Methods of dynamic spectral analysis by self-exciting autoregressive moving average models and their application to analysing biosignals

Dynamic Factor Analysis Models With Time-Varying Parameters

Dynamic factor analysis models with time-varying parameters offer a valuable tool for evaluating multivariate time series data with time-varying dynamics and/or measurement properties. We use the Dynamic Model of Activation proposed by Zautra and colleagues (Zautra, Potter, & Reich, 1997) as a motivating example to construct a dynamic factor model with vector autoregressive relations and time-varying cross-regression parameters at the factor level. Using techniques drawn from the state-space literature, the model was fitted to a set of daily affect data (over 71 days) from 10 participants who had been diagnosed with Parkinson's disease. Our empirical results lend partial support and some potential refinement to the Dynamic Model of Activation with regard to how the time dependencies between positive and negative affects change over time. A simulation study is conducted to examine the performance of the proposed techniques when (a) changes in the time-varying parameters are represented using the true model of change, (b) supposedly time-invariant parameters are represented as time-varying, and

Analysis of time-variant quadratic phase couplings in the tracé alternant EEG by recursive estimation of 3rd-order time–frequency distributions

The quantification of transient quadratic phase couplings (QPC) by means of time-variant bispectral analysis is a useful approach to explain several interrelations between signal components. A generalized recursive estimation approach for 3rd-order time-frequency distributions (3rd-order TFD) is introduced. Based on 3rd-order TFD, time-variant estimations of biamplitude (BA), bicoherence (BC) and phase bicoherence (PBC) can be derived. Different smoothing windows and local moment functions for an optimization of the estimation properties are investigated and compared. The methods are applied to signal simulations and EEG signals, and it can be shown that the new time-variant bispectral analysis results in a reliable quantification of QPC in the tracé alternant EEG of healthy neonates.

Time-varying analysis of heart rate variability signals with a Kalman smoother algorithm

A time-varying parametric spectrum estimation method for analysing non-stationary heart rate variability signals is presented. As a case study, the dynamics of heart rate variability during an orthostatic test is examined. In this method, the non-stationary signal is first modelled with a time-varying autoregressive model and the model parameters are estimated recursively with a Kalman smoother algorithm. The benefit of using the Kalman smoother is that the lag error present in a Kalman filter, as well as in all other adaptive filters, can be avoided. The spectrum estimates for each time instant are then obtained from the estimated model parameters. Statistics of the obtained spectrum estimates are derived using the error propagation principle. The obtained spectrum estimates can further be decomposed into separate components and, thus, the time variation of low- and high-frequency components of heart rate variability can be examined separately. By using the presented method, high resolution time-varying spectrum estimates with no lag error can be produced. Other benefits of the method are the straightforward procedure for evaluating the statistics of the spectrum estimates and the option of spectral decomposition.

Time-frequency filtering of MEG signals with matching pursuit

Time-frequency signal analysis based on various decomposition techniques is widely used in biomedical applications. Matching Pursuit is a new adaptive approach for time-frequency decomposition of such biomedical signals. Its advantage is that it creates a concise signal approximation with the help of a small set of Gabor atoms chosen iteratively from a large and redundant set. In this paper, the usage of Matching Pursuit for time-frequency filtering of biomagnetic signals is proposed. The technique was validated on artificial signals and its performance was tested for varying signal-to-noise ratios using both simulated and real MEG somatic evoked magnetic field data.

Multiplicity in the high-frequency signals during the short-latency somatosensory evoked cortical activity in humans

OBJECTIVE

Recent studies using electroencephalography or magnetoencephalography have shown that peripheral nerve stimulations produce short-latency high-frequency signals in the human somatosensory cortex. The present study tested whether they consist of more than one distinct type of signal.

METHODS

Somatic evoked magnetic fields (SEFs) elicited by electrical stimulation of the median nerve were measured in 12 healthy volunteers. They were analyzed using a time-frequency analysis method based on Gabor filters and another based on autoregressive moving average, and also with bispectrum and bicoherence techniques and a new dispersion curve method.

RESULTS

Signals in two separate high-frequency bands (200 and 600 Hz) were distinguished from the main signal in the low frequency (LF) range during the time period of N20m and P25m. The novel 200 Hz-band signal was seen reliably in those channels where the LF band signal was weak, so that the former was not masked by the latter. The 600 Hz signal consisted of two distinct components or parts (p1 and p2) in 10 out of 12 subjects, one peaking during ascending slope and the second during the descending slope of the N20m. The latency of the p1 was shorter than the latencies of the 200 Hz and LF signals according to the dispersion curve analysis. The inter-peak interval of p1 became shorter for later peaks in all 12 subjects. Bicoherence analysis revealed a significant phase coupling between the 200 and 600 Hz bands.

CONCLUSIONS

There are three distinct types of signal during the time period of the short-latency cortical components of the SEF -- LF which gives rise to the commonly seen waveform of the SEF, the newly found 200 Hz signal and the 600 Hz signal which consists of two components. The possible origins of the high frequency signals are discussed in light of the new set of evidence found in the present study.