# Lecture%203:%20Quantization - PowerPoint PPT Presentation

View by Category
Title:

## Lecture%203:%20Quantization

Description:

### Lecture 3: Quantization The last major stage of an A/D converter is the conversion of the sampled signal to a digital signal: quantized signal – PowerPoint PPT presentation

Number of Views:54
Avg rating:3.0/5.0
Slides: 10
Provided by: Timot272
Category:
Tags:
Transcript and Presenter's Notes

Title: Lecture%203:%20Quantization

1
Lecture 3 Quantization
• The last major stage of an A/D converter is the
conversion of the sampled signal to a digital
signal

quantized signal
sampled analog signal
A/D converter
vin
vout
B bits/sample
vout
example mapping from input to output
vin
2
Quantization
• Key parameters for an A/D converter
• full-scale voltage range R
• number of bits B
• number of quantization levels 2B
• quantization width Q R / 2B

quantized signal
3 bit unsigned binary code
8Q
input signal
111
7Q
110
6Q
101
5Q
R
100
4Q
011
3Q
010
2Q
001
Q
000
0
t
3
Quantization Error
• The rounding operation replaces each sample by
the nearest quantized value.
• quantization error e then lies in the interval
• maximum error (magnitude) Q/2

average error 0
error
Q/2
average square error Q2/12
vout
Vin Q/2
Vout- Q/2

-Q/2
4
Quantization Error
• Signal to Noise Ratio (SNR) or Dynamic Range
• maximum signal range R
• maximum noise range Q
• 6 dB per bit
• Example The human ear has a dynamic range of
about 100 dB. This requires approximately 16
bits which is the number of bits associated with
CD quality recording.

5
Quantization Error
• Large dynamic ranges can be obtained with fewer
bits, provided
• the sampling rate is increased and
• noise-shaping is performed.

6
D/A Conversion
• unipolar natural binary
• bipolar offset binary
• twos complement

b1
b2
input bits
analog output
DAC
b3
x
bB
R
7
D/A Conversion
• Horners algorithm

sum 0 b1 1-b1 for iB, B-1, B-2, , 1
sum 0.5(sum bi) end x R(sum - 0.5)
8
A/D Conversion
• Successive approximation (rounding)

comparator
x
successive approximation register
u(x-xQ)

xQ
-
b1
b2
b3
bB
Q/2
digital output
b1
b2
b3
bB
DAC
R
9
A/D Conversion
• Example
• 4 bits
• bipolar twos complement
• R 5 V (Q 0.3125 V)
• input voltage -1.8V