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128
Iterated random functions
 SIAM Review
, 1999
"... Abstract. Iterated random functions are used to draw pictures or simulate large Ising models, among other applications. They offer a method for studying the steady state distribution of a Markov chain, and give useful bounds on rates of convergence in a variety of examples. The present paper surveys ..."
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Cited by 133 (1 self)
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Abstract. Iterated random functions are used to draw pictures or simulate large Ising models, among other applications. They offer a method for studying the steady state distribution of a Markov chain, and give useful bounds on rates of convergence in a variety of examples. The present paper surveys the field and presents some new examples. There is a simple unifying idea: the iterates of random Lipschitz functions converge if the functions are contracting on the average. 1. Introduction. The
Estimating and Interpreting the Instantaneous Frequency of a Signal
 Proceedings of the IEEE
, 1992
"... The frequency of a sinusoidal signal is a well defined quantity. However, often in practice, signals are not truly sinusoidal, or even aggregates of sinusoidal components. Nonstationary signals in particular do not lend themselves well to decomposition into sinusoidal components. For such signals, t ..."
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Cited by 128 (2 self)
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The frequency of a sinusoidal signal is a well defined quantity. However, often in practice, signals are not truly sinusoidal, or even aggregates of sinusoidal components. Nonstationary signals in particular do not lend themselves well to decomposition into sinusoidal components. For such signals, the notion of frequency loses its effectiveness, and one needs to use a parameter which accounts for the timevarying nature of the process. This need has given rise to the idea of instantaneous frequency. The instantaneous frequency (IF) of a signal is a parameter which is often of significant practical importance. In many situations such as seismic, radar, sonar, communications, and biomedical applications, the IF is a good descriptor of some physical phenomenon. This paper discusses the concept of instantaneous frequency, its definitions, and the correspondence between the various mathematical models formulated for representation of IF. The paper also considers the extent to which the IF corresponds to our intuitive expectation of reality. A historical review of the successive attempts to define the IF is presented. Then the relationships between the IF and the groupdelay, analytic signal, and bandwidthtime (BT) product are explored, as well as the relationship with timefrequency distributions. Finally, the notions of monocomponent and multicomponent signals, and instantaneous bandwidth are discussed. It is shown that all these notions are well described in the context of the theory presented. I.
Improving Regression Estimation: Averaging Methods for Variance Reduction with Extensions to General Convex Measure Optimization
, 1993
"... ..."
Frequency content of randomly scattered signals
 PART I, WAVE MOTION
, 1990
"... The statistical properties of acoustic signals reflected by a randomly layered medium are analyzed when a pulsed spherical wave issuing from a point source is incident upon it. The asymptotic analysis of stochastic equations and geometrical acoustics is used to arrive at a set of transport equatio ..."
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Cited by 72 (20 self)
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The statistical properties of acoustic signals reflected by a randomly layered medium are analyzed when a pulsed spherical wave issuing from a point source is incident upon it. The asymptotic analysis of stochastic equations and geometrical acoustics is used to arrive at a set of transport equations that characterize multiply scattered signals observed at the surface of the layered medium. The results of extensive numerical simulations are presented, illustrating the scope of the theory. A number of inverse problems for randomly layered media are also formulated where we
Interdisciplinary application of nonlinear time series methods
 Phys. Reports
, 1998
"... This paper reports on the application to field measurements of time series methods developed on the basis of the theory of deterministic chaos. The major difficulties are pointed out that arise when the data cannot be assumed to be purely deterministic and the potential that remains in this situatio ..."
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Cited by 44 (5 self)
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This paper reports on the application to field measurements of time series methods developed on the basis of the theory of deterministic chaos. The major difficulties are pointed out that arise when the data cannot be assumed to be purely deterministic and the potential that remains in this situation is discussed. For signals with weakly nonlinear structure, the presence of nonlinearity in a general sense has to be inferred statistically. The paper reviews the relevant methods and discusses the implications for deterministic modeling. Most field measurements yield nonstationary time series, which poses a severe problem for their analysis. Recent progress in the detection and understanding of nonstationarity is reported. If a clear signature of approximate determinism is found, the notions of phase space, attractors, invariant manifolds etc. provide a convenient framework for time series analysis. Although the results have to be interpreted with great care, superior performance can be achieved for typical signal processing tasks. In particular, prediction and filtering of signals are discussed, as well as the classification of system states by means of time series recordings.
Multivariate autoregressive modeling of fmri time series. NeuroImage
, 1477
"... We propose the use of Multivariate Autoregressive (MAR) models of fMRI time series to make inferences about functional integration within the human brain. The method is demonstrated with synthetic and real data showing how such models are able to characterise interregional dependence. We extend lin ..."
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Cited by 37 (9 self)
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We propose the use of Multivariate Autoregressive (MAR) models of fMRI time series to make inferences about functional integration within the human brain. The method is demonstrated with synthetic and real data showing how such models are able to characterise interregional dependence. We extend linear MAR models to accommodate nonlinear interactions to model topdown modulatory processes with bilinear terms. MAR models are time series models and thereby model temporal order within measured brain activity. A further benefit of the MAR approach is that connectivity maps may contain loops, yet exact inference can proceed within a linear framework. Model order selection and parameter estimation are implemented using Bayesian methods. 2 1
Finding the Embedding Dimension and Variable Dependences in Time Series
, 1994
"... : We present a general method, the ffitest, which establishes functional dependencies given a sequence of measurements. The approach is based on calculating conditional probabilities from vector component distances. Imposing the requirement of continuity of the underlying function, the obtained va ..."
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Cited by 33 (3 self)
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: We present a general method, the ffitest, which establishes functional dependencies given a sequence of measurements. The approach is based on calculating conditional probabilities from vector component distances. Imposing the requirement of continuity of the underlying function, the obtained values of the conditional probabilities carry information on the embedding dimension and variable dependencies. The power of the method is illustrated on synthetic timeseries with different timelag dependencies and noise levels and on the sunspot data. The virtue of the method for preprocessing data in the context of feedforward neural networks is demonstrated. Also, its applicability for tracking residual errors in output units is stressed. 1 pihong@thep.lu.se 2 carsten@thep.lu.se Introduction The behaviour of a dynamical system is often modeled by analyzing a time series record of certain system variables. Using artificial neural networks (ANN) to model such systems has recently attr...
Optimal Ensemble Averaging of Neural Networks
 Network
, 1997
"... Based on an observation about the different effect of ensemble averaging on the bias and variance portion of the prediction error, we discuss training methodologies for ensembles of networks. We demonstrate the effect of variance reduction and present a method of extrapolation to the limit of an inf ..."
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Cited by 30 (4 self)
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Based on an observation about the different effect of ensemble averaging on the bias and variance portion of the prediction error, we discuss training methodologies for ensembles of networks. We demonstrate the effect of variance reduction and present a method of extrapolation to the limit of an infinite ensemble. A significant reduction of variance is obtained by averaging just over initial conditions of the neural networks, without varying architectures or training sets. The minimum of the ensemble prediction error is reached later than that of a single network. In the vicinity of the minimum, the ensemble prediction error appears to be flatter than that of the single network, thus simplifying optimal stopping decision. The results are demonstrated on the sunspots data, where the predictions are among the best obtained, and on the 1993 energy prediction competition dataset B. 1 Introduction In recent years, the use of artificial neural networks (NN) for time series prediction has g...
Digital Audio Restoration
 Applications of Digital Signal Processing to Audio and Acoustics
, 1997
"... This chapter is concerned with the application of modern signal processing techniques to the restoration of degraded audio signals. Although attention is focussed on gramophone recordings, film sound tracks and tape recordings, many of the techniques discussed have applications in other areas where ..."
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Cited by 28 (10 self)
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This chapter is concerned with the application of modern signal processing techniques to the restoration of degraded audio signals. Although attention is focussed on gramophone recordings, film sound tracks and tape recordings, many of the techniques discussed have applications in other areas where degraded audio signals occur, such as speech transmission, telephony and hearing aids. We aim to provide a wide coverage of existing methodology while giving insight into current areas of research and future trends. 1 Introduction The introduction of high quality digital audio media such as Compact Disk (CD) and Digital Audio Tape (DAT) has dramatically raised general awareness and expectations about sound quality in all types of recordings. This, combined with an upsurge in interest in historical and nostalgic material, has led to a growing requirement for restoration of degraded sources ranging from the earliest recordings made on wax cylinders in the nineteenth century, through disc reco...