Biomedical Engineering Reference
In-Depth Information
5.3.1 Noise
In all of the examples, the ultimate electrical signal will be accompanied by some form
of noise. This noise could come from other physiological activities, from external in-
terference, or, for the smaller signals, from thermal noise generated by the acquisition
electronics. It may be random, or it may be repetitive or even periodic, depending on
its source. There is therefore no single signal processing technique that can be used to
minimize the noise and hence to maximize the signal-to-noise ratio.
5.3.1.1 Thermal Noise
Thermal noise is electrical noise generated by random fluctuations of the voltage or current
due to the thermal agitation of electrons within a conductor. It is therefore common to any
electrical circuit associated with biomechatronic sensors.
More formally, if
v(
t
)
is the thermal noise voltage across the terminals of a resistor,
R
,
then if this voltage is measured at regular intervals over a long period the mean value, ¯
v
,is
m
j
=
1
v
j
1
m
v
=
(5.1)
Measurements show that in the limit as
m
→∞
the mean value approaches zero. This
result can be justified by considering the random motion of large numbers of electrons
that produce fluctuations in the potential. These must average out to zero in the long-term;
otherwise, they would result in the flow of a current.
The time-averaged squared signal ¯
v
2
is determined in a similar way:
m
1
m
2
2
j
v
¯
=
1
v
(5.2)
j
=
2
(V
2
In the limit as
m
→∞
this mean squared value,
v
)
, can be shown to approach
2
v
=
4
kT R
f
¯
(5.3)
10
−
23
J/K),
T
(Kelvin) is the absolute tempera-
ture,
R
(ohms) is the resistance value, and
f
(Hz) is the bandwidth (Young, 1990).
If samples of the noise voltage are taken over a long period and the results are plotted
as a histogram with bin widths,
dV,
a distribution of the form shown in Figure 5-3 is
produced (Brooker, 2008).
The probability
p
{
V
}
dV
that any future measurements will fall in the range
V
where
k
is Boltzmann's constant (1
.
38
×
→
V
dV
is given by this plot, which is known as the PDF. This function approximates the
normal or Gaussian distribution (Walpole and Myers, 1978), which can be described by
+
1
σ
√
2
e
−
V
2
2
/
2
σ
p
{
V
}
dV
=
(5.4)
π
2
, because the distribution
is Gaussian. Its value is a measure of how wide the distribution is; hence, it is a useful
indicator of the amount of noise present. However, in practice it is more common to specify
the noise level in terms of the root mean square (RMS) quantity, where
v
rms
is
v
2
, equates to the variance,
σ
The time-averaged squared value, ¯
√
¯
v
rms
=
v
2
(5.5)
