Biomedical Engineering Reference
In-Depth Information
21.
The ion exchange process of a cell is estimated to have the following impulse response:
h
ð
t
Þ¼
e
4
t
u
ð
t
Þ
.
(a)
Explain what type of general information would be available to the researcher if this
estimation of
) were accurate.
(b)
If sodium ions are injected into the system for two seconds in the form of a brief pulse
approximated by the equation
h
(
t
, how would the cell respond to
(e.g., pump out ions) such input? Find the answer using time domain procedures.
(Hint: Convolve the input and the impulse response.)
22.
An ECG recording of the electrical activity of the heart during ventricular fibrillation is
digitized, and the signal begins with the data sequence [-90.0, 10.0, -12.0, -63.0, 7.0, -22.0].
The units of the data sequence are given in mV. What is the
x
ð
t
Þ¼
3
u
ð
t
Þ
3
u
ð
t
2
Þ
z-
transform of this data sequence
of the biosignal?
23.
For the systems described by the following equations, determine which of the systems is
linear and which is not.
dy
dt
þ
2
(a)
2
y
ð
t
Þ¼
f
ð
t
Þ
dy
dt
þ
2
(b)
3
ty
ð
t
Þ¼
t
f
ð
t
Þ
dy
dt
þ
y
ð
t
Þ¼
f
ð
t
Þ
df
dt
2
(c)
y
ð
t
Þ¼
Ð
t
1
f
ð
(d)
t
Þ
d
t
24.
Examine the characteristics of the digital filter
1
4
x
ð
k
Þþ
1
4
x
ð
k
1
2
y
ð
k
y
ð
k
Þ¼
1
Þþ
1
Þ:
H
0
(
H
0
(
Find the impulse response,
H
(
z
) and
O
). Use MATLAB to calculate and plot |
O
)| for
0
. Observe the difference between this filter and the filter in Example Problem
10.12. Why is this a better low-pass filter? What is the output if the input sequence is
x
ð
k
Þ¼
< O < p
? What is the output if the input sequence is
p
2
k
þ
p
8
100 sin
x
ð
k
Þ¼
100
u
ð
k
Þ
?
25.
Find the
z
-transform of
(a)
x
ð
k
Þ¼
u
ð
k
Þ
x
ð
k
Þ¼
a
k
u
ð
k
Þ
(b)
(c)
x
ð
k
Þ¼
cos
ð
b
k
Þ
u
ð
k
Þ
26.
Find the
z
-transform of the following:
k
u
ð
k
Þ
1
2
(a)
x
½
k
¼
O
k
Þ
u
½
k
27.
Find the first four outputs of the discrete system
(b)
x
½
k
¼ð
cos
y
½
k
3
y
½
k
1
þ
2
y
½
k
2
¼
f
½
k
1
3
k
u
½
k
:
if
y
½
1
¼
2,
y
½
2
¼
3, and
f
½
k
¼
