Biomedical Engineering Reference
In-Depth Information
The cell's voltage output in the frequency domain is determined as
A
j o þ
j o ¼ A
1
A
j o þ
V ðoÞ¼ H ðoÞ I ðoÞ¼
=t
j o
1
1
=t
Next, using the derived transfer function, the transfer function magnitude is obtained as
s
A
q
H ð
A
A
o 2
j
H ð
o
Þ
j ¼
o
Þ H ð
o
Þ
*
¼
t
¼
p
j
o
þ
1
=
j
o
þ
1
=
t
þ
1
=t 2
where
(o)* is the complex conjugate transfer function. In MATLAB the transfer function magni-
tude is plotted as follows:
H
%Cell Membrane Magnitude Response
tau
¼
0.01;
¼
A
1/tau^2;
¼
w
0:0.1:500;
¼
þ
H
1/tau^2);
plot(w/2/pi,H,'k')
axis([0 500/2/pi 0 1.2])
xlabel('Frequency (Hz)')
ylabel('Magnitude')
A./(w.^2
The results are shown in Figure 11.19. Note that the transfer function tends to preserve the low
frequencies while rejecting the high frequencies. Thus, the cell membrane behaves like a low-pass
filter.
1
0.8
0.6
0.4
0.2
0
0
10
20
30
40
Frequency (Hz)
50
60
70
FIGURE 11.19 Cell membrane transfer function magnitude. Note that the cell behaves like a low-pass filter.
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