Biomedical Engineering Reference
In-Depth Information
increases as the number of bits increases. A 16-bit A/D converter has better resolution than
an 8-bit A/D converter, since it is capable of representing a total of 65,536 amplitude levels,
compared to 256 for the 8-bit converter. The resolution of an A/D converter is determined
by the voltage range of the input analog signal divided by the numeric range (the possible
number of amplitude values) of the A/D converter.
EXAMPLE PROBLEM 11.3
Find the resolution of an 8-bit A/D converter when an input signal with a 10 V range is
digitized.
Solution
input voltage range
2
N
10
V
256
¼
¼
0
:
0391
V
=
bit
¼
39
:
1
mV
=
bit
EXAMPLE PROBLEM 11.4
The frequency content of an analog EEG signal is 0.5-100 Hz. What is the lowest rate at which
the signal can be sampled to produce an accurate digital signal?
Solution
Highest frequency in analog signal
¼
100 Hz.
f
nyquist
¼
2
f
max
¼
2
100 Hz
¼
200 samples/second.
Another problem often encountered is determining what happens if a signal is not sam-
pled at a rate high enough to produce an accurate representation of the signal. A direct
result of the sampling theorem is that all frequencies of the form [f - kf
s
], where
1
k
1
and f
s
¼
1/T, look the same once they are sampled.
EXAMPLE PROBLEM 11.5
A 360 Hz signal is sampled at 200 samples/second. What frequency will the “aliased” digital
signal contain?
Solution
According to the preceding formula, f
s
¼
200, and the pertinent set of frequencies that look
alike is in the form of [360 - k 200]
.]. The only signal in this group
that will be accurately sampled is 40 Hz, since the sampling rate is more than twice this value.
Note that for real signals
¼
[
...
360 160
40
240
...
40 Hz and
þ
40 Hz are equivalent—that is, cos(
o
t)
¼
cos(
o
t) and
sin(
o
t)
¼
sin(
o
t). Thus, the sampled signal will exhibit a period of 40 Hz. The process is shown
in Figure 11.6.
