Spectral Analysis - Signal Processing of Random Physiological Signals - page 164

1. show hidden Periodicities in frequency domain;

2. obtain descriptive statistics, for example, distribution, mean, mode, bandwidth

of the spectral from a random signal;

3. get an overview of the frequencies in a function, F ( ω );

4. in obtaining parameter estimation and/or feature extraction, that is, clinical EEG

bands; and

5. in classification testing and discrimination analysis.

There are several methods for calculating the power spectra. The most commonly
used spectral estimation methods are calculated via

1. the autocorrelation function,

2. the direct or fast fourier transform,

3. the autoregression, which is briefly included in this chapter, but this method

of spectral estimation will not be covered in the course, since an autoregression
course is offered by the statistics department.

It should be noted, however, that there are other methods. The power spectrum
(periodogram), most commonly used by engineers, is an estimator of the “raw power
spectrum” and must undergo smoothing to clearly reveal informative features (preferred
by statisticians). Autoregressive spectral estimation is a powerful tool that estimates the
power spectrum without employing any smoothing techniques.
Before commencing with the spectral analysis of a signal, the signal has to be quali-
fied as deterministic (periodic) or random. The random data must be tested for normality
of distribution, independence, and stationarity. If any of these statistical properties are
not met, the data is a nonstationary process. If the data is nonstationary, appropriate
steps should be followed to make the data independent and stationary before proceeding
with spectral analysis; however, nonstationary processes are beyond the scope of this
topic.