Digital Signal Processing Reference
In-Depth Information
Table 11.1
Signal
Level
Closest 8-Bit
Representation
Hexadecimal
Value
Actual
Error
Error As A Percent
Of Signal Level
0.50300
0.5000000
0 40
0.00300
0.596%
0.50300
0.5078125
0 41
0.0048128
0.957%
0.05030
0.0468750
0 06
0.003425
6.809%
0.05030
0.0546875
0 07
0.0043875
8.722%
0.00503
0.000000
0 00
0.00503
100%
0.00503
0.0078125
0 01
0.0027825
55.32%
processing. It can be modeled as an injection of noise when
simulated in an algorithm with unlimited numerical precision.
When the signal level is fairly large for the allowable range,
(0.503 is close to one half the maximum value), the percentage
error is small
less than 1%. As the signal level gets smaller, the
error percentage gets larger, as the table indicates.
Quantization noise is always present and is, on average, the
same level (any noise-like signal will rise and fall randomly, so we
usually concern ourselves with the average level). But as the input
signal decreases in level, the quantization noise becomes rela-
tively more significant. Eventually, for very small input signal
levels, the quantization noise can become so significant that it
degrades the quality of whatever signal processing is to be per-
formed. Think of it as like static on a car radio: as you get further
from the radio station, the radio signal gets weaker, and eventu-
ally the static noise makes it difficult or unpleasant to listen to,
even if you increase the volume.
So what can we do if our signal is sometimes strong (0.503 for
example), and sometimes weak (0.00503 for example)? Another
way of describing this is to say that the signal has a large dynamic
range. The dynamic range describes the ratio between the largest
and smallest value of the signal, in this case 100.
Suppose we exchange our 8-bit representation with 12-bit
representation? Then our maximum range is still from
e
1,
but our step size is now 1 / 2048, which is 0.000488. Let's make
a 12-bit table similar to the 8-bit example.
This is a significant difference. The actual error is always less
than our step size, 1 / 2048. But the error as a percentage of signal
level is dramatically improved and this is our concern in signal
processing. Because of the much smaller step size of the 12-bit
1to
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