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Waveform Coding Techniques: Dr. S. C. Chan, HKU
1
WAVEFORM CODING TECHNIQUES
CONTENTS
1. INTRODUCTION
2. QUANTIZATION TECHNIQUES
3. DECORRELATION TECHNIQUES
SUBBAND CODING, TRANSFORM CODING,
LINEAR PREDICTION
REFERENCES:
N. S. JAYANT AND P. NOLL,
DIGITAL CODING OF WAVEFORMS
ENGLEWOOD CLIFFS, NJ: PRENTICE-HALL, INC., 1989.
Waveform Coding Techniques: Dr. S. C. Chan, HKU
2
1. INTRODUCTION
In waveform coding, we try our best to approximate the waveform of the
input signal using some distortion measure such as mean squared error
.
Decorrelation Quantization Entropy Coding
Fig. 1.1 General structure of a waveform coding system.
Decorrelation
Decorrelation techniques such as transformation or prediction are
frequently used to reduce the redundancy (e.g. statistical) in the input
signal.
Waveform Coding Techniques: Dr. S. C. Chan, HKU
3
Quantization
The output of the decorrelator is usually of small amplitude. Significant
compression can be achieved by quantizing the signal to small number of
discrete symbols (Lossy).
Entropy Coding
The symbols are then losslessly encoded using entropy coding (Huffman,
arithmetic codes, etc).
Waveform Coding Techniques: Dr. S. C. Chan, HKU
4
2. QUANTIZATION TECHNIQUES
Quantization (such as A/D convertion) is the process of transforming a
given (signal) value into
a finite set of possible output values.
The L-level scalar quantizer Q is a mapping
C
RQ →: , (2-1)
which maps the real line R to a
finite set of reconstruction
values or representation levels,
, called the
codebook:
k
y
RyyyC
L
⊂
=
},...,,{
21
. (2-2)
Uniform Midrise
Uniform Midtread
xx
yy
x
i
x
i+1
y
i
I
i
Fig 2.1 Midrise and Midtread Quantizers.
The quantizer partitions R into L cells, ,
k
I
})(:],({
1 kkkk
yxQxxxI
=
∈
=
+
L
k
,...,2,1
=
. (2-3)
Waveform Coding Techniques: Dr. S. C. Chan, HKU
k
x
are called the decision levels.
5
The L-ary number k is transmitted to the receiver. If
R
L 2
=
, then a bit rate
of bits/samples
LR
2
log=
is needed. At the receiver, is recovered from the index using a
lookup
table
.
k
y
The quantizer characteristic consists of N treads, or horizontal steps, with
a riser or vertical segment jointing successive levels. For a symmetric
quantizer and with L even, we obtain a mid-rise quantizer while for L odd,
we obtain a mid-tread quantizer.
Expression for quantizer output,
where
∑
=
=
L
i
ii
xSyxQ
1
)()(
=
0
1
)(xS
i
otherwise
I
x
i
∈
.
(2-4)
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