Waveform Quantization and Compression - Digital Signal Processing: Fundamentals and Applications - page 514

adaptive predictor is then added to this quantized difference signal to produce the reconstructed
version of the input xðnÞ . Both the reconstructed signal and the quantized difference signal are
operated on by an adaptive predictor, which generates the estimate of the input signal, thereby
completing the feedback loop.
The decoder shown in Figure 11.12B includes a structure identical to the feedback part of the
encoder as depicted in Figure 11.12A . It first converts the received 4-bit data IðnÞ to the quantized
difference signal d q ðnÞ using the adaptive quantizer. Then, at the second stage, the adaptive predictor
uses the recovered quantized difference signal d q ðnÞ and recovered current output xðnÞ to generate the
next output. Notice that the adaptive predictors of both the encoder and the decoder change corre-
spondingly based on the signal to be quantized. The details of the adaptive predictor will be discussed.
Now, let us examine the ADPCM encoder principles. As shown in Figure 11.12A , the difference
signal is computed as

dðnÞ¼xðnÞxðnÞ (11.7)

A 16-level nonuniform adaptive quantizer is used to quantize the difference signal dðnÞ . Before
quantization, dðnÞ is converted to a base-2 logarithmic representation and scaled by yðnÞ , which is
computed by the scale factor algorithm. Four binary codes IðnÞ are used to specify the quantized signal
level representing d q ðnÞ , and the quantized difference d q ðnÞ is also fed to the inverse adaptive
quantizer. Table 11.6 shows the quantizer normalized input and output characteristics.
The scaling factor for the quantizer and the inverse quantizer yðnÞ is computed according to the
4-bit quantizer output IðnÞ and the adaptation speed control parameter a l ðnÞ , the fast (unlocked) scale
factor y u ðnÞ , the slow (locked) scale factor y l ðnÞ , and the discrete function WðIÞ , defined in Table 11.7 :
y u n ¼ 1 2 5 y n þ 2 5 W I n (11.8)

where 1 : 06 y u ðnÞ 10 : 00.
The slow scale factor y l ðnÞ is derived from the fast scale factor y u ðnÞ using a lowpass filter as follows:
y l

1 2 6

y l n 1 y u þ 2 6

n ¼ n (11.9)

Table 11.6 Quantizer Normalized Input and Output Characteristics
Normalized Quantizer
Input Range:
log 2 jdðnÞjLyðnÞ

Normalized Quantizer
Output:
log 2 jd q ðnÞjLyðnÞ

Magnitude:
jIðnÞj

7 3.32

[3.12, þ N )

[2.72, 3.12) 6 2.91

[2.34, 2.72) 5 2.52

[1.91, 2.34) 4 2.13

[1.38, 1.91) 3 1.66

[0.62, 1.38) 2 1.05

[0.98, 0.62) 1 0.031

0

( N , 0.98) N