Showing papers on "White noise published in 1978"

Stability and Control of Stochastic Systems with Wide-band Noise Disturbances. I

Abstract: For dynamical systems with external influences which are approximately white noise (wide-band noise), we show that stability and other properties of the white noise problem that depend on the infinite time interval, continue to hold away from white noise but not far from it.

Adaptive enhancement of multiple sinusoids in uncorrelated noise

Abstract: The steady-state behavior of the adaptive line enhancer (ALE), a new implementation of adaptive filtering that has application in detecting and tracking narrow-band signals in broad-band noise, is analyzed for a stationary input consisting of multiple sinusoids in white noise. It is shown that the steady-state performance of an L-weight ALE for this case can be modeled by the L × L Wiener-Hopf matrix equation and that this matrix equation can be transformed into a set of 2N coupled linear equations, where N is the number of sinusoids. It is also shown that the expected values of the ALE weights in steady state can be written as a sum of sinusoids and that the amplitude of each sinusoid is coupled to that of all other sinusoids by coefficients that approach zero as the number of ALE weights becomes large. The analytical results are compared to experimental results obtained with a hardware implementation of the ALE of variable length (up to 256 weights) and show good agreement. Theoretical expressions for linear predictive spectral estimates are also derived for multiple sinusoids in white noise. Comparisons are made between the magnitude of the discrete Fourier transform of the ALE weights and the linear predictive spectral estimate for two sinusoids in white noise.

The Cramér-Rao estimation error lower bound computation for deterministic nonlinear systems

Abstract: For continuous-time nonlinear deterministic system models with discrete nonlinear measurements in additive Ganssian white noise, the extended Kalman filter (EKF) convariance propagation equations linearized about the true unknown trajectory provide the Cramer-Rao lower bound to the estimation error covariance matrix. A useful application is establishing the optimum filter performance for a given nonlinear estimation problem by developing a simulation of the nonlinear system and an EKF linearized about the true trajectory.

Evaluation of an adaptive comb filtering method for enhancing speech degraded by white noise addition

Abstract: An intelligibility test was performed to evaluate an adaptive comb filtering method proposed by Frazier [2] for enhancement of degraded speech due to additive white noise. Results indicate that independent of S/N ratio the adaptive comb filtering scheme does not increase speech intelligibility.

Performance of a model for a local neuron population

Abstract: A model of a local neuron population is considered that contains three subsets of neurons, one main excitatory subset, an auxiliary excitatory subset and an inhibitory subset. They are connected in one positive and one negative feedback loop, each containing linear dynamic and nonlinear static elements. The network also allows for a positive linear feedback loop. The behaviour of this network is studied for sinusoidal and white noise inputs. First steady state conditions are investigated and with this as starting point the linearized network is defined and conditions for stability is discovered. With white noise as input the stable network produces rhythmic activity whose spectral properties are investigated for various input levels. With a mean input of a certain level the network becomes unstable and the characteristics of these limit cycles are investigated in terms of occurence and amplitude. An electronic model has been built to study more closely the waveforms under both stable and unstable conditions. It is shown to produce signals that resemble EEG background activity and certain types of paroxysmal activity, in particular spikes.

Study of the Random Vibration of Nonlinear Systems by the Gaussian Closure Technique

Abstract: A technique is developed to study random vibration of nonlinear systems. The method is based on the assumption that the joint probability density function of the response variables and input variables is Gaussian. It is shown that this method is more general than the statistical linearization technique in that it can handle non-Gaussian excitations and amplitude-limited responses. As an example a bilinear hysteretic system under white noise excitation is analyzed. The prediction of various response statistics by this technique is in good agreement with other available results.

Detection in Laplace Noise

Abstract: The discrete time detection of a known constant signal in white stationary Laplace noise is considered. Exact expressions describing the performance of both the Neyman-Pearson optimal detector and the suboptimal linear detector are presented. Also, graphs of the receiver operating characteristics are given. The actual performance of the Neyman-Pearson optimal detector is compared to that predicted by a Gaussian approximation to the distribution of the test statistic.

Frequency estimation by linear prediction

Abstract: The application of linear prediction to frequency estimation for sinusoidal signals in noise is investigated. It is shown that improved performance is obtained by processing a complex-valued version of the real-valued input signal, with the corresponsing sampling rate reduced by one-half. The case of a single sinusoid in white noise is studied in detail, including the eigenvalues of the covariance matrix, zeros of the inverse filter polynomial, frequency bias, and frequency variance as a function of input SNR and prediction order.

Spectral Estimation: Fact or Fiction

Abstract: The spectral estimation problem for a discrete time series generated by a linear time-invariant process can be described in terms of three models: autoregressive (AR), moving average (MA), and autoregressive-moving average (ARMA). Application of a particular spectral estimator to an inappropriate model can result in serious errors. The AR and MA models lead, respectively, to the maximum entropy method (MEM) and classical lag-window approaches. For the ARMA model, we have developed an iterative least squares technique which has an important property, namely, that the feedback component of this response has the minimum delay property. Finally, we present a study to illustrate the degradation in performance resulting from application of the incorrect spectral estimation method to given synthetic data sets.

Maximum entropy spectral estimation using the analytical signal

Abstract: Using maximum entropy power spectral estimation, the estimate of the frequency of a sinusoid in white noise has been shown to be very sensitive to the initial sinusoidal phase. This phase dependence can be significantly reduced by replacing the real data by its analytic form, reducing the sampling rate by two, and employing the power spectral estimate for complex data.

Maximum entropy spectral analysis of multiple sinusoids in noise

Abstract: An analytical technique based on the method of undetermined coefficients is applied to the problem of computing the theoretical spectral estimate by the maximum entropy method (MEM) when the autocorrelation function of the data is known exactly and corresponds to N sinusoids in additive white noise and to N sinusoids in additive 1-pole, low‐pass noise. For the white noise case, the L prediction filter coefficients are expanded directly in terms of the input sinusoids. This expansion leads to a transformation of the L × L normal equations for the prediction filter coefficients to a set of 2N × 2N equations. The transformed equations are a smaller set of equations to be solved whenever L > 2N and provide a convenient description of the interaction between the various frequency components of the sinusoids which occurs in the MEM estimate. Further, for certain cases where there is little interaction between some of the frequency components of the sinusoids, the solution of the 2N × 2N equations may be approxi...

On the choice of noise for the analysis of the peripheral auditory system

Abstract: The cross-correlation between output and input of a system containing nonlinearities, when that system is stimulated with Gaussian white noise, is a good estimate of the linear properties of the system. In practice, however, when sequences of pseudonoise are used, great errors may be introduced in the estimate of the linear part depending on the properties of the noise. This consideration assumes special importance in the analysis of the linear properties of the peripheral auditory system, where the rectifying properties of the haircells constitute a second order nonlinearity. To explore this problem, a simple model has been designed, consisting of a second order nonlinearity without memory and sandwiched between two bandpass filters. Different types of pseudonoise are used as input whereupon it is shown that noise based on binary m-sequences, which is commonly used in noise generators, will yield totally incorrect information about this system. Somewhat better results are achieved with other types of noise. By using inverse-repeat sequences the results are greatly improved. Furthermore, certain anomalies obtained in the analysis of responses from single fibers in the auditory nerve are viewed in the light of the present results. The theoretical analysis of these anomalies reveals some information about the organization of the peripheral auditory system. For example, the possibility of the existence of a second bandpass filter in the auditory periphery seems to be excluded.

Single-channel white-noise estimators for deconvolution

Abstract: The Wiener filtering approach to deconvolution is limited by certain modeling assumptions, which may not always be valid. We develop a Kalman filtering approach to deconvolution which permits more flexible modeling assumptions than the Wiener filtering approach. Our approach is applicable to time‐varying or time‐invariant wavelets as well as to nonstationary or stationary noise processes. We develop equations herein for minimum‐variance estimates of the reflection coefficient sequence, as well as error variances associated with these estimates. Our estimators are compared with an ad hoc “prediction error filter,” which has recently been reported on in the geophysics literature. We show that our estimators perform better than the prediction error filter. Simulation results are included, for both time‐invariant and time‐varying situations, which support our theoretical developments.

Notes on separate-bias estimation

Abstract: Properties of the separate-bias estimation technique introduced in 1969 [1] are reviewed, including the interpretation of the result as the estimation of a constant embedded in white noise. The equations may be rearranged to permit a simpler calculation of the bias which is particularly useful if only infrequent estimates of the bias are needed. It is also shown that the assumption of a nondecreasing bias-covariance matrix leads to a time-invariant filter without steady-state errors in estimation of the state or the bias.

Some consideration of decomposition of a time series

Abstract: SUMMARY Suppose that an observable Gaussian time series Z1 can be written as the sum of an unobservable signal component T1 and a white noise component e1. This paper proposes a

Estimation-detection of object boundaries in noisy images

Abstract: Estimation of boundaries of objects in noisy images is considered when the objects and the background are statistically characterized. The noise is assumed white, additive, and Gaussian. Optimal recursive estimators in a joint estimation-detection context are derived. Applications to binary pictures are illustrated.

Radio receiver alignment indicator

Abstract: A predetermined frequency alignment signal and a white noise source signal are alternately switched through the intermediate frequency amplifier stage (IF) of the receiver being aligned. A series connected integrating capacitor and tuning meter couple between the receiver's detector output and ground potential. In operation, during the interval of white noise being applied to the IF the tuning meter is shorted and the capacitor is charged to a net voltage V n which is representative of the center frequency of the IF. When the alignment signal is applied to the IF, the tuning meter short is removed and a signal V s appears across the capacitor-meter circuit, whereby the meter reading is indicative of V s -V n which represents relative receiver alignment.

Detection of Narrowband Signals Using Time-Domain Adaptive Filters

Abstract: The detection performance of a conventional narrowband analyzer is compared with two adaptive processor mechanizations based on the Widrow least mean squares algorithm. Comparisons are based on both analysis and extensive digital simulation. With a narrowband signal in stationary, white background noise, the performance of the three systems is shown to be essentially the same. With nonstationary background noise, the performance of the conventional system degrades by an amount proportional to the processing time-bandwidth product. The adaptive systems appear to be less sensitive to the nonstationary background, resulting in a potential performance advantage relative to the conventional system.

Near-maximum-likelihood detection processes for distorted digital signals

Abstract: The paper describes six detection processes that are developments of the Viterbi-algorithm detector and are suitable for use in a synchronous serial data-transmission system operating at a transmission rate of up to 20,000 bit/s over a slowly-time-varying channel. The processes are first described and the results of computer simulation tests are then presented, comparing the tolerances of the detection processes to additive white Gaussian noise with the tolerances of both the Viterbi-algorithm detector and a conventional non-linear transversal equalizer. Several different time-invariant channels are used in the tests. It is shown that, under the appropriate conditions, a near optimum tolerance to noise can be achieved by a detection process that involves very much less storage than the Viterbi-algorithm detector and requires only a very small fraction of the number of operations.

Clincal Use of Pseudorandom Binary Sequence White Noise in Assessment of the Human Vestibulo-Ocular System

Abstract: White noise rotational stimulation has been used to evaluate the human vestibulo-ocular response for 30 normal subjects over the frequency range from 0.02 to 1.6 Hz and is being extended to characterize response of patients having documented abnormalities. For clinical use, the white noise stimulus has the advantages of shortening the test time by presenting all stimulus frequencies simultaneously, and being well-tolerated by both normal subjects and patients alike. Cross spectral calculations which compare the computer reconstructed slow phase eye velocity response to the pseudorandom acceleration stimulus yield a set of linear and nonlinear estimates of the vestibulo-ocular response. Pilot data indicate that a classification of the disease state can be made using this set of estimates. This classification will be presented and discussed.

Minimum MSE Equalization of Digital Fiber Optic Systems

Abstract: The optimum minimum MSE equalization, both linear and decision feedback, of a digital fiber optic transmission system with Poisson signal statistics and additive wide-sense stationary noise is considered. The problem is reduced to the solution of a certain integral equation, with solutions obtained for certain special cases, including white and band-limited additive noise. Numerical results are given for white noise and an exponential input pulse.

The two-dimensional white noise problem and localisation in an inversion layer

Abstract: The density of states in the two-dimensional white noise problem is calculated from the coherent potential approximation at high energy and from fluctuation theory at low energies; both the exponent and the power of E in the prefactor for the density of fluctuation states are evaluated. Comparison is made with the results of a tight binding simulation of the white noise problem, and good agreement between theory and calculation is obtained. Calculation of the conductivity of different sized samples enables the mobility edge to be determined, and it is found that the critical value of g=n(Ec)/n0 is more than 0.8, in contrast with much lower values suggested earlier. The metallic conductivity is compared with the CPA result, and found to be lower by a factor of 0.4. Some modifications are introduced into the theory when account is taken of orbital degeneracy. Comparison is made with Pollitt's experiments on the inversion layer.

Single-threshold detection of a random signal in noise with multiple independent observations. 1: Discrete case with application to optical communications.

Abstract: A single-threshold processor is derived for a wide class of classical binary decision problems involving the likelihood-ratio detection of a signal embedded in noise. The class of problems we consider encompasses the case of multiple independent (but not necessarily identically distributed) observations of a nonnegative (nonpositive) signal, embedded in additive, independent, and noninterfering noise, where the range of the signal and noise is discrete. We show that a comparison of the sum of the observations with a unique threshold comprises optimum processing, if a weak condition on the noise is satisfied, independent of the signal. Examples of noise densities that satisfy and violate our condition are presented. The results are applied to a generalized photocounting optical communication system, and it is shown that most components of the system can be incorporated into our model. The continuous case is treated elsewhere [ IEEE Trans. Inf. TheoryIT-25, (March, 1979)].

Time-allocation matching between punishing situations.

Abstract: In the presence and absence of white noise, response-independent aversive events were delivered to rats according to several variable-time electric-shock schedules. The animals could switch from the noise component to the no-noise component and vice versa by making a single lever-press response. If the schedule in one component was not in operation when the animal was in the other component, the proportion of time allocated to one component equalled or matched the proportion of obtained punishers in the other component. If both schedules were always in operation, minimizing tended to occur: the animals allocated almost all of their time to the component having the lower shock rate. An analysis of these results, in terms of the expected time until an aversive event, is presented.