Spectral Analysis - Signal Processing of Random Physiological Signals - page 163

CHAPTER 15

Spectral Analysis

15.1 INTRODUCTION
Spectral analysis is the process by which we estimate the energy content of a time-varying
function (or signal) as a function of frequency. For signals with very little frequency
content, the spectral density function can be represented by a “line spectrum.” The
variations in the frequency resolution of spectra are due to different window lengths. As
the signal becomes more complex (in terms of frequency content), the power spectrum
resembles a more continuous function, hence, spectral density functions. The sharp peaks
that correspond to the raw estimates of the energy for the main frequency components
will be present; however, a certain amount of signal conditioning (i.e., smoothing) is
necessary prior to this final estimation of the “Smoothed Power Spectral Estimate.”
Notice that at times, the text will refer to the Spectral Density Function as the “Power
Spectrum” (singular) or “Power Spectra” (plural). Units for the power spectra are in power
per frequency band (spectral resolution, T ).

The harmonic analysis of a random process will yield some frequency information,
whereas the power spectrum is a useful tool in analysis of a random process. So let us ex-
amine what information can be obtained from the power spectrum. The power spectrum
has four major uses. The first is to get an overview of the function's frequency distribution.
Second is for comparison of distribution via statistical testing or by discriminate analysis.
Third, the power spectrum can be used to obtain estimates the parameters of interest.
And last, but probably the most important application is that power spectra can be used
to show hidden periodicities. In summary, spectral estimates are used primarily to

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