Biomedical Engineering Reference
In-Depth Information
we get:
V
1
e i f
S
(
f
)=
2 ,
z
=
(2.59)
p
k
0 a k z k
=
The AR spectral estimate is maximum entropy method. The entropy of informa-
tion (strictly speaking the entropy rate for infinite process) is connected with power
spectral density function by the formula [Smylie et al., 1973]:
Z + F N
1
4 F N
En
=
log S
(
f
)
df
(2.60)
F N
It was pointed out by [Ulrych and Bishop, 1975] that AR spectral estimate is equiv-
alent to the estimate fulfilling maximum entropy condition, which means that the AR
estimate expresses maximum uncertainty with respect to the unknown information
but is consistent with the known information.
An illustrative comparison of parametric and non-parametric spectra estimates
for EEG signal is shown in Figure 2.9. Estimates obtained with the AR model and
FIGURE 2.9: Comparison of AR and Fourier spectra. a) Spectra: thick line—
spectrum of AR model with the lowest AIC, thin black line—power spectral density
estimate via Welch's method window length is 1/10 signal length and the overlap
is half the window length, gray line-modified periodogram with Blackmann-Harris
window. b) AIC for different model orders, estimated for the signal c) (minimum is
marked with a circle). c) An epoch of EEG signal; sampling frequency 128Hz.
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