Waveform Quantization and Compression - Digital Signal Processing: Fundamentals and Applications - page 498

Binary code

x q

111

3

110

2

101

x

100 000 /

0

4 2 2 3 4

001

010

2

011

3

e q

/2
/2

x

FIGURE 11.1

Characteristics of a 3-bit midtread quantizer.

this section, we focus on a linear midtread quantizer, which is used in digital communications (Rod-
dy and Coolen, 1997; Tomasi, 2004), and its use to quantize speech waveforms. The linear midtread
quantizer is similar to the bipolar linear quantizer discussed in Chapter 2 except that the midtread
quantizer offers the same decoded magnitude range for both positive and negative voltages.
Let us look at a midtread quantizer. The characteristics and binary codes for a 3-bit midtread
quantizer are depicted in Figure 11.1 , where the code is in a sign magnitude format. Positive voltage is
coded using a sign bit of logic 1, while negative voltage is coded by a sign bit of logic 0; the next two
bits are the magnitude bits. The key feature of the linear midtread quantizer is noted as follows: when
0 x < D = 2, the binary code of 100 is produced; when D = 2 x < 0, the binary code of 000 is
generated, where D is the quantization step size. However, the quantized values for both codes 100 and
000 are the same and equal to x q ¼ 0. We can also see details in Table 11.1 . For the 3-bit midtread

Table 11.1 Quantization Table for the 3-bit Midtread Quantizer
Binary Code Quantization Level x q (V) Input Signal Subrange (V)

011
010
001
000
100
101
110
111

3D
2D
D
0
0
D
2D
3D

3 : 5D x < 2 : 5D
2 : 5D x < 1 : 5D
1 : 5D x < 0 : 5D
0 : 5 x < 0
0 x < 0 : 5D
0 : 5D x < 1 : 5D
1 : 5D x < 2 : 5D
2 : 5D x < 3 : 5D

2 3 Note: Step size ¼ D ¼ðx x Þ=ð 1 Þ ; x ¼maximum voltage; and x ¼x max . Coding format: a. sign bit:

max min max min

1¼ plus, 0 ¼minus; b. 2 magnitude bits.