Spectral Analysis - Signal Processing of Random Physiological Signals - page 171

1. Filtering : Analog filtering is the first major consideration for the acquisition and

processing of data. The engineer must determine the appropriate cutoff frequen-
cies within the signal. Both high- and low-frequency cutoff should be determined
and appropriate analog filters with sufficient attenuation in the bandstop regions
should be employed. The high-pass filter should be used to remove the DC
component of the signal and to remove trends. An antialias filter (low-pass fil-
ter) should be employed to eliminate “Aliasing” of the data. It is important to
use an analog antialias filter prior to sampling of the data; any subsequent digital
filtering should be done after sampling.

2. Frequency resolution : Frequency resolution is defined as the smallest unit of fre-

quency in the spectrum. The “Fundamental Frequency” or resolution of the
spectrum ( T ) is equal to the inverse of time the signal segment (length

of time in seconds: T ) that is being analyzed by Spectral Analysis. The segment
time is also referred to as the window of observation or analysis. The energy in the
spectrum of the signal is identified as harmonics of the fundamental frequency,
that is, multiples of the fundamental frequency.

f 0 = 1 /

3. Digitizing and the Nyquist criterion : Probably the most important rule to follow

in spectral analysis is the Nyquist Criteria in digital sampling of the signal. The
sampling rate must be twice the highest frequency of the signal bandwidth (W).
Sampling at a frequency lower than the Nyquist frequency causes aliasing of the
spectrum, which will then yield an erroneous spectral estimator.

4. Windowing : A “Window” function should be applied prior to obtaining the esti-

mation of the “Spectral Density Function.” Windowing is a process by which the
sampled data points are “weighted” in the time domain. The effect is smoothing
of the signal at the beginning and end of the record to prevent the occurrence
of discontinuities and Gibb's Phenomenon in the data. Improper windowing
produces “Leakage” in the spectrum, which adversely affects estimation of the
Spectral Density Function. There are numerous window functions that can be
applied. The problem lies in deciding which window function is the best to apply
on the signal being studied.