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Lecture Outline (Week 5, lecture 2)
Digitizing Analog Signals  Quantization
Reading:
text1 4.3.1
Supplementary:
Text2 6.5.1
Material covered:
1. Nyquist Sampling Theorem Reexamined
•
Sampling at transmitter and low pass filtering at receiver:
∑


=
n
nT
t
T
nT
t
T
nT
x
t
x
)
(
))
(
sin(
)
(
)
(
~
π
•
Sampling of signal by impulse train
Time Domain
Frequency Domain
•
Signal reconstruction:
)
(
)
(
~
t
x
t
x
=
if
0

)
(

f
X
only for
W
f
≤


and
W
T
f
s
2
/
1
≥
=
.
Time Domain (Interpolation)
Frequency domain (LP filtering)
•
For a signal with highest frequency
f
, it is sufficient to sample 2
f
times per second
•
Each sample, an analog value, is converted into a digital value
•
For speech of 4KHz, we sample 8000 times per second.
•
Each sample is digitized into 8 bits, yielding a bit stream at 64Kb/s.
2. Scalar Quantization
1
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Why quantization?
•
Finite precision is sufficient
•
Infinite precision destroyed
by channel noise.
•
Reliable reproduction of bits
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 Spring '09
 Hui

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