Databases Reference
In-Depth Information
F I GU R E 11 . 12
A signal sampled at two different rates.
(two-level) quantizer. With a two-level quantizer with output values
±
, we can only represent
a sample-to-sample difference of
. If, for a given source sequence, the sample-to-sample
difference is often very different from
, then we may incur substantial distortion. One way
to limit the difference is to sample more often. In Figure
11.12
we see a signal that has been
sampled at two different rates. The lower-rate samples are shown by open circles, while the
higher-rate samples are represented by
. It is apparent that the lower-rate samples are not
only further apart in time, they are also further apart in value.
The rate at which a signal is sampled is governed by the highest frequency component of
a signal. If the highest frequency component in a signal is
W
, then in order to obtain an exact
reconstruction of the signal, we need to sample it at least at twice the highest frequency, or
2
W
(see Section 12.7). In systems that use delta modulation, we usually sample the signal at
much more than twice the highest frequency. If
F
s
is the sampling frequency, then the ratio of
F
s
to 2
W
can range from almost 1 to almost 100 [
134
]. The higher sampling rates are used
for high-quality A/D converters, while the lower rates are more common for low-rate speech
coders.
If we look at a block diagram of a delta modulation system, we see that, while the block
diagram of the encoder is identical to that of the DPCM system, the standard DPCM decoder is
followed by a filter. The reason for the existence of the filter is evident fromFigure
11.13
, where
we show a source output and the unfiltered reconstruction. The samples of the source output
are represented by the filled circles. As the source is sampled at several times the highest
frequency, the staircase shape of the reconstructed signal results in distortion in frequency
bands outside the band of frequencies occupied by the signal. The filter can be used to remove
these spurious frequencies.
The reconstruction shown in Figure
11.13
was obtained with a delta modulator using a
fixed quantizer. Delta modulation systems that use a fixed step size are often referred to as
linear delta modulators. Notice that the reconstructed signal shows one of two behaviors. In
regions where the source output is relatively constant, the output alternates up or down by
+
;
these regions are called the
granular regions
. In the regions where the source output rises or
falls fast, the reconstructed output cannot keep up; these regions are called the
slope overload
regions
.
small.
However, this will make it more difficult for the reconstruction to follow rapid changes in the
input. In other words, it will result in an increase in the overload error. To avoid the overload
condition, we need to make the step size large so that the reconstruction can quickly catch up
with rapid changes in the input. However, this will increase the granular error.
If we want to reduce the granular error, we need to make the step size
