Epilepsy Detection and Monitoring - Quantitative EEG Analysis Methods and Clinical Applications - page 146

1. Univariate time-series analyses are time-series analyses that consist of a
single observation recorded sequentially over equal time increments. Some
examples of univariate time series are the stock price of Microsoft, daily
fluctuations in humidity levels, and single-channel EEG recordings. Time is
an implicit variable in the time series. Information on the start time and the
sampling rate of the data collection can allow one to visualize the univariate
time series graphically as a function of time over the entire duration of data
recording. The information contained in the amplitude value of the recorded
EEG signal sampled in the form of a discrete time series x ( t ) x ( t i ) x ( i Δ t ), ( i

t is the sampling interval) can also be encoded through the
amplitude and the phase of the subset of harmonic oscillations over a range
of different frequencies. Time-frequency methods specify the map that
translates between these representations.
2. Multivariate time-series analyses are time-series analyses that consist of
more than one observation recorded sequentially in time. Multivariate
time-series analysis is used when one wants to understand the interaction
between the different components of the system under consideration.
Examples include records of stock prices and dividends, concentration of
atmospheric CO and global temperature, and multichannel EEG recordings.
Time again is an implicit variable.

1, 2, ..., N and Δ

In the following sections some of the most commonly used measures for EEG
time-series analysis will be discussed. First, a description of the linear and nonlinear
univariate measures that operate on single-channel recordings of EEG data is given.
Then some of the most commonly utilized multivariate measures that operate on
more than a single channel of EEG data are described.
The techniques discussed next were chosen because they are representative of
the different approaches used in seizure detection. Time-frequency analysis, nonlin-
ear dynamics, signal correlation (synchronization), and signal energy are very broad
domains and could be examined in a number of ways. Here we review a subset of
techniques, examine each, and discuss the principles behind them.

6.4 Univariate Time-Series Analysis

6.4.1 Short-Term Fourier Transform
One of the more widely used techniques for detecting or predicting an epileptic sei-
zure is based on calculating the power spectrum of one or more channels of the EEG.
The core hypothesis, stated informally, is that the EEG signal, when partitioned into
its component periodic (sine/cosine) waves, has a signature that varies between the
ictal and the interictal states. To detect this signature, one takes the Fourier trans-
form of the signal and finds the frequencies that are most prominent (in amplitude)
in the signal. It has been shown that there is a relationship between the power spec-
trum of the EEG signal and ictal activity [16]. Although there appears to be a corre-
lation between the power spectrum and ictal activity, the power spectrum is not used
as a stand-alone detector of a seizure. In general, it is coupled with some other
time-series prediction technique or machine learning to detect a seizure.