Digital Signal Processing Reference
In-Depth Information
200
200
0
0
−200
−200
0
20
40
60
80
0
20
40
60
80
(a) Sample
(c) Sample
200
200
0
0
−200
−200
0
20
40
60
80
0
20
40
60
80
(b) Sample
(d) Sample
Figure 3.19:
(a) A portion of an analog 10 Hz sine wave (solid), quantized using 3 bits (1 Sign, 2 Mag-
nitude), input biased one-half LSB, LSB = 113.33 volts (stem plot); (b) Quantization Noise; (c) Analog
10 Hz sine wave (solid), quantized using 4 bits (1 Sign, 3 Magnitude), input biased one-half LSB (stem
plot); (d) Quantization Noise.
We would need (170 volts/1.25 volts/level) = 136 levels per side, or 273 levels total. Investigating
powers of two, we see that 2
8
256 is inadequate, but 2
9
512 will work—so, in addition to the sign
bit, we need to employ nine bits of quantization, which will give the LSB as (170 volts/255 levels) = 0.667
volts/level.
=
=
Example 3.23.
Suppose we wanted to quantize, using 3 bits and the Offset method, a 340 volt peak-
to-peak sine wave (this would correspond to a sine wave varying between -170 and 170 volts which has
been offset toward the positive by 170 volts such that there are no longer any negative voltages). What
would be the value of the LSB? State the possible binary outputs and the corresponding input voltages
they represent.
With Offset Coding, we get 2
3
distinct levels, one of which is the lowest level, zero. There are
therefore 2
3
7 = 48.57 volts.
The possible binary output codes would be 000, 001, 010, 011, 100, 101, 110, 111, which would
represent quantized voltages of 0, 48.57, 97.14, 145.71, 194.28, 242.85, 291.42, and 340.00 volts, respec-
tively.
−
1 = 7 levels to reach the highest level, which would yield the LSB as 340
÷
