Ulrich Appel

Adaptive sequential segmentation of piecewise stationary time series

Abstract The problem of adaptive segmentation of time series with abrupt changes in the spectral characteristics is addressed. Such time series have been encountered in various fields of time series analysis such as speech processing, biomedical signal processing, image analysis and failure detection. Mathematically, these time series often can be modeled by zero mean gaussian distributed autoregressive (AR) processes, where the parameters of the process, including the gain factor, remain constant for certain time intervals and then jump abruptly to new values. Identification of such processes requires adaptive segmentation: the times of parameter jumps have to be estimated thoroughly to constitute boundaries of “homogeneous” segments which can be described by stationary AR processes. In this paper, a new effective method for sequential adaptive segmentation is proposed, which is based on parallel application of two sequential parameter estimation procedures. The detection of a parameter change as well as the estimation of the accurate position of a segment boundary is effectively performed by a sequence of suitable generalized likelihood ratio (GLR) tests. Flow charts as well as a block diagram of the algorithm are presented. The adjustment of the three control parameters of the procedure (the AR model order, a threshold for the GLR test and the length of a “test window”) is discussed with respect to various performance features. The results of simulation experiments are presented which demonstrate the good detection properties of the algorithm and in particular an excellent ability to allocate the segment boundaries even within a sequence of short segments. As an application to biomedical signals, the analysis of human electroencephalograms (EEG) is considered and an example is shown.

A comparative study of three sequential time series segmentation algorithms

Abstract Modelling of instationary 1 D-signals by means of quasistationary process with sudden parameter jumps makes it necessary to define stationary segments within the signals analyzed. The purpose of this paper is to present a comparison study of several recently published segmentation procedures, regarding mainly their performance as measured by the ability to detect and localize segment boundaries correctly. The three algorithms selected for this purpose share useful common features, like adaptive and sequential (not block-wise) processing, which makes them good candidates for real-time processing of time series. Performance is measured by applying these algorithms to various simulated time series with well defined properties and by comparing the results obtained with the ‘true’ signal source model. In all these simulations, the ‘generalized likelihood ratio’ algorithm developed by one of the authors yields the best results, regarding both the false alarm and the missed detection rate as well as the positioning of detected boundaries. This is due to the optimum matching of the procedure to the assumed statistical model of piecewise stationary segments. When applying these segmentation algorithms to human electroencephalogram (EEG) data, where the assumption of quasistationarity is only a rough approximation of the real statistics, the same rank of performance evolves. The advantage of the new algorithm, however, has to be weighed against its higher computational load in comparison to both other algorithms, which have been developed particularly as computationally effective methods for EEG data processing.

Realtime Loudspeaker Linearization

Electrodynamic loudspeakers exhibit a nonlinear behaviour especially at low frequencies which shows up in harmonic and intermodulation distortions. Their nonlinear transfer function can be modeled by a Volterra series expansion and prefiltering of the loud speaker input signal by an appropriate Volterra, inverse filter can reduce the distortions. Problems with real time application arise from the requirement of large computational power to realize Volterra filters of high orders and long memories. To over come these problems approximations to the loud speaker model must be made. This paper presents a new Volterra kernel decomposition with good performance and small computational load. The pre-distortion filters were implemented on a DSP system and tested with several electrodynamic loudspeakers. The results show that the nonlinear distortions can be reduced significantly.

Recursive lattice algorithms with finite-duration windows

Most recursive adaptive lattice-filter algorithms use (IIR) exponential weighting of the signal elements necessary to calculate the filter parameters. In this paper, recursive algorithms for finite window (FIR) weighting are derived instead and applied to the parameter estimation process. Adaptation and steady state performance of adaptive lattice filters is calculated approximately for arbitrary weightings, allowing a comparison of the performance of different windows. As an example, a lattice filter with HAMMING windowing is compared to one with standard exponential weighting.

Efficient equalization of nonlinear communication channels

Nonlinear intersymbol interference (ISI) often arises in voice-band communication channels at high transmission rates or in satellite channels due to nonlinearities in power amplifiers. The proposed equalizers for the cancellation of the nonlinear interference are mainly based on the Volterra series expansion, which is an elegant but very complex model. This paper presents a decision feedback equalizer (DFE) which is based on a new nonlinear filter structure. It is composed only of linear taped delay line filters and multipliers. Hence, the complexity of this still very general structure is comparable to linear filtering. Simulation of data transmission over a telephone channel show that the proposed DFE clearly outperforms the conventional DFE and is also superior to the Volterra DFE with a comparable complexity.

Automatic event detection in surface EMG of rhythmically activated muscles

Precise detection of discrete events in the surface electromyogram (EMG) like the phasic change in the activity pattern associated with the initiation of a rapid motor response is an important issue in the analysis of the human motor system. However, accurate detection is difficult when the muscle is already involved in a secondary motor task, and two superimposed activation patterns have to be separated. This paper describes a method which allows automatic detection of phasic events that arise during simultaneous execution of rhythmical and discrete motor tasks by the same muscle. Based on a nonlinear signal model, events are identified as characteristic changes in the variance of the original EMG signal by using a two-window scheme and the generalized likelihood ratio test. Both, the beginning as well as the end of epochs with prominent EMG activity related to the rhythmical movement and the onset of phasic activity indicating initiation of a discrete contraction can be detected. Problems arising from modelling the EMG by a sequence of independent Gaussian random variables modulated by a deterministic control pattern are discussed.

Application of a cepstral distance measure in evoked potential processing

Transient evoked potentials (EPs) are variations of the on-going electroencephalogram (EEG) in response to the application of sensory stimuli. Since their amplitudes are very small in comparison to the spontaneous EEG, signal extraction methods must be applied to improve the signal-to-noise ratio. A short review of commonly used signal processing methods in EP research is given, concentrating on their assumptions and limitations. Subsequently a parametric system model is proposed which considers the characteristics of the on-going EEG preceding the stimulus in the EP processing. In order to show the advantage of this approach some results are given and their impact on the aforementioned methods is discussed.

Parallel identifiers for parameter estimation of strongly disturbed ARMA-processes

Several output error (or parallel) identifiers for parametric identification of discrete time autoregressive, moving-average (ARMA) systems with low signal-to-noise ratio were studied. An additional identification difficulty thereby was the estimation from a few number of data. Two kinds of adaptive recursive methods - model reference adaptive system algorithms (M.R.A.S.) and hyperstable adaptive recursive identifiers (HARF, e.g.) - were tested in simulation runs. The results are compared with an off-line (iterative) output error method and discussed. As a special case study modelling of human electroencephalogram (EEG) data is presented.

Enhancement Of Visual Evoked Potentials By Adaptive Processing

Transient evoked potentials (EP) are variations of the on-going electroencephalogram (EEG) in response to the application of sensory stimuli. Since their amplitudes are very small in comparison to the spontaneous EEG, signal extraction methods must be applied to them before their characteristics are measureable. Several signal ex-traction methods which are actually used in EP research are outlined, especially those showing an adaptive characteristic. As a further development, a new method is proposed which considers the on-going EEG preceding the stimulus application for the EP processing. The computational procedure will be described and some preliminary results are given.

Visual evoked potentials and reaction times: influence of stimulus parameters

Manual reaction time measurements were used to investigate the transmission characteristics of the visual channel by analyzing the input-output relationship for different stimuli. A stimulus-dependent influence is neglected by the assumption of a constant delay time of the motor system. In order to check this approach, visual evoked EEG potentials were measured, and their latencies were compared to the reaction time data. Good agreement between measures was shown only on the basis of the mean values. On the single-trial level, no systematic correlation could be found. Methodological problems of processing single-trial visual evoked potentials are discussed, and the results are interpreted with respect to models of the sensory-motor system.<<ETX>>