Showing papers on "White noise published in 1976"

The enhancement of speech intelligibility in high noise levels by high-pass filtering followed by rapid amplitude compression

Abstract: This paper presents the results of an examination of rapid amplitude compression following high-pass filtering as a method for processing speech, prior to reception by the listener, as a means of enhancing the intelligibility of speech in high noise levels. Arguments supporting this particular signal processing method are based on the results of previous perceptual studies of speech in noise. In these previous studies, it has been shown that high-pass filtered/clipped speech offers a significant gain in the intelligibility of speech in white noise over that for unprocessed speech at the same signal-to-noise ratios. Similar results have also been obtained for speech processed by high-pass filtering alone. The present paper explores these effects and it proposes the use of high-pass filtering followed by rapid amplitude compression as a signal processing method for enhancing the intelligibility of speech in noise. It is shown that this new method resuits in a substantial improvement in the intelligibility of speech in white noise over normal speech and over previously implemented methods.

LPC analysis/Synthesis from speech inputs containing quantizing noise or additive white noise

Abstract: An important problem in some communication systems is the performance of linear prediction (LPC) analysis with speech inputs that have been corrupted by (signal-correlated) quantization distortion or additive white noise. To gain a first insight into this problem, a high-quality speech sample was deliberately degraded by using various degrees (bit rates of 16 kbps and more) of differential PCM (DPCM), and delta modulation (DM) quantization, and by the introduction of additive white noise. The resulting speech samples were then analyzed to obtain the LPC control signals: pitch, gain, and the linear prediction coefficients. These control parameters were then compared to the parameters measured in the original, high quality signal. The measurements of pitch perturbations were assessed on the basis of how many points exceeded an appropriate difference limen. A distance measure proposed by Itakura was used to compare the original LPC coefficients with the coefficients measured from the degraded speech. In addition, the measured control signals were used to synthesize speech for perceptual evaluation. Results suggest that LPC analysis/synthesis is fairly immune to the degradation of DPCM quantization. The effects of DM quantization are more severe and the effects of additive white noise are the most serious.

Modelling and Recursive Estimation for Double Indexed Sequences

Abstract: Publisher Summary Linear recursive processing is a practical solution to the main drawback of digital technology, which is its slowness for many real time signal processing applications. It seems reasonable to try natural generalizations of the various equivalent characterizations of linear recursive time invariant transformations: (1) the algebraic characterization as finite-rank linear operators and (2) the “behavioral” characterization as a transformation described by a finite-order autoregressive form relating the inputs and the outputs. The approach presented in this chapter is to generalize the algebraic characterization that turns to be very fertile and allows building a self-contained theory for statistical recursive processing for a large class of double-indexed sequences. The chapter introduces a model for double-indexed space invariant linear transformations along with a class of double-indexed Gaussian sequences built as “output” of such linear transformations “driven” by white noise. A realization theory is developed leading to an algebraic characterization of those transformations, an approximation property, and a minimal realization algorithm. . After an approximation theorem proving the generality of this class of sequences, the study of their correlation function leads to stochastic identification algorithms and throws some light on spectral factorization properties of double-indexed sequences. The chapter yields a recursive solution to filtering and smoothing problems involving Gaussian sequences.

Confidence intervals for regression (MEM) spectral estimates

Abstract: The probability density and confidence intervals for the maximum entropy (or regression) method (MEM) of spectral estimation are derived using a Wishart model for the estimated covariance. It is found that the density for the estimated transfer function of the regression filter may be interpreted as a generalization of the student's t distribution. Asymptotic expressions are derived which are the same as those of Akaike. These expressions allow a direct comparison between the performance of the maximum entropy (regression) and maximum likelihood methods under these asymptotic conditions. Confidence intervals are calculated for an example consisting of several closely space tones in a background of white noise. These intervals are compared with those for the maximum likelihood method (MLM). It is demonstrated that, although the MEM has higher peak to background ratios than the MLM, the confidence intervals are correspondingly larger. Generalizations are introduced for frequency wavenumber spectral estimation and for the joint density at different frequencies.

Stochastic processes in estimation theory

Abstract: We describe the role of various stochastic processes, especially martingales and related concepts, in estimation theory. It is shown, in the simplest context, that in nonlinear estimation theory martingales play the same fundamental role as uncorrelation and white noise do in linear estimation.

Linear filtering of singularly perturbed systems

Abstract: This short paper considers the properties of singularly perturbed systems with white noise input. The theory of singular perturbations is then applied to the filtering problem for such systems. The resulting filter may be approximately decomposed into two filters in different time scales yielding the estimates of the slow-mode and the fast-mode states.

Stochastic realization of Gaussian processes

Abstract: A Gaussian stochastic process (y t ) with known covariance kernel is given: we investigate the generation of (y t ) by means of Markovian schemes of the type dx t = F(t)x t dt + dw t y t = H(t)x t . Such a generation of (y t ) as the "output of a linear dynamical system driven by white noise" is possible under certain finiteness conditions. In fact, this was shown by Kalman in 1965. We emphasize the probabilistic aspects and obtain an intrinsic characterization of the state of the process as the state of an externally described stochastic I/O map. Realizations of (y t ) can be constructed with respect to any increasing family of ω-fields; in particular, when the family of ω-fields is induced by the process itself, the driving white noise reduces to the innovation process of (y t ). The corresponding realization has been referred to as the "innovation representation" of (y t ).

On Optimal Control of Linear Systems in the Presence of Multiplicative Noise

Abstract: This correspondence considers the problem of optimal regulator design for discrete time linear systems subjected to white state-dependent and control-dependent noise in addition to additive white noise in the input and the observations. A pseudo-deterministic problem is first defined in which multiplicative and additive input disturbances are present, but noise-free measurements of the complete state vector are available. This problem is solved via discrete dynamic programing. Next is formulated the problem in which the number of measurements is less than that of the state variables and the measurements are contaminated with state-dependent noise. The inseparability of control and estimation is brought into focus, and an "enforced separation" solution is obtained via heuristic reasoning in which the control gains are shown to be the same as those in the pseudo-deterministic problem. An optimal linear state estimator is given in order to implement the controller.

First Passage Probability for Nonlinear Oscillators

Abstract: An approximate method of calculating the probability that a nonlinear oscillator will fail within a specified interval of time is developed, where failure is assumed to occur at the instant the response amplitude first exceeds a critical level. It is shown for oscillators driven by white noise that the energy envelope of the response process is well represented as a one-dimensional Markov process. From the appropriate Fokker-Planck equation of this process simple differential equations for the moments of the time to failure are derived, and integrated numerically in certain cases. In the case of an oscillator with linear damping but a nonlinear spring of the power law type, a complete analytical solution is found in terms of hypergeometric functions. A comparison with digital simulation results indicates that the proposed theory yields a lower bound from the mean time to failure which is close when the damping is very light.

Stastical Estimation of the Intrinsic Dimensionality of a Noisy Signal Collection

Abstract: Let W be an N-dimensional vector space and let the signal locus V be a K-dimensional topological hypersurface in W. The intrinsic dimensionality problem can be stated as follows. Given M randomly selected points (signals) v i , v i ? V, estimate K, which is the dimensionality of V and is called the intrinsic dimensionality of the points v i . A statistical method, which is developed from geometric considerations, is used to estimate the dimensionality. This ad hoc statistical method avoids the approximations and assumptions required by the maximum likelihood solution. The problem of estimating dimensionality in the presence of additive white noise is also considered. A pseudo, signal-to-noise ratio, which has meaning with respect to estimating the dimensionality of a noisy signal collection, is defined. A filtering method, based on this ratio, is used to estimate the dimensionality of a noisy signal collection. The accuracy of the method is demonstrated by estimating the dimensionality of a collection of pulsed signals which have four free parameters.

Analysis of bilinear noise models in circuits and devices

Abstract: There are a number of applications in which linear noise models are inappropriate. In the paper, the use of bilinear noise models in circuits and devices is considered. Several physical problems are studied in this framework. These include circuits involving varying parameters (such as variable resistance circuits constructed using field-effect transistors), the effect of switching jitter on sampled data system performance and communication systems involving voltage-controlled oscillators and phase-lock loops. In addition, several types of analytical techniques for stochastic bilinear systems are considered. Specifically, the moment equations of Brockett for bilinear systems driven by white noise are discussed, and closed-form expressions for certain bilinear systems (those that evolve an Abelian or solvable Lie groups) driven by white or colored noise are derived. In addition, an approximate statistical technique involving the use of harmonic expansions is described.

Linear minimum variance filters applied to carrier tracking

Abstract: A new approach is taken to the problem of tracking a fixed amplitude signal with a Brownian motion phase process. Classically, a first-order phase-lock loop (PLL) is used; here, the problem is treated via estimation of the quadrature signal components. In this space, the state dynamics are linear with white multiplicative noise. Therefore, linear, minimum-variance filters, which have a particularly simple mechanization, are suggested. The resulting error dynamics are linear at any signal/noise ( S/N ) ratio unlike the classical PLL. During synchronization, and above threshold, this filter with constant gains degrades by 3 percent in output rms phase error with respect to the classical loop. However, up to 80 percent of the maximum possible noise improvement is obtained below threshold where the classical loop is nonoptimum, as demonstrated by a Monte Carlo analysis. Filter mechanizations are presented for beth carrier and baseband operation. An interesting bandpass filter interpretation is given.

Distribution of Multivariate White Noise Autocorrelations

Abstract: Multivariate white noise processes arise in a variety of contexts; for example, as error terms in multivariate regression models, as innovations in multiple time series models, or simply as random samples from multivariate normal distribution. Here we study the asymptotic properties of white noise autocorrelations in detail to determine their use in testing the adequacy of fit.

On optimal soft-decision demodulation

Abstract: Wozencraft and Kennedy have suggested that the appropriate demodulator criterion of goodness is the cutoff rate of the discrete memoryless channel (DMC) created by the modulation system; the criterion of goodness adopted in this paper is the "symmetric" cutoff rate which differs from the former criterion only in that the signals are assumed equally likely. Massey's necessary condition for optimal coherent demodulation of binary signals is generalized to M -ary signals. It is shown that the optimal demodulator decision regions in likelihood space are bounded by hyperplanes. An iterative method is formulated for finding these optimal decision regions from an initial "good guess." For additive white Gaussian noise (AWGN), the corresponding optimal decision regions in signal space are bounded by hypersurfaces with hyperplane asymptotes; these asymptotes themselves bound the decision regions of a demodulator which, in several examples, is shown to be virtually optimal. In many cases, the necessary condition for demodulator optimality is also sufficient, but a counterexample to its general sufficiency is given.

Design Criteria for Noncoherent Gaussian Channels with MFSK Signaling and Coding

Abstract: This paper presents data and criteria to assess and guide the design of modems for coded noncoherent communication systems subject to practical system constraints of power S , bandwidth W , noise spectral density N 0 , coherence time T c , and number of orthogonal signals M . Three basic receiver types are analyzed for the noncoherent multifrequency-shift keying (MFSK) additive white Gaussian noise channel: hard decision, unquantized (optimum), and quantized (soft decision). Channel capacity and computational cutoff rate R comp are computed for each type and presented as functions of the predetection signal-to-noise ratio ST/N_{0} and the number of orthogonal signals M = 2TW . This relates the channel constraints of power, bandwidth, coherence time, and noise power to the optimum choice of signal duration T \leq T_{c} and signal number M .

A nonlinear control law for a stochastic infinite time problem

Abstract: The expectation of a particular class of nonquadratic performance criterion involving even powers of the state variables up to sixth order is minimized, over an infinite horizon, subject to a linear stochastic system. The process noise is composed of both additive white noise and state dependent white noise processes. The resulting controller is composed of a linear and cubic function of the state. Furthermore, this controller depends upon the noise variances of both the additive and state dependent noise processes. For partially observable systems with no state dependent noise, similar results as the completely observable system are implied by the separation theorem. For state dependent noise alone, a stochastic Lyapunov function is obtained from which simple probability bounds for the trajectory to exit from a given region of the state space are determined.

A separation theorem for the stochastic sampled-data LQG problem. [control of continuous linear plant disturbed by white noise]

Abstract: This paper considers the control of a continuous linear plant disturbed by white plant noise when the control is constrained to be a piecewise constant function of time: i.e. a stochastic sampled-data system. The cost function is the integral of quadratic error terms in the state and control, thus penalizing errors at every instant of time while the plant noise disturbs the system continuously. The problem is solved by reducing the constrained continuous problem to an unconstrained discrete one. It is shown that the separation principle for estimation and control still holds for this problem when the plant disturbance and measurement noise are Gaussian.

The Separation Principle in Stochastic Control via Girsanov Solutions

Abstract: This paper deals with the separation of estimation and control for linear systems with additive Gaussian white noise and nonquadratic cost function. All measurable functions of the observations are admissible as controls, the corresponding solutions being defined by the Girsanov measure transformation. The separation principle is established, under certain conditions, if the dimension of the observation process is equal to that of the state; if there are fewer observations, then additional ones of arbitrarily low signal-to-noise ratio can be adjoined such that there is a separated policy based on the augmented observations which is superior to any policy using the original observations.

Radon-Nikodym derivatives of a class of weak distributions on Hilbert spaces

Abstract: The problem of derivatives of weak distributions is studied in the context of likelihood ratios of signals in noise, the ‘independent’ case. We show that the derivative is defined in that case and obtain a formula for it. The main result is in Section 2; the necessary introductory material is in Section 1. The application to the linear case is given in Section 3, and in Section 4, a non-linear example, in which we show for the first time that the correction term in the white noise version of the Girsanov formula is a random variable whose expected value is the mean square estimation error.

Likelihood ratios for signals in additive white noise

Abstract: We present a formula for likelihood functionals for signals in which the corrupting noise is modelled as white noise rather than the usual Wiener process. The main difference is the appearance of an additional term corresponding to the conditional mean square error. By way of one application we consider the ‘order-disorder’ problem of Shiryayev.

Linearization techniques for non-linear dynamical systems

Abstract: This dissertation is concerned with the application of linearization techniques to the study of the response of non-linear dynamical systems subjected to periodic and random excitations. A general method for generating an approximate solution of a multi-degree-of-freedom non-linear dynamical system is presented. This method relies on solving an optimum equivalent linear substitute of the original system. The applicability of the method for determination of the amplitudes and phases of the approximate steady-state solution of a multi-degree-of-freedom non-linear system under harmonic monofrequency excitation is considered. The implementation of the method for several special classes of non-linear functions is discussed in detail. In addition, the manner in which the method may be applied to generate an approximate solution for the covariance matrix of the stationary random response of a multi- degree- of freedom dynamical system subjected to stationary Gaussian excitation is outlined. The potential of the method to treat transient solutions of non-linear systems is indicated in the context of the non-stationary response of a lightly damped and weakly non-linear oscillator subjected to monofrequency harmonic or to a Gaussian white noise disturbance. For both classes of excitation the method produces a first-order differential equation governing the response amplitude. The results pertinent to the harmonically excited oscillator are compared with existing solutions. A non-stationary solution of the Fokker-Planck equation associated with the stochastic differential equation governing the response amplitude of the randomly excited oscillator is accomplished by perturbation techniques; the stationary solution is determined without making any approximation in the Fokker-Planck equation. The new method for transient response is applied to the random response of a Duffing Oscillator and a Hysteretic System. The solution for the Duffing Oscillator is compared with data obtained by a Monte Carlo study.

Information measures and performance bounds for array processors

Abstract: Information measures and performance bounds are derived for frequency-domain linear array processors deployed in homogeneous Gaussian random fields. J -divergence, a measure of the (net) information rate of an array, is shown to be a useful measure of how effectively detection and estimation functions can be performed in optimum and conventional array processing structures. In a detection context, J - divergence becomes a detection index that can be interpreted in terms of array gain and output signal-to-noise ratio (SNR). Comparisons between the divergence of optimum and conventional processors indicate, for example, that optimum processing can provide on the order of a 13 dB gain over conventional processing when trying to detect a 20 dB signal in the presence of a 20 dB interference located within the Rayleigh limit of the array. In an estimation context, J-divergence can be used to derive "critical divergence" and Cramer-Rao bounds on resolution variance. These bounds indicate that approximately 25 dB output signal-to-noise ratio is required to obtain a 10:1 improvement over the classical Rayleigh resolution limit. The Rayleigh limit is argued to have significance only at output SNR's of approximately 10 dB. The argument is based on a new resolution limit termed the critical divergence limit. This limit is shown to give resolution limits approximately three times the Cramer-Rao bound, indicating that the latter bound is perhaps an optimistic resolution limit.

Synthesis of Optimal Inputs for Multiinput-Multioutput (Mimo) Systems with Process Noise Part I: Frequenc Y-Domain Synthesis Part II: Time-Domain Synthesis

Abstract: Publisher Summary The problem of input design has been the subject of several recent studies. Most of the results obtained have been confined to single-input systems without process noise. However, many of the industrial applications involve multiple inputs and process noise. This chapter presents a complete treatment of such systems along with practical algorithms for the computation of optimal input designs. The procedure for obtaining the information matrix is more general and yields results not easily derived from the previous approach. The min–max conditions for single-input systems are replaced by min–max–max conditions. An asymptotic expression for the average per sample information matrix is derived and certain important properties of the set of information matrices, which are used to show the equivalence of the D-optimal design to a min–max design, are discussed. An algorithm for the computation of optimal inputs is also given. Time-domain input design is considered and results similar to frequency domain results are obtained in the chapter.

Noise and social interaction as simultaneous stressors

Abstract: This study investigated some of the combined effects of noise and stress of social interaction on group behavior and performance. Three independent groups of college students participated in the simulation game Starpower while exposed to different levels of noise. Intermittent white noise at 61 dB (A) and 75 dB (A) was used for the Noisy and Very Noisy conditions, respectively, and the ambient sound level of 51 dB (A) was used for Quiet. Tests were administered to each group several days prior to playing the game and again immediately after the game; changes in subject's scores were then calculated. The Self-evaluation Scale of Group Behavior, used as a measure of behavioral change, indicated that significant change had resulted from superimposing relatively low levels of noise on social interaction. Subjects in groups subjected to noisier environments perceived the behavior of others as more disagreeable, disorganized, and threatening. The combined stressors failed to produce decremental performance on t...

Random rounding: Some principles and applications

Abstract: Truncation and rounding operations in digital signal processing introduce harmonic and intermodulation distortion for low level inputs or pure signal inputs. A two step random rounding procedure alleviates these problems by introducing "white" quantization noise. Some results bearing on the quantization noise levels as a function of input level and on linearity are presented. In one application a simple recursive integrator is found to have dramatic correlated quantization error affects unless random rounding is employed.