Databases Reference
In-Depth Information
9.5.1 Forward Adaptive Quantization
Let us first look at approaches for adapting to changes in input variance using the forward
adaptive approach. This approach necessitates a delay of at least the amount of time required
to process a block of data. The insertion of side information in the transmitted data streammay
also require the resolution of some synchronization problems. The size of the block of data
processed also affects a number of other things. If the size of the block is too large, then the
adaptation processmay not capture the changes taking place in the input statistics. Furthermore,
large block sizes mean more delay, which may not be tolerable in certain applications. On the
other hand, small block sizes mean that the side information has to be transmitted more often,
which in turn means the amount of overhead per sample increases. The selection of the block
size is a trade-off between the increase in side information necessitated by small block sizes
and the loss of fidelity due to large block sizes (see Problem 7 at the end of this chapter).
The variance estimation procedure is rather simple. At time
n
we use a block of
N
future
samples to compute an estimate of the variance:
N
−
1
1
N
q
x
n
+
i
σ
=
(20)
i
=
0
Note that we are assuming that our input has a mean of zero. The variance information also
needs to be quantized so that it can be transmitted to the receiver. Usually, the number of bits
used to quantize the value of the variance is significantly larger than the number of bits used
to quantize the sample values.
Example9.5.1:
In Figure
9.13
, we show a segment of speech quantized using a fixed 3-bit quantizer. The step
size of the quantizer was adjusted based on the statistics of the entire sequence. The sequence
was the
testm.raw
sequence from the sample data sets, consisting of about 4000 samples
of a male speaker saying the word “test.” The speech signal was sampled at 8000 samples per
second and digitized using a 16-bit A/D.
We can see from the figure that, as in the case of the example of the sinusoid earlier in
this chapter, there is a considerable loss in amplitude resolution. Sample values that are close
together have been quantized to the same value.
The same sequence quantized with a forward adaptive quantizer is shown in Figure
9.14
.
For this example, we divided the input into blocks of 128 samples. Before quantizing the
samples in a block, the standard deviation for the samples in the block was obtained. This
value was quantized using an 8-bit quantizer and sent to both the transmitter and receiver. The
samples in the block were then normalized using this value of the standard deviation. Notice
that the reconstruction follows the input much more closely, though there seems to be room
for improvement, especially in the latter half of the displayed samples.
Example9.5.2:
In Example 9.4.1, we used a uniform quantizer with the assumption that the input is uniformly
distributed. Let us refine this source model a bit and say that while the source is uniformly
