Biomedical Engineering Reference
In-Depth Information
parameters of the model. This section introduces the concept of system identification in
both the frequency and time domain.
A variety of signals is available to the biomedical engineer, as described earlier. Those
produced by the body include action potentials, EEGs, EKGs, EMGs, EOG, and pressure
transducer output. Additional signals are available through ultrasound, x-ray tomography,
MRI, and radiation. From these signals a model is built and parameters estimated according
to the modeling plan in Figure 13.1. Before work on system identification begins, under-
standing the characteristics of the input and output signals is important as described in
Chapter 10—that is, knowing the voltage range, frequency range, whether the signal is
deterministic or stochastic, and if coding (i.e., neural mapping) is involved. Most biologi-
cally generated signals are low frequency and involve some coding. For example, EEGs
have an upper frequency of 30 Hz and eye movements have an upper frequency under
100 Hz. The saccadic system uses neural coding that transforms burst duration into saccade
amplitude, as described earlier in this chapter. After obtaining the input and output signals,
these signal must be processed. A fundamental block is the amplifier, which is character-
ized by its gain and frequency, as described in Chapter 8. Note that the typical amplifier
is designed as a low-pass filter (LPF), since noise amplification is not desired. Interestingly,
most amplifiers have storage elements (i.e., capacitors and inductors), so the experimenter
must wait until the transient response of the amplifier has been completed before any
useful information can be extracted. An important point to remember is that the faster
the cutoff of the filter, the longer the transient response of the amplifier.
In undergraduate classes, a system (the transfer function or system description) and
input are usually provided and a response or output is requested. While this seems diffi-
cult, it is actually much easier than trying to determine the parameters of a physiological
system when all that is known are the input (and perhaps not the direct input as described
in the saccadic eye movement system) and noisy output characteristics of the model. In the
ideal case, the desired result here is the transfer function, which can be determined from
H
ð
s
Þ¼
V
o
ðÞ
V
i
ðÞ
ð
13
:
60
Þ
13.10.1 Classical System Identification
The simplest and most direct method of system identification is sinusoidal analysis.
A source of sinusoidal excitation is needed that usually consists of a sine wave generator,
a measurement transducer, and a recorder to gather frequency response data. Many mea-
surement transducers are readily available for changing physical variables into voltages,
as described in Chapter 9. Devices that produce the sinusoidal excitation are much more
difficult to obtain and are usually designed by the experimenter. Recording the frequency
response data can easily be obtained from an oscilloscope. Figure 13.60 illustrates the essen-
tial elements of sinusoidal analysis.
V
i
=
A
cos(
w
x
t
+
q
)
h
(
t
)
V
0
=
B
cos(
w
x
t
+
f
)
FIGURE 13.60
Impulse response block diagram.
