Showing papers on "White noise published in 1982"
TL;DR: The spatial parameters that describe the visual detection of spatio-temporal correlation in moving two-dimensional noise patterns were determined and the span of the elementary correlators rose monotonically with the velocity to which the correlator is most sensitive.
Abstract: We obtained movement detection thresholds for two-dimensional random speck-patterns ("Julesz" patterns) homogeneously moving over the whole target field (5.21 x 5.31 degrees of visual angle). We alternated between two uncorrelated but otherwise similar patterns, one moving with velocity leads to V1, the other with velocity leads to V2, such that each pattern was on for T ms. We masked this pattern (signal) with spatio-temporal white noise ("snow"). The total r.m.s. contrast was kept constant, whereas the ration of the r.m.s. contrasts of signal and noise was varied. The square of this ratio was designated SNR. At low SNR values the pattern was not perceptually different from the snow alone. At high SNR values the subject detected spatio-temporal correlation (e.g., movement). In these experiments we determined the threshold SNR values as a measure of the detectability of spatio-temporal correlation as a function of the parameters T, leads to V1, and leads to V2. When leads to V1 and leads to V2 were sufficiently dissimilar one of three percepts occurred: for very large T the alternation could be followed, for very small T two transparent, simultaneously moving sheets of noise-pattern with different velocities could be seen. For intermediate T-values no systematic movement at all could be observed. At these T-values the threshold SNR was maximal. This "'critical" T-value decreased with increasing velocity. We found that it was possible to have more than one percept of uniform smooth movement at a single location in the visual field if these movements had velocity vectors with an angular difference of at least 30 deg or if their magnitudes differed by at least a factor of 4.
219 citations
TL;DR: In this paper, a central limit theorem for the sample covariances of a linear process is proved for the parameter estimation of a fitted spectral model, which does not necessarily include the true spectral density of the linear process.
Abstract: A central limit theorem is proved for the sample covariances of a linear process. The sufficient conditions for the theorem are described by more natural ones than usual. We apply this theorem to the parameter estimation of a fitted spectral model, which does not necessarily include the true spectral density of the linear process. We also deal with estimation problems for an autoregressive signal plus white noise. A general result is given for efficiency of Newton-Raphson iterations of the likelihood equation.
155 citations
TL;DR: It is shown then that a non-singular linear transformation of the instruments gives a new and still consistent estimate.
Abstract: Consistency conditions for instrumental-variable methods applied to Hammerstein models are derived and analysed. It is necessary to have a model that is not over-parametrized and an input that is ‘ strongly persistently exciting ’, i.e. the inputs and their powers are jointly persistently exciting. Some specific choices of the instruments are proved to give consistency. Those instruments are formed as filtered inputs and powers of the input. Consistency can be guaranteed if either the input is white noise or if a certain transfer function is positive-real. The vector of instruments is, in general, of larger dimension than the parameter vector. It is shown then that a non-singular linear transformation of the instruments gives a new and still consistent estimate. Some simulations using the IV variants proposed in this paper are also included.
152 citations
TL;DR: By using spatial interaction models, this paper develops restoration algorithms that do not require the availability of the original image or its prototype, and the specific structure of the underlying lattice enables the implementation of the filters using fast Fourier transform (FFT) computations.
Abstract: This paper is concerned with developing fast nonrecursive algorithms for the minimum mean-squared error restoration of degraded images. The degradation is assumed to be due to a space invariant, periodic, nonseparable known point-spread function, and additive white noise. Our basic approach is to represent the images by a class of spatial interaction models, namely the simultaneous autoregressve models and the conditional Markov models defined on toroidal lattices, and develop minimum mean-squared error restoration algorithms using these models. The restoration algorithms are optimal, if the parameters characterizing the interaction models are exactly known. However, in practice, the parameters are estimated from the images. By using spatial interaction models, we develop restoration algorithms that do not require the availability of the original image or its prototype. The specific structure of the underlying lattice enables the implementation of the filters using fast Fourier transform (FFT) computations, Several restoration examples are given.
145 citations
TL;DR: A new spectral estimator is developed from the high-order Yule-Walker equations and pseudoinverse solutions to the equations that provides high resolution spectral estimates as substantiated by simulation results and produces a constant false alarm rate detector for a single sinusoid in noise.
Abstract: A new spectral estimator is developed from the high-order Yule-Walker equations and pseudoinverse solutions to the equations. The approach circumvents the usual difficulties associated with inverting ill-conditioned matrices and allows the choice of high model order. It also provides high resolution spectral estimates as substantiated by simulation results. A byproduct of this spectral estimator is a constant false alarm rate detector for a single sinusoid in noise. The detector's receiver operating characteristics curves are constructed from histograms, based on 1000 runs, of the detection statistics.
123 citations
TL;DR: Experimental results are shown and compared to the standard Wiener filter results and other earlier attempts involving nonstationary filters.
Abstract: The restoration of images degraded by an additive white noise is performed by nonlinearly filtering a noisy image. The standard Wiener approach to this problem is modified to take into account the edge information of the image. Various filters of increasing complexity are derived. Experimental results are shown and compared to the standard Wiener filter results and other earlier attempts involving nonstationary filters.
86 citations
TL;DR: A new method for estimating the parameters of an ARMA process is presented, which consists of three linear least-squares estimations, and it is shown that the resultant estimator is 'p-consistent' and ' p-efficient' (the asymptotic efficiency approaches the theoretical maximum as p tends to infinity).
66 citations
TL;DR: In this article, the authors derived and analyzed optimal detectors for the general class of digitally modulated signals in which the sequence of symbols is unknown a priori and information data are not of interest.
Abstract: In this paper optimal detectors are derived and analyzed for the general class of digitally modulated signals in which the sequence of symbols is unknown a priori and information data are not of interest. The detectors test the signal present condition in background white Gaussian noise versus the null condition of noise alone. Particular attention is focused upon cases in which the SNR per symbol is low compared to unity. The models employed herein are sufficiently general to include most forms of spread-spectrum signals as well as other digital type communication signals.
64 citations
TL;DR: Weighted least squares and related stochastic approximation algorithms are studied for parameter estimation, adaptive state estimation and adaptive N -step-ahead prediction, in both white and colored noise environments.
Abstract: Weighted least squares, and related stochastic approximation algorithms are studied for parameter estimation, adaptive state estimation, adaptive N -step-ahead prediction, and adaptive control, in both white and colored noise environments. For the fundamental algorithm which is the basis for the various applications, the step size in the stochastic approximation versions and the weighting coefficient in the weighted least squares schemes are selected according to a readily calculated stability measure associated with the estimator. The selection is guided by the convergence theory. In this way, strong global convergence of the parameter estimates, state estimates, and prediction or tracking errors is not only guaranteed under the appropriate noise, passivity, and stability or minimum phase conditions, but the convergence is also as fast as it appears reasonable to achieve given the simplicity of the adaptive scheme.
60 citations
TL;DR: In this article, an intensive optical and IR monitoring program of the flux and polarization characteristics of BL Lac was conducted, and it was found that the polarization variations increase in amplitude with increasing time interval, and that the path traced out by the polarization vector in the Q-U plane is a random walk.
Abstract: Results are presented from an intensive optical and IR monitoring program of the flux and polarization characteristics of BL Lac It is found that the polarization variations increase in amplitude with increasing time interval, and that the path traced out by the polarization vector in the Q-U plane is a random walk In view of earlier measurements of BL Lac, the polarization fluctuations can be represented at low frequencies by the flat power spectrum of white noise, up to a frequency of 005 cycles/day Above this frequency, the spectrum steepens to that of a random walk A model for BL Lac suggested by the polarimetric noise can be constructed from independent sources of light with randomly oriented, strong polarization Small random differences in spectral index from source to source could also explain the variable wavelength dependence of polarization
58 citations
TL;DR: In this article, the authors discuss controllability for stochastic systems and derive necessary and sufficient algebraic conditions for the control of the state and the output of white and colored noise linear systems.
TL;DR: In this article, a speech analysis-synthesis system for the narrow band transmission of a speech signal is proposed. But the system is not suitable for speech analysis in the general speech domain.
Abstract: In a speech analysis-synthesis system for the narrow band transmission of a speech signal, speech is separated into a plurality of spectrum information (Ki), average (V0) of linear prediction error signal, pitch period (L), voiced/unvoiced decision signal (V/UV), a pseudo exciting signal (I) which is a part of a linear prediction error signal or an impulse response of the same, and a frame information which determines the interval and the duration of the spectrum analyzation, then, in a receive side, the product of said pseudo excitation signal (I) and said pitch period (L), a white noise is switched according to said voiced/unvoiced decision signal (V/UV), and the output of the switch is applied to a synthesis filter which attaches correlation components to an input signal according to spectrum information (Ki) to provide synthesized speech.
TL;DR: This paper examines the merits of a detector based upon the autoregressive spectral estimator and shows that when the actual received signal departs appreciably from the signal assumed in a conventional detector, i.e., a bank of matched filters, the AR detection performance exceeds that of the conventional detector.
Abstract: The problem of detecting a signal with an unknown Doppler shift and random phase in white noise is essentially a problem in spectral analysis. This paper examines the merits of a detector based upon the autoregressive spectral estimator. Some advantages of the auto-regressive detector are that the detection performance is independent of Doppler shift and phase and the false alarm rate is independent of noise level. Also, the performance does not depend upon the exact signal form but only upon its autocorrelation function, leading to a robust detector. For the first order autoregressive model investigated, the computational and storage requirements of the autoregressive detector are less than that for a conventional bank of matched filters detector. It is shown by example that when the actual received signal departs appreciably from the signal assumed in a conventional detector, i.e., a bank of matched filters, the AR detection performance exceeds that of the conventional detector.
TL;DR: The sensitivity of human observers with respect to the detection of transients in otherwise uniformly moving two-dimensional random-dot patterns is reported on, and the detection performance is independent of the direction of either the average or difference-velocity withrespect to the border, and can be completely described in terms of a minimum requirement for the magnitude of the difference-VELocity.
Abstract: We report on the sensitivity of human observers with respect to the detection of transients in otherwise uniformly moving two-dimensional random-dot patterns. The target field is divided into two halfs that each contains a moving random-dot pattern. The patterns in the two halffields are mutually uncorrelated. Parameters are the average velocity and the difference-velocity for the two halfs. These velocities are both vectors that can be varied in magnitude and in their direction with respect to the border of the two halffields. In order to quantify the sensitivity of the visual system to such patterns, we added (linear addition) spatio-temporal white noise ("snow") to the pattern. Then the sensitivity is quantified by way of the threshold signal-to-noise ratio necessary to discriminate the composite pattern from a single smoothly uniformly moving pattern. The signal-to-noise ratio specifies the square of the ratio between the signal r.m.s. contrast and the r.m.s. contrast of the masking stimulus (spatio-temporal white noise or "snow"). The r.m.s. contrast of the complex pattern (signal and noise) is kept invariant. We find that the detection performance is independent of the direction of either the average or difference-velocity with respect to the border, and can be completely described in terms of a minimum requirement for the magnitude of the difference-velocity. The magnitude of the difference-velocity must exceed the magnitude of the average velocity in order to lead to a perceivable transient. In his formulation the Weberlaw for the detection of velocity transients in uniformly moving noise patterns is applicable to both differences in magnitude and direction of the velocities.
TL;DR: In this paper, two numerical models previously developed by Rice for modeling Gaussian, white-noise, electronic signals are used to simulate in the frequency domain nonlinear random ocean waves in water of finite depth.
Abstract: Two numerical models previously developed by Rice for modeling Gaussian, white-noise, electronic signals are used to simulate in the frequency domain nonlinear random ocean waves in water of finite depth. The following two models were developed by Rice: (1) Nondeterministic Spectral Amplitude model (NSA), and (2) Deterministic Spectral Amplitude model (DSA). These two Rice models are used with finite Fourier transform (FFT) algorithm to simulate linear Gaussian random wave realizations by the process of filtering Gaussian white noise in the frequency domain. A nonlinear random wave interaction matrix then operates on the linear Gaussian wave spectra to generate a complex-valued nonlinear random wave spectrum that is correct to second-order in the Stoke's wave perturbation parameter. Both the lineear and the nonlinear realizations obtained from both of Rice's two simulation models are compared with a realization obtained from hurricane-generated real ocean waves measured in the Gulf of Mexico. Statistical comparisons indicate that the NSA Rice model is better for both linear and nonlinear random wave simulations when band-limited white noise is digitally filtered.
TL;DR: In this article, a one-dimensional steady state probabilistic river water quality model is developed to compute the joint and marginal probability density functions of BOD and DO at any point in a river.
Abstract: A one-dimensional steady state probabilistic river water quality model is developed to compute the joint and marginal probability density functions of BOD and DO at any point in a river. The model can simultaneously consider randomness in the initial conditions, inputs, and coefficients of the water quality equations. Any empirical or known distribution can be used for the initial conditions. Randomness in each of the water quality equation inputs and coefficients is modeled as a Gaussian white noise process. The joint probability density function (pdf) of BOD and DO is determined by numerically solving the Fokker-Plank random differential equation. In addition, moment equations are developed which allow the mean and variance of BOD and DO to be calculated independently of their joint pdf. The probabilistic river water quality model is examined through sensitivity study and an application to a hypothetical river system.
TL;DR: The results show that the performance of the IJF-OQPSK is superior to that of QPSK, OQPSk, and MSK in narrow-band nonlinear channels.
Abstract: New power and bandwidth efficient modulation techniques, named intersymbol interference and jitter-free (IJF)-QPSK and IJF-OQPSK, are presented. The properties of the IJF-QPSK and IJF-OQPSK signals in linear and nonlinear earth-station-satellite systems are studied. A finite-state Markov chain model is used to calculate power spectra of hard-limited IJF-QPSK and IJF-OQPSK. The model provides insights into the spectral spreading action of the ideal hard-limiter on the IJF-QPSK and IJF-OQPSK signals, Experimental, simulation, and theoretical results are in good agreement. The results indicate that the IJF-OQPSK modulated signal exhibits much less spectrum spreading than QPSK, OQPSK, and MSK. The error probability (P e ) performance of IJF-QPSK and IJFOQPSK in an additive white Gaussian noise and adjacent-channel interference environment is evaluated. The results show that the P e performance of the IJF-OQPSK is superior to that of QPSK, OQPSK, and MSK in narrow-band nonlinear channels.
TL;DR: In this article, the authors combined the techniques of statistical and harmonic linearization to develop a linearized approximation theory for the calculation of the second-order statistics (i.e., autocorrelation functions and spectral densities) of nonlinear systems driven by both random and periodic forces.
Abstract: We have combined the techniques of statistical and harmonic linearization to develop a linearized approximation theory for the calculation of the second-order statistics (i.e., autocorrelation functions and spectral densities) of nonlinear systems driven by both random and periodic forces. For the special case of a Duffing oscillator (a damped anharmonic oscillator with a cubic nonlinearity) driven by Gaussian white noise and by a sinusoidal force, explicit expressions for the renormalized (linearized) frequency, the autocorrelation function, and the spectral density of the oscillator displacement in terms of all the system parameters have been derived. We have determined the region of the parameter space in which the applied periodic force has a significant influence on the second-order statistics of the oscillator.
DOI•
01 Aug 1982TL;DR: In this paper, a maximum likelihood processor for estimating the elevation angle of a target in the combined presence of specular multipath and receiver noise, as encountered in a low-angle tracking-radar environment is described.
Abstract: A new maximum-likelihood processor is described for estimating the elevation angle of a target in the combined presence of specular multipath and receiver noise, as encountered in a low-angle tracking-radar environment. The processor makes special use of the symmetry of the incident direct and specular multipath components with respect to the normal to the receiving array. The theory of the processor is supported by both computer simulation and experimental results. The effect of deviation from perfect symmetry is also examined.
TL;DR: This work shows that in the white noise case a single adaptation algorithm suffices to establish that, with probability one, the systems input, output and the output tracking error are sample mean-square bounded.
Abstract: Recent papers on adaptive stochastic control have established global convergence for the general delay-colored noise case. However, for delays k greater than unity they require the implementation of k interlaced adaptation algorithms. Using an indirect adaptive control approach, we show that in the white noise case a single adaptation algorithm suffices to establish that, with probability one, the systems input, output and the output tracking error are sample mean-square bounded. Moreover, the conditional variance of the output tracking error is shown to converge to its global minimum value with probability one.
TL;DR: In this article, the covariance functions for the transient response of a linear MDOF-system due to stationary time limited exitation with an arbitrary frequency content are related directly to spectral density functions of the stationary response.
Abstract: The covariance functions for the transient response of a linear MDOF-system due to stationary time limited exitation with an arbitrary frequency content are related directly to the covariance functions of the stationary response. For rational spectral density functions closed form expressions for the covariance functions are obtained. In case of white noise excitation the expressions simplify considerably, and an approximative method for including the main effects of an actual spectral density function is derived based on a white noise analogy. The theory is applied to a multistorey frame structure, and it is demonstrated that it offers an efficient way to calculate the time-dependent second-order moments. The approximation appears to yield fully adequate results for many practical applications involving lightly damped structures.
TL;DR: In this paper, the optimal least squares coefficients and frequency response of the D-step predictor for sinusoids (real or complex) in additive colored noise were derived for the whitening application.
Abstract: The extraction of sinusoids in white noise using least squares predictors has attracted a lot of attention in the past, mainly in the context of the adaptive line enhancer (ALE). However, very few results exist for the practical colored noise case or for the whitening performance of the predictors. We use a matrix formulation to derive the optimal least squares coefficients and frequency response of the D-step predictor or ALE for sinusoids (real or complex) in additive colored noise. Several cases are considered, and in particular, new formulas for the amplitude gain are obtained. In low-pass background noise, the amplitude gain of the sinusoids becomes essentially a monotonically increasing function of their frequency, and a decreasing function for high-pass noise. For the whitening application, signal-to-noise ratio (SNR) bounds of the output are derived when the input is a white signal plus a sinusoidal interference. We also give a state-space model and stochastic interpretations of our analysis of the D-step predictor, providing connections to other related areas. To enable filtering of nonstationary complex inputs, as well as multichannel and multiexperiment data, a complex vector version of the ladder algorithm is presented that can be used to implement the ALE, noise cancelling, and noise inversion for narrow-band interference rejection.
TL;DR: In this article, a musical sequence can be reproduced repeatedly after actuating a start switch (11) on a visual display (13) and/or with an acoustic output (34) in a frequency which is selected with the help of a switch (20).
Abstract: On a first keyboard (4) the time value of each musical note and/or the time value of each pause of the musical sequence to be reproduced is introduced. After the introduction of each note value, the respective pitch value of this note can be introduced with the aid of a second keyboard (50). The introduced sequence can include up to 8 measures and is reproduced repeatedly after actuating a start switch (11) on a visual display (13) and/or with an acoustic output (34) in a frequency which is selected with the help of a switch (20). The visual display (13) has (4) seven segments elements which show the sequence continuously, measure after measure. The acoustic output (34) can produce, at choice, white noise signals or sounds. The white noise signals have impulses which decrease exponentially from a maximum.
01 Jan 1982
TL;DR: In this paper, the restoration of images degraded by additive white noise is performed by nonlinearly filtering anoisy image using the standard Wiener approach, modified to take into account the edge information of the image.
Abstract: The restoration ofimages degraded byanadditive white noise isperformed bynonlinearly filtering anoisy image. Thestandard Wiener approach tothis problem ismodified totakeinto account the edgeinformation oftheimage. Various filters ofincreasing complexity arederived. Experimental results areshownandcompared tothe standard Wiener filter results andother earlier attempts involving non- stationary filters.
01 Dec 1982
TL;DR: In this paper, the conditional probability law of the current state given past observations is shown to admit a set of sufficient statistics which are recursively computable as outputs of a finite-dimensional system.
Abstract: The filtering problem for partially observed linear systems in additive Gaussian white noise is studied when the initial state condition has arbitrary, thus a priori non-Gaussian, statistics. The conditional probability law of the current state given past observations is shown to admit a set of sufficient statistics which are recursively computable as outputs of a finite-dimensional system. These results are read off an explicit expression for the conditional characteristic function, obtained with no assumption on the moments or the absolute continuity of the initial state distribution. The methodology behind the computation is briefly outline: the derivation is probabilistic and relies on an absolutely continuous change of measure combined to standard results of linear filtering theory.
14 Jun 1982
TL;DR: This work optimize over a class of suboptimal detection laws based on local likelihood ratio tests for detecting a known signal in noise which is correlated between sensors, and that of detecting an unknown signal in white noise.
Abstract: We consider the problem of detection using distributed sensors and limited communication. In particular we examine the case of detecting a known signal in noise which is correlated between sensors, and that of detecting an unknown signal in white noise. As the optimal detection law cannot be determined, we optimize over a class of suboptimal detection laws based on local likelihood ratio tests. Numerical examples illustrate the performance of these laws in comparison to naive decentralized and to centralized decision laws.
TL;DR: In this paper, a Markovian jump process with finite state space, feeding the parameters of a nonlinear diffusion process X, is considered, and an algorithm is investigated which will produce a finite filter if it halts after a finite number of steps.
Abstract: We consider a Markovian jump process θ, with finite state space, feeding the parameters of a nonlinear diffusion process X. We observe θ and X in white noise, and—given a function f—we want to construct a finite filter for the f(X t )-process. An algorithm is investigated which will produce a finite filter if it halts after a finite number of steps, and we give necessary and. sufficient conditions for this to happen.
Journal Article•