M. Jachan

We present a novel formulation of nonstationary autoregressive (AR) models in terms of time-frequency (TF) shifts. The parameters of the proposed TFAR model are determined by "TF Yule-Walker equations" that involve the expected ambiguity function and can be solved efficiently due to their block-Toeplitz structure. For moderate model orders, we also propose approximate TF Yule-Walker equations that have Toeplitz/block-Toeplitz structure

Abstract The time-frequency ARMA (TFARMA) model is introduced as a time-varying ARMA model for nonstationary random processes that is formulated in terms of time shifts and frequency (Doppler) shifts. We present Akaike and minimum description length ...

Cerebral autoregulation (CAR) is a control mechanism of the brain keeping cerebral blood flow constant albeit the arterial blood pressure varies. Impaired CAR may be associated with an increased risk of cerebral ischemic events in patients with obstructive cerebrovascular disease. Spontaneous blood pressure oscillations are analyzed using a nonparametric and two parametric transfer function estimators, i.e. the autoregressive-moving-average model with exogenous inputs or the vector-autoregressive model. Performance of the methods was compared using data from patients with unilateral stenosis or occlusion. We also analyzed reproducibility by comparing partitions of the data an with data from other patients which have been measured twice. Results show that there is no significant difference between methods (ANOVA, p > 0.27), and that CAR measurements can be performed reproducibly (Kendall's tau, p < 0.0016) by all three methods. In conclusion, CAR measurements by means of spontaneous oscillations can be obtained stably and the presented parametric approaches can serve for future online application of CAR measurement.

The inference of causal interaction structures in multivariate systems enables a deeper understanding of the investigated network. Analyzing nonlinear systems using partial directed coherence requires high model orders of the underlying vector-autoregressive process. We present a method to overcome the drawbacks caused by the high model orders. We calculate the corresponding statistics and provide a significance level. The performance is illustrated by means of model systems and in an application to neurological data.

Estimating the functional topology of a network from multivariate observations is an important task in nonlinear dynamics. We introduce the nonparametric partial directed coherence that allows disentanglement of direct and indirect connections and their directions. We illustrate the performance of the nonparametric partial directed coherence by means of a simulation with data from synchronized nonlinear oscillators and apply it to real-world data from a patient suffering from essential tremor.

The inference of interaction structures in multidimensional time series is a major challenge not only in neuroscience but in many fields of research. To gather information about the connectivity in a network from measured data, several parametric as well as non-parametric approaches have been proposed and widely examined. Today a lot of interest is focused on the evolution of the network connectivity in time which might contain information about ongoing tasks in the brain or possible dynamic dysfunctions. Therefore an extension of the current approaches towards time-resolved analysis techniques is desired. We present a parametric approach for time variant analysis, test its performance for simulated data, and apply it to real-world data.

The analysis of multi-dimensional biomedical systems requires analysis techniques, which are able to deal with multivariate data consisting of both time series as well as point processes. Univariate and bivariate analysis techniques in the frequency domain for time series and point processes are established and investigated, although the number of investigations is strongly biased towards time series. Actual multivariate techniques for time series or hybrids of time series and point processes are scarcely addressed. Here, we present spectral analysis techniques which are able to analyse point processes as well as time series. Thereby, univariate, bivariate as well as multivariate techniques are discussed. Applications to simulated as well as real-world data reveal the abilities of the proposed techniques.