Quantitative Sleep Monitoring - Quantitative EEG Analysis Methods and Clinical Applications - page 275

C3-A2

C4-A1

O1-A2

O2-A1

Figure 10.8 Stages 3 and 4 of NREM sleep are depicted by delta activity. (Courtesy of James Geyer
and Paul Carney.)

C3-AVG

C4-AVG

O1-AVG

O2-AVG

Figure 10.9 Sawtooth theta waves, shown by the solid line, are a clear indication that the patient is
in REM sleep. (Courtesy of James Geyer and Paul Carney.)

∞ ∞

() () ( ) () ( )

∫ ∫

F k = f t cos − 2 π kx dx + f t i sin − 2 π kx dx (10.1)

−∞ −∞

Due to Euler's formula, this can also be written as shown in (10.2):

∞

() ()

Fk =

∫

fte

− 2 π ikx

dx (10.2)

−∞

Any time-varying signal can be represented as a summation of sine and cosine
waves of varying magnitude and frequencies [44]. The Fourier transform is repre-
sented with the power spectrum (or spectral density). The power spectrum has a
value for each harmonic frequency that indicates how strong that frequency is in the
given signal. The magnitude of this value is calculated by taking the modulus of the
complex number that is calculated from the Fourier transform for a given frequency
[ |F ( k ) | ].
After the EEG signal has been transformed to the frequency domain using the
Fourier transform, the actual frequencies that create the original signal can be
noted. The existence (or lack thereof) of certain bandwidths can then be used to
determine the stage of sleep the patient was in at the time the EEG segment was
recorded. Alpha waves (8 to 13 Hz) are an indication that the patient is in the wake
state or stage 1 of NREM sleep. Delta waves (<4 Hz) are an indication of being in
stage 3 or 4 of NREM sleep. Theta waves (4 to 7 Hz) are an indication of REM
sleep.
These characteristics are shown in Figures 10.10 through 10.13. Figure 10.10
shows a normalized power spectrum for a segment of an EEG channel monitoring
stage 1 of NREM sleep. Sleep spindles cause a relative increase in the 12- to 14-Hz
range when the patient is in stage 2 of NREM sleep (Figure 10.11). Then an increase
in the delta frequency band, specifically those bands less than 2 Hz, can be seen in
Figure 10.12, when the patient is in stages 3 and 4 of NREM sleep. Finally, after the