameters from noisy measurements

Abstract: This correspondence describes a method for estimating the parameters of an autoregressive (AR) process from a finite number of noisy measurements The method uses a modified set of Yule-Walker (YW) equations that lead to a quadratic eigenvalue problem that, when solved, gives estimates of the AR parameters and the measurement noise variance

Phase noise in oscillators: DAEs and colored noise sources

Abstract: Oscillators are key components of electronic systems. Undesired perturbations, i.e. noise, in practical electronic systems adversely affect the spectral and timing properties of oscillators resulting in phase noise, which is a key performance limiting factor, being a major contributor to bit-error-rate (BER) of RF communication systems, and creating synchronization problems in clocked and sampled data systems. We first present a theory and numerical methods for nonlinear perturbation and noise analysis of oscillators described by a system of differential algebraic equations (DAEs), which extends our recent results on perturbation analysis of autonomous ordinary differential equations (ODEs). In developing the above theory, we rely on novel results we establish for linear periodically time varying (LPTV) systems: Floquet theory for DAEs. We then use this nonlinear perturbation analysis to derive the stochastic characterization, including the resulting oscillator spectrum, of phase noise in oscillators due to colored (e.g., 1/f noise), as opposed to white noise sources. The case of white noise sources has already been treated by us in a recent publication (A. Demir et al., 1998). The results of the theory developed in this work enabled us to implement a rigorous and effective analysis and design tool in a circuit simulator for low phase noise oscillator design.

Measurements of the binaural temporal window using a detection task

Abstract: Two experiments investigated the shape of the binaural temporal window using a detection task. In experiment 1, a 10-ms tone burst was presented binaurally out-of-phase during a burst of white noise, which changed from being interaurally uncorrelated, to correlated, and back to uncorrelated. The tone occurred during the correlated portion of the noise in one interval of each 2I-FC trial. Detection thresholds were recorded using a 2-down/1-up adaptive procedure. Thresholds were measured for different durations of correlated noise (0–960 ms), frequencies of tone burst (125, 250, 500, and 1000 Hz) and levels of noise [20, 30, 40, and 50 dB(SPL)/Hz]. Window shapes based on nine candidate functions were fitted to the data using the assumption that the binaural masking release was related to the overall interaural correlation of noise admitted by the window. Fitted windows included both a forward and a backward lobe. Gaussian functions tended to give closer fits than exponential and rounded-exponential functions, and simple functions gave more parsimonious fits that those which included dynamic-range-limiting terms. Using simple Gaussian fits, the shape of the window was largely independent of frequency and level, and the windows for individual listeners had equivalent rectangular durations ranging from 55 to 188 ms. The asymmetry was variable, although forward lobes were generally shorter than backward lobes. Experiment 2 ruled out the possibility that the forward lobe might be an artefact caused by distraction of the listener, when the interaural phase change in the noise closely followed the signal. In this experiment, the out-of-phase tone was presented during a burst of partially correlated noise which changed, after a variable interval, to a fully correlated noise. Thresholds for detecting the tone rose (i.e., performance worsened) as the interval was increased. Distraction would have produced the opposite effect.

Asymptotic equivalence for nonparametric generalized linear models

Abstract: We establish that a non-Gaussian nonparametric regression model is asymptotically equivalent to a regression model with Gaussian noise. The approximation is in the sense of Le Cam's deficiency distance Δ; the models are then asymptotically equivalent for all purposes of statistical decision with bounded loss. Our result concerns a sequence of independent but not identically distributed observations with each distribution in the same real-indexed exponential family. The canonical parameter is a value f(ti) of a regression function f at a grid point ti (nonparametric GLM). When f is in a Holder ball with exponent \(\) we establish global asymptotic equivalence to observations of a signal Γ(f(t)) in Gaussian white noise, where Γ is related to a variance stabilizing transformation in the exponential family. The result is a regression analog of the recently established Gaussian approximation for the i.i.d. model. The proof is based on a functional version of the Hungarian construction for the partial sum process.