Biomedical Engineering Reference
In-Depth Information
the interval can be divided at most into 2
n
discrete numbers. This interval is divided into
quantization step size of
2(
v
)
2
n
=
E
0
(6.9)
The size of the quantization step (
E
0
) or aperture introduces an amplitude approximation
which limits the potential accuracy of the subsequent processing. For example, a 4-bit
A/D converter with an input range of
5 volts had a resolution (
E
0
) of 10 volts
divided by 16 levels, results in a quantizing step with a voltage resolution of 0.625 volts
as given by (6.10):
−
5to
+
10
v
2
4
10
16
=
=
0
.
625 volts
(6.10)
A change in the least significant bit will cause a step from one level to the next.
The most common types of sample quantization are as follows:
1)
Rounding
: The quantization level nearest the actual sample values is used to
approximate the sample;
2)
Truncation
: The sample value is approximated by the highest quantization level
that is
not
greater than the actual value;
and
3)
Signed Magnitude Truncation
: Positive samples are truncated but negative values
are approximated by the nearest quantization level that is not less than the actual
sample values.
The digital signal
X
(
nT
) can often be expressed as two components:
X
(
nT
)
=
nT
and
e
(
nT
) is an added error signal called “Quantization noise.” The error signal
e
(
nT
)
is modeled as a uniformly distributed random sequence with the exact nature of the
distribution dependent on the type of quantization involved. The variance for Truncation
X
0
(
nT
)
+
e
(
nT
), where
X
0
(
nT
) can be thought of as the actual signal value at
t
=
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