HY530

1
HY530 ??F????S ???????O???S

• QUANTIZATION

2
??ad??as?a µetat??p?? a?a??????? se ??f?a?? (ADC)

??a?????? s?µa
?eta t?? de??µat?????a
?ßa?t?sµe?? s?µa
3
Kßa?t?sµ?? - Quantization

• ?a s?µata s??e???? ?????? ?f?sta?ta?
  de??µat?????a ?ata ta?ta ??????a d?ast?µata
• ? de??µat?????a de? e?sa?e? ?p??ad?p?te
  pa?aµ??f?s? a? ???e? µe ???µ? µe?a??te?? ap? t??
  ???µ? Nyquist.
• ?a a?a?????a de??µata e???? t?µe? se e?a s??e?e?
  d?ast?µa t?µ?? ?a? ??e?a?eta? ape???? a???µ??
  bits ??a t?? pa?astas? t??? µe te?e?a a???ße?a.
• ?ßa?t?sµ?? (Quantization) e??a? ? d?ad??as?a t??
  p??se???s?? e??? a?a??????? (s??e????) de??µat??
  µe e?a pepe?asµe?? a???µ? bits.
• O ?ßa?t?sµ?? e?sa?e? pa?t?te pa?aµ??f?s?.
  ?p????µe ?a t?? µe??s??µe a? a???s??µe t?? a???µ?
  t?? bits µe ta ?p??a pa??sta???µe e?a de??µa.

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S?µß???sµ?? s?et???? µe t?? ?ßa?t?sµ?

• ?st? ? µ?a t??a?a µetaß??t? p?? pa??sta?e? t?
  de??µa e??? a?a??????? s?µat?? t? ?p??? ?f?stata?
  de??µat?????a.
• ??te e??a? ? ?ßa?t?sµe?? t?µ?
  t?? ?.
• ??a? ?ßa?t?st?? e?e? ? ep?peda ?ßa?t?sµ??
• ?a ???a t?? ????? ?ßa?t?sµ?? ??????ta? ap? t?? ?
  1 t?µe?
• x0, x1, , xM, ?p?? x0 -?, xM ?
• ?ts? ??a
• ?a?e ep?ped? ?ßa?t?sµ?? µp??e? ?a a?t?st????s?e?
  se e?a?
• log2M bit d?ad??? a???µ?

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G?af??? pa?astas? t?? ?ßa?t?sµ??

111
?
x83.5
110
M8
101
100
-3 -2 -1 1 2 3

3
-3
x0 x1
x7 x8
011
-?
?
010
001
?
000
x1-3.5
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S???pt??? pa?astas? ?ßa?t?st?

• S?????? a??e? ? ?a????sµ?? t?? ep?ped??
  ?ßa?t?sµ??
• ?a?ade??µa -3.5,-2.5, -1.5, -0.5, 0.5, 1.5,
  2.5, 3,5
• G?at??
• ?p??et??µe ?t? ??a ta de??µata ?ßa?t????ta? st?
  p??s?este?? ep?ped? ?ßa?t?sµ??
• ??t? ?a?????e? ta ???a t?? ????? ?ßa?t?sµ??, e?
  p???e?µe?? st? µes?? µeta?? t?? ep?ped??
  ?ßa?t?sµ?? d??ad?
• -?, -3.0, -2.0, -1.0, 0, 1.0,
  2.0, 3.0, ?
• ?a?e a??? ???? a??a?e? t? sfa?µa ?ßa?t?sµ??
  (?e???µa Loyd-Marx)

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???p???s? t?? ?ßa?t?st?

• ??a? µetat??pea? a?a???????-se-??f?a?? (ADC
  Analog to Digital Converter) p??se????e? t? s?µa
  (de??µa) st?? e?s?d? t?? µe e?a ap? ta ? ep?peda
  ?ßa?t?sµ??.
• ??a ?????µa se???a??? e??d?? (SIO Serial Input
  Output) µetat?epe? t? ep?ped? ?ßa?t?sµ?? se
  a???????a ap? nlog2M bits.

n bits
x
ADC
SIO
Quantizer
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??a?t???? t??p?? ?atas?e??? ADCs

• Counting or Ramp ADC
• ??a tas? a?af??a? a??a?e? ?ata sta?e?a ß?µata
  µe??? ?a ???e? µe?a??te?? ap? t? de??µa. ?
  d?ad???? a???µ?? p?? a?t?st???e? st??? pa?µ???
  t?? ???????? p?? ??e?ast??a? ?? a?t? e??a? ?
  ?ßa?t?sµe?? t?µ? t?? de??µat??
• Serial or Successive Approximation ADC (Se???a???
  ADC ? d?ad?????? p??se???se?? ADC)
• ???s?µ?p??e? d?ad??? e?e??a (µe??? ?a f?ase? st??
  ep???µ?t? a???ße?a ) ??a ?a p??sd????se? t?? ????
  ?ßa?t?sµ?? t?? de??µat?? e?s?d??.
• Parallel or Flash ADC (?a?a?????? ?
  ast?ap?a???)
• ?? de??µa e?s?d?? s??????eta? ta?t?????a µe ??a
  ta d??ata ep?peda ?ßa?t?sµ??. ?p??e?eta? t?
  ?????te?? ap? ta ep?peda ?ßa?t?sµ?? p?? e??a?
  µ????te?a t?? s?µat??

?e?a??te?? ta??t?ta
M????te?? p???p????t?ta
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??d? T???ß?? st?? ?ßa?t?st?

• T???ß?? ?ßa?t?sµ?? (Quantization Noise)
• ?µfa???eta? ??at? ? t?µ? t?? de??µat?? x
  a?t??a??stata? ap? t?? t?µ? t?? p??s?este???
  ep?ped?? ?ßa?t?sµ??. ?? sfa?µa ?ßa?t?sµ?? ??a e?a
  de??µa e??a? nQ x fQ(x) ?a? e??a?
  µ????te??, ?ata ap???t? t?µ?, ap? t? ?µ?s? t??
  µe?e???? t?? ????? ?ßa?t?sµ??.
• T???ß?? ?pe?f??t?s?? (Overload Noise)
• ?µfa???eta? ?ta? t? s?µa e?s?d?? e??a? µe?a??te??
  ap? t? µe?a??te?? ep?ped? ?ßa?t?sµ?? µe
  ap?te?esµa t?? ?a???d?sµ? t??.
• ?????d?? T???ß?? (Granularity Noise)
• ?µfa???eta? ?ta? ta ep?peda ?ßa?t?sµ?? de? e??a?
  a??eta p???a ??a ?a p??se???s??? µe a???ße?a t?
  de??µa. ???a? p?? eµfa??? ?ta? ?? t?µe? t??
  de??µat?? ??µa????ta? e?af?a ???? ap? e?a ????
  pe?????? ?ßa?t?sµ??.
• ?? ? a???µ?? t?? ep?ped?? ?ßa?t?sµ?? ? e??a?
  sta?e??? t?te ?pa??e? a?ta??a?? µeta?? t??
  ????ß?? ?ßa?t?sµ?? ?a? ?pe?f??t?s??

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?a?aµ??f?s?

• ? ?ßa?t?sµ?? e?sa?e? pa?aµ??f?s? st? s?µa
• Te???µe ?a e?a??st?p???s??µe t?? µes? pa?aµ??f?s?
  D, ?p??
• ?p?? f(x) ? pdf t?? s?µat??.
• ??t? t? µet?? pa?aµ??f?s?? ???µa?eta? ?a? µes?
  tet?a?????? sfa?µa (MSE Mean Square Error)
• To MSE µe?e???e? ta µe?a?a sfa?µata pe??ss?te??
  ap? ta µ???a.

?
? fQ(?)
?ßa?t?st??
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??a e?a??a?t??? ?e???s? t?? ?ßa?t?sµ??

• ? ?ßa?t?sµ?? p??s?ete? e?a t??a?? ????ß? nQ x
  - x st?? p?a?µat??? t?µ? x t?? de??µat??.
• ?ts? ? pa?aµ??f?s? D ? t? MSE EnQ2 µp??e? ?a
  ?e????e? ?t? e??a? ? ?s??? t?? ????ß?? ?ßa?t?sµ??
• ?p????µe ?a ???s??µe µ?a s?µat?????ß??? s?es?
  (SNR Signal to Noise Ratio) ??a ?a
  ?a?a?t???s??µe t?? s?µpe??f??a t?? ?ßa?t?st?.
  SNR?s??? s?µat?? x / ?s??? ????ß?? nQ

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?p?????sµ?? t?? s?µat?????ß???? s?es??

• ?es? t?µ? t?? s?µat?????ß???? s?es?? (SNR)
• SNR (S/N)avg ?s??? s?µat?? x / ?s??? ????ß??
  nQ
• ?p????µe ?a ???s??µe ?a? t?? µe??st? SNR (peak
  SNR)
• ????te?? ???s?µ?. ?e? ?a t?? ???s?µ?p???s??µe...

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?a?ade??µa ?p?????sµ?? SNR

• ?st? ?ßa?t?st?? µe ep?peda ?ßa?t?sµ?? ? x1,
  x2,x8
• x1-3.5, x2-2.5, x3-1.5, x4-0.5, x50.5,
  x61.5, x72.5, x83.5
• H pdf f(x) t?? s?µat?? e?s?d?? e??a? ?µ???µ??f?
  µe t?µ? 1/8 st?
• d?ast?µa -4, 4
• ? ?s??? t?? s?µat?? X e??a?
• ? pa?aµ??f?s? D e??a?

f(x)
-4 0 4 x
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?a?ade??µa ?p?????sµ?? SNR (s??e?e?a)

• ?? e?etas??µe t?? ??? ??a k5
• ?a? ?? 12 ???? t?? a????sµat?? e??a? ?s?? ? MSE
  D 1/12 ?
• ?? SNR se db e??a? (S/N)avg 10?log10(64)
  10?log10(26) 6?3 18
• ??a? eµpe?????? ?a???a? ????e? ?t? ?a?e p??s?et?
  bit st?? ??d???p???s? t?? de??µat?? p??s?ete? 6
  db st?? s?µat?-????ß??? s?es? t?? ?µ???µ??f??
  ?ßa?t?st? ?ta? ta s?µata e?s?d?? e???? ?µ???µ??f?
  pdf

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?ßa?t?st?? 3 bit , 8 ep?ped??

x8
Sfa?µa

x1
S?µa ??s?d?? x
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?ßa?t?st?? ?26 64 ep?ped??
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(No Transcript)
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SNR ??a ?µ???µ??f? ?ßa?t?st? (s?????)

• Ge???? ap?te?esµa (µp??e? ?a ap?de???e? e????a)
• ????p??ese??
• ?µ???µ??f?? ?ßa?t?st?? ? ep?ped??
• ?a de??µata e?s?d?? e???? ?µ???µ??f? ?ata??µ?, µe
  pe????? t?µ?? ?s? µe t?? pe????? t?µ?? p??
  ?a??pte? ? ?ßa?t?st??.
• ?µpe?????? ?a???a?
• ?a?e p??s?et? bit ( d?p?as?asµ?? ep?ped??)
  
• a??a?e? t? SNR ?ata 6 db (tet?ap?as?asµ??
  SNR)

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?a?µ???d??? ??aµ??f?s? (PCM)

• ? ?a?µ???d??? ??aµ??f?s? pa?a?e? e?a s?µa
  ?as???? ????? t? ?p??? ap?te?e?ta? ap? se??a
  pa?µ?? p?? p??e????ta? ap? t?? se???a?? e??d?
  e??? ?ßa?t?st?.
• ?e???e? f??e? ? ???? PCM ???s?µ?p??e?ta?
  e?a??a?t??a ??a t?? ??? ?ßa?t?sµ??.

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????? ????? s?µat?? PCM

• ?µ???µ??f?? ?ßa?t?st?? n bits ?a? 2n M
  ep?ped??
• ? ???µ?? de??µat?????a? e??a? fs
  de??µata/sec.
• ? ???µ?? pa?a????? d?ad???? s?µß????, d??ad? ?
  ???µ?? ??d???p???s?? st? e??d? t?? ?ßa?t?st?,
  e??a?
• fs log2M fs n
  bits/sec.
• To e?a??st? apa?t??µe?? e???? fasµat?? (µe
  ße?t?st? µ??f? pa?µ?? ) e??a? fs n/2 Hz.
• To e???? fasµat?? p??t?? µ?de??sµ?? (µe
  ?????????? µ??f? pa?µ??) e??a? fs n Hz.
• Ta a?afe????µe se ep?µe?a µa??µata st??
  ep?d?as? t?? µ??f?? t?? pa?µ?? ep? t?? e?????
  fasµat?? t?? s?µat?? PCM

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?a?ade??µa ?p?????sµ?? ??a s?µa PCM

• ???ß??µa ??a a?a?????? µ??s??? s?µa e?e? e????
  fasµat?? 15 kHz ?a? ta de??µata t?? µp?????
  ?a ?e??????? ?t? e???? ?µ???µ??f? pdf.
• ?a ß?e?e? t? e?a??st? e???? fasµat?? ??a t??
  µetad?s? t?? s?µat?? µe d?aµ??f?s? PCM ?a? µe
  µes? pa?aµ??f?s? ?a???te?? ap? 58db.
• ??s?
• S????t?ta de??µat?????a? fs ? 2B 30.000
  de??µata/sec.
• 10?log10M2 ? 58db ? M ? 102.9?103 ?210 ? n ? 10
  bits/sample
• ??a??st?? ???µ?? pa?a????? ded?µe??? R fs n ?
  300.000 b/s
• ??a??st? e???? fasµat?? BW R/2 ? 150 kHz.
  (?p?t??eta? ?t? ???s?µ?p????µe pa?µ? ße?t?st??
  µ??f??)

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?? ?µ???µ??f?? ?ßa?t?st??

• ??a? ?ßa?t?st??, µe ?sape???ta ep?peda
  ?ßa?t?sµ??, d??ad? µe xk-1 xk ?, ?k ?
  1,2,,M ???µa?eta? ?µ???µ??f?? ?ßa?t?st??.
• Se µe???e? pe??pt?se?? e??a? ?a???te?a ?a e???µe
  ep?peda ?ßa?t?sµ?? µe d?af??et??e? ap?stase??
  µeta?? t???.
• ?? e?etas??µe t?? µes? pa?aµ??f?s? (MSE) D
• ß?ep??µe ?t? ??a ?a ???e? t? D e?a??st?
  p?epe? ?a ep??e???µe ta
• ep?peda ?ßa?t?sµ?? xk ets? ?ste t? sfa?µa
  (x- x)2 ?a ???eta? µ???? ?ta? ? pdf f(x) e?e?
  µe?a?? t?µ? ?a? ?a de??µaste ?a e??a? µe?a??te??
  ?p?? ? f(x) e?e? µ???? t?µ?.
• ?as??? a??? ??e? ?p?? ? pdf e?e? µe?a?? t?µ?
  e???µe s?ss??e?s? t?? ep?ped?? ?ßa?t?sµ??

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?? ?µ???µ??f?? ?ßa?t?st??

• ?a?ade??µa s?ss??e?s?? t?? ep?ped?? ?ßa?t?sµ??
  st?? pe????e? ?p?? ? pdf e?e? µe?a??te?e? t?µe?.

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???????µ?? Lloyd-Max

• ?p?t?epe? t?? s?ed?as? ße?t?st?? ?ßa?t?st? ??a
  ?p???d?p?te a???µ? ep?ped?? ?a? ??a ?a?e f(x).
• ? a??????µ?? Lloyd-Max apa?ta se d?? ßas??e?
  e??t?se??
• G?a ded?µe?? s????? ep?ped?? ?ßa?t?sµ??, p??a
  e??a? ta ße?t?sta ???a t?? ????? ?ßa?t?sµ???
• G?a ded?µe?? s????? ????? ?ßa?t?sµ??, p??a e??a?
  ta ße?t?sta ep?peda ?ßa?t?sµ???
• ?a? a?te? ?? e??t?se?? te???? ?a? apa?t?????
  d?ad????a, t?s? ?? ???e? ?s? ?a? ta ep?peda
  ?ßa?t?sµ?? s????????? sta ße?t?sta.

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???t?s? 1 ???a e??a? ta ße?t?sta ???a t?? ?????
??a ded?µe?? s????? ep?ped?? ?ßa?t?sµ??

• ??deta? e?a s????? ep?ped?? ?ßa?t?sµ?? x1,
  x2,x?
• ?p??e???µe e?a s????? ????? ??a t?? ???e?
  ?ßa?t?sµ??,
• x0, x1,,x? ?p?te ? µes? pa?aµ??f?s? D
  ?s??ta? µe
• ?p??et??µe ?t? f(x) const µesa st?? ????
  ?ßa?t?sµ??.
• ?a ße?t?sta ???a t?? ????? ?ßa?t?sµ?? ep??e???ta?
  ets? ?ste
• ???s???µe ?t? p?epe? pa?t?te ?a ?ßa?t????µe st?
  p??s?este?? ep?ped? ?ßa?t?sµ??, d??ad?

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???t?s? 2 ???a e??a? ta ße?t?sta ep?peda ??a
ded?µe?a ???a ????? ?ßa?t?sµ???

• ??deta? e?a s????? ????? ????? ?ßa?t?sµ?? x0,
  x1,, x?
• ?p??e???µe e?a s????? ep?ped?? ?ßa?t?sµ?? x1,
  x2,, x?.
• ?a ße?t?sta xi ??a??p????? t?? s?es?

???ad? t? xk e??a? t? ?e?t??e?de? t?? ?????
?ßa?t?sµ??
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?e?????? t?? ???????µ?? Lloyd-Max

• ?p??e???µe e?a a????? s????? ep?ped?? ?ßa?t?sµ??
  
• x1, x2,,xM.
• ?a ???a t?? ????? ?ßa?t?sµ?? p?epe? ?a e??a? st?
  µes?? t?? ep?ped?? ?ßa?t?sµ??, d??ad?
• ?a ep?peda ?ßa?t?sµ?? e??a? ta ?e?t??e?d? t??
  ?????
• ?pa?a?aµßa???µe ta d?? te?e?ta?a ß?µata µe????
  ?t??

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?a?ade??µa efa?µ???? t?? ???????µ?? Lloyd-Max

• ??deta? ? t??a?a µetaß??t? x µe pdf

?st? ?t? ta a????a ep?peda ?ßa?t?sµ?? e??a? ta
1,2,3,4
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?a?ade??µa efa?µ???? t?? ???????µ?? Lloyd-Max (2)

• ?a ???a t?? ????? ?ßa?t?sµ?? e??a?
• x00, x1(12)/21.5, x2 (23)/22.5,
  x3(34)/23.5, x4?.
• H pa?aµ??f?s? st?? pe??pt?s? a?t? e??a?
• ?a ?ea ep?peda ?ßa?t?sµ?? e??a?

S??e?e?a
30
?a?ade??µa efa?µ???? t?? ???????µ?? Lloyd-Max (3)

• ?ea ep?peda ?ßa?t?sµ?? (s??e?e?a)
• ?.?.?. St?? p??a?a s????????µe t?? ??? d?ad??as?a

?pa?a????
?p?peda xk
???a ????? xk
MSE
1, 2, 3, 4 0, 1.5, 2.5,
3.5, ? 0.329
??????
1 0.57, 1.92, 2.92, 4.5
0, 1.24, 2.42, 3.71, ?? 0.152
2 0.50, 1.72, 2.93, 4.71
0, 1.11, 2.32, 3.82, ? 0.131
5 0.41, 1.45, 2.80, 4.85
0, 0.93, 2.12, 3.82, ? 0.116
10 0.37, 1.31, 2.59, 4.66
0, 0.84, 1.95, 3.63, ? 0.111
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??a a??? pa?ade??µa ??a t?? ???????µ? Lloyd-Max

• ??deta? ? Gaussian pdf
• ?????? e?t?µ?s? ep?ped?? ?ßa?t?sµ??
• x1 -2, x2 -1, x31, x42
• ?pa?a???? ?p?peda xk ???a
  ????? xk MSE
• ?????? -2, -1, 1 2
  -?, -1.5, 0, 1.5, ? 0.29
• -1.94, -0.62, 0.62, 1.94 -?,
  -1.28, 0, 1.28, ? 0.14
• -1.75, -0.56, 0.56, 1.75 -?,
  -1.16, 0, 1.16, ? 0.13
• 5 -1.56, -0.48, 0.48, 1.56
  -?, -1.02, 0, 1.02, ? 0.12
• -1.51, -0.45, 0.45, 1.51 -?,
  -0.98, 0, 0.98, ? 0.118
• ?? ?µ???µ??f?? ?ßa?t?st?? D0.1175, EX21,
  (S/N)avg9.3db
• ?µ???µ??f?? ?ßa?t?st?? (S/N)avg9.25 db
• G?a ???a ep?peda ?ßa?t?sµ?? de? e?e? ?a?
  µe?a?? d?af??a

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?? ep?d?se?? ße?t?????ta? ??a µe?a??te?a ?

• ?a?ade??µa 2?
• ? ?ßa?t?sµ?? µ?a? Gaussian t??a?a?
  µetaß??t??
• ? SNR (db) ?µ???µ??f?? SNR (db)
  ??-?µ???µ??f??
• 2 4.4
  4.4
• 4 9.25
  9.30
• 8 14.27
  14.62
• 16 19.38
  20.22
• 32 24.57
  26.00
• 64 29.83
  31.89
• 128 35.13
  37.81

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?a?at???se?? ep? t?? ???????µ?? Lloyd-Max

• G?a ded?µe?? pdf ß??s?e? t?? ße?t?st?
  µ?-?µ???µ??f? ?ßa?t?st?.
• ?p??e? ?a ??e?as???? a??ete? epa?a???e?? ??a ?a
  s??????e? (e?a?tata? ap? t?? a????? e?t?µ?s?).
• ???a? d??at?? ?a ep??e???? pdfs ?a? a????e?
  e?t?µ?se?? ??a t?? ?p??e? ? a??????µ?? Lloyd-Max
  s??????e? se t?p??? ße?t?st?.
• ??? ß??s???µe t?? ße?t?st? µ?-?µ???µ??f?
  ?ßa?t?st? a? ? pdf de? e??a? ???st??? gt
  Ge???e?µe??? ???????µ?? Lloyd-Max.
• ??? µp????µe ?a p??se???s??µe ?a???te?a t? ????
  ???µ?? pa?aµ??f?s???? gt ??a??sµat????
  ?ßa?t?st??

34
S?es? ???µ?? R ?a? pa?aµ??f?s?? D

• S?ed?ast???? st???? ?ßa?t?st??
• G?a ded?µe?? ???µ? ??d???p???s?? R, ?a
  e?a??st?p????e? ? pa?aµ??f?s? D, G?a ded?µe??
  pa?aµ??f?s? D, ?a e?a??st?p????e? ? ???µ??
  ??d???p???s?? R
• ?pe???µ?s? R fs n bits/sec.
• Teµe???de? ???? ? ?e???a p????f????? ap?de????e?
  ?t? ??a e?a ded?µe?? µet?? pa?aµ??f?s?? D,
  ?pa??e? µ?a s??a?t?s? ???µ??-pa?aµ??f?s?? R(D)
  ? ?p??a d??e? e?a p??se???s?µ? ?at?te?? ???? st??
  ???µ? ??d???p???s?? R ??a ded?µe?? pa?aµ??f?s? D.

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S??a?t?s? ???µ??-pa?aµ??f?s?? R(D) ??a
Gaussian p??e?

• ?? ? x e??a? µ?a Gaussian t??a?a µetaß??t? µe
  t?p??? ap????s? sx
• d??ad?
  t?te ? s??a?t?s?
  ???µ??-pa?aµ??f?s?? R(D) ?s??ta? p???
• ?a?at???se?? 1) ? µe??st? ?e???t??? pa?aµ??f?s?
  e??a? Dsx2.
• ?p?t???a?eta? ??d???p????ta? ???e de??µa µe 0
  (?p?te R0).
• 2) D0 de? ep?t???a?eta? µe ?a?e?a R

36
??? ???? t?? R(D)

• Te???µa ? Gaussian p??? apa?te? t?? µe??st?
  ???µ? ??d???p???s?? µeta?? ???? t?? a???? p????
  ??a s???e???µe?? ep?ped? t?? µes?? tet?a???????
  pa?aµ??f?s??. ??t? s?µa??e? ?t? ? Gaussian
  ap?te?e? worst case scenario
• ?p?µe??? ??a t????sa s??a?t?s? ?ata??µ??
  p??a??t?ta? e??a?
• ?????ta? ?? p??? D ??a µ?a Gaussian p??? e???µe
  Dsx2 2-2R
• ?a? se dB
• D 10?log10(sx2) -6R dB

37
???ß??µata µe t?? µ???d?astat? ?ßa?t?st?

• ???µa ?a? µe t?? ße?t?st? µ???d?astat? (scalar)
  ?ßa?t?st?, ?? ep?d?se?? de? f?a???? t??
  p??ß?ep?µe?e? ap? t?? Te???a ???µ??-pa?aµ??f?s??
  .
• ??s? ?µad?p???s? t?? de??µat?? se blocks ?a?
  ?ßa?t?sµ?? ???? t?? block ded?µe??? ?a?e f??a-
  ??a??sµat???? ?ßa?t?st?? Vector Quantizer.
• ? d?a??sµat???? ?ßa?t?st?? e?e? ?a?a ap?te?esµata
  d??t?
• ??µeta??e?eta? t?? s?s?et?s? µeta?? de??µat??,
  ?a?
• ???µa ?a? a? de? ?pa??e? s?s?et?s? pa?e?e? e?a
  ?e?d?? sto SNR µe??? 1.52 db (shaping gain)

38
??a??sµat???? ?ßa?t?st?? Vector Quantizer (VQ)

• ?ßa?t????µe blocks ded?µe??? ? (y1,,yn).
• n e??a? ? d?astas? t?? ?ßa?t?st?.
• ?a ? ep?peda ?ßa?t?sµ?? a?t??a??stata? ap? ?
  d?a??sµata ?ßa?t?sµ??.
• ?? ???e? ?ßa?t?sµ?? a?t??a??sta?ta? ap? t??
  pe????e? ?ßa?t?sµ??
• ?a?e s?µe?? se ded?µe?? pe????? ?ßa?t?sµ??
  p??se????eta? (?ßa?t??eta?) ap? t? a?t?st????
  d?a??sµa ?ßa?t?sµ??.
• ???µ?? ?ßa?t?sµ?? R (log2M) / n bits/sample.
• ???a? d??at?? ?a e???µe ??asµat????? ???µ???

39
?µ???µ??f?? ?ßa?t?st?? 2 d?astase?? ?16, n2

• ??d??ta? ta d?? s?µata x1 ?a? x2. ?? ?ßa?t?s??µe
  ???e s?µa ????sta µe ?ßa?t?st? 4 ep?ped??
  ??e?a??µaste 2 bits/sample.
• ?? ???s?µ?p???s??µe d?a??sµat??? ?ßa?t?st? 16
  ep?ped?? ?p?? t?? s??µat?? ??e?a??µaste R
  (log2M) / n 2 bits/sample.
• ?d? de? ?pa??e? d?af??a µeta?? ßa?µ?t?? ?a?
  d?a??sµat???? ?ßa?t?st?

x2
40
??a??sµat???? ?ßa?t?st???8 pe????e? ?ßa?t?sµ??
, n2 d?astase??
???µ?? ?ßa?t?sµ?? R (log2M) / n 3/2
41
? Bivariate Gaussian pdf
42
G?at? e??a? ap?te?esµat???? e?a? VQ
??µeta??e?eta? t?? s?s?et?s? µeta?? d?? t??a???
s?µat?? x1 ?a? x2
?? ?? x1 ?a? x2 e??a? ap? ?????? Gaussian µe
????? s?s?et?s? ?? ?s???e?? ?aµp??e? t?? ap?
?????? pdf ?a e??a? ?p?? st? s??µa
?????te?? pa?aµ??f?s?
43
G?at? e??a? ap?te?esµat???? e?a? VQ (2)
???µa ?a? a? de? e???µe s?s?et?s?, ? VQ ep?t?epe?
t?? ?a????sµ? pe?????? ?ßa?t?sµ?? µe p??
?ata????? µ??f?. ?? x1 ?a? x2 e??a? as?s?et?ste?
ap? ?????? Gaussian ?e?d?? µ??f?p???s?? gt
µe??? ?a? 1.52 db ße?t??s? t?? D
44
??af??e? µeta?? ?µ???µ??f?? ?a? µ?-?µ???µ??f??
?ßa?t?st?

• ?st? ?t? t? s?µa e?e? Gaussian pdf, d??ad?
• f(x)exp(-x2/2)/?2p
• ?st? ?t? x1 -1.494, x2 -0.498, x3 0.498,
  x4 1.494.
• ?e a???µ?t??? ????????s? ß??s???µe
• D 0.1188, EX21, (S/N)avg
  10?log10(1/0.1188) 9.25 db
• ? µ? ?µ???µ??f?? ?ßa?t?st?? e?e? ?a???te?a
  ap?te?esµata.
• ? ?a???te??? d??at?? (µ?-?µ???µ??f??) ?ßa?t?st??
  4 ep?ped?? e?e? (S/N)avg 12 db (ap? t?? s?es? D
  10?log10(sx2) -6R dB)

45
Companding (s?st???d?ast???)

• ?? µ?-?µ???µ??f?? ?ßa?t?ste? µp?????, ??a ta
  pe??ss?te?a s?µata, ?a d?s??? ?a???te?a
  ap?te?esµata ap? t??? ?µ???µ??f??? ?ßa?t?ste?.
• ???a? ?µ?? p??? f????te?? ?a ?atas?e?as??µe ADC
  µe ?µ???µ??f??? ?ßa?t?ste?.
• ? s?st???d?ast??? (companding compressing
  expanding) e?sa?e? µ?a µ? ??aµµ???t?ta st? s?µa
  p??? t?? ?ßa?t?sµ?.
• ? µ?-??aµµ???t?ta e??e?eta? ets? ?ste t?
  p????pt?? s?µa ?a e?e? pdf ? ?p??a ?a p??s?a?e?
  ?ata t? d??at?? t?? ?µ???µ??f? ?ata??µ?.
• ??a? t?p???? ADC µe ?µ???µ??f? ap?stas? ep?ped??
  ?ßa?t?sµ?? µp??e? ?a ???s?µ?p????e? µeta t??
  compandor.
• H e?sa??e?sa µ?-??aµµ???t?ta a?a??e?ta? µe t??
  e?sa???? t?? a?t?st??f?? µ?-??aµµ???t?ta? ?ata
  t?? µetat??p? se a?a??????

46
??f?a?? s?st?µa ep????????a? µe compandor

• S?µa
• ??s?d??
• S?µa
• ???d??

x
Compressor
ADC
??µp??
g(x)
?a?a??
g-1(x)
x
0
?e?t??
DAC
Expandor
47
??p??e? µ?-??aµµ???t?te? p?? ???s?µ?p?????ta? se
compandors

• Mu-Law (???s?µ?p??e?ta? st?? ?. ?µe???? ?a? st??
  ?ap???a).
• A-Law (???s?µ?p??e?ta? st?? ????p?)
• s?????? ? 87.6

s?????? µ 255
48
S?es? e?s?d??-e??d?? t?? µ-Law Compandor
µ-Law
g(x)
x
49
H pdf e??? s?µat?? p??? ?a? µeta t?? µ Law
compandor

• PDF p???
  PDF µeta

?p???µ?t? pdf
?p???µ?t?
50
64 kbit/sec PCM ??a ??f?a?? t??ef???a

• ???s?µ?p??e?ta? companding µe µ 255 (?.
  ?µe????) ?a? ?87.6 (????p?).
• G??eta? de??µat?????a t?? f???? µe 8.000
  de??µata/sec.
• ?a?e de??µa ??d???p??e?ta? µe 8 bits (?
  ?ßa?t?st?? e??a? 256 ep?ped??).
• ? ???µ?? µetad?s?? ded?µe??? e??a? 8x8.000 64
  kbits/sec

51
?et??s? t?? pa?aµ??f?s?? ?µ???a?

• ??t?? ap? t? MSE e???µe ?a? e?a??a?t??e? µe??d???
  µet??s?? t?? pa?aµ??f?s?? t?? ?µ???a?
• ? ?ata pe????e? SNR (segmental SNR)
• Itakura-Saito fasµat??? ap?stas?
• Log Spectral Distance
• Perceptually weighted MSE
• http//dynamo.ecn.purdue.edu/ctanner/Distortion_M
  easures/distortion_measures.html
• ?a?e?a ap? ta p?? pa?? ???t???a de? a??e? µ???
  t?? ??a ?a pe????a?e? µe a???ße?a t?? a???st???
  p???t?ta µ?a? ?µ???a?.
• ?atafe????µe se ?p??e?µe???? ????????s? t??
  p???t?ta? t?? f???? µe t? Mean Opinion Score
  Testing (MOST)
• ????ate? ßa?µ??????? t?? p???t?ta µ?a? ?µ???a? µe
  ßa?µ??? p?? ??µa????ta? µeta?? 1 (a?ata???t?) ?a?
  5 (te?e?a ?µ???a).
• ? t??ef?????? p???t?ta? f??? s??????
  ßa?µ????e?ta? µe 4.3

52
?e????e? ??d???p???s?? ??a f???

• ??e? ?? µe??d?? ??d???p???s?? f???? ???s?µ?p?????
  ?ßa?t?sµ?.
• ????e? ?a???? ep?p?e?? ???s? ?d?a?te???
  ?a?a?t???st???? t?? f????
• ??d???p???s? ???????? ??µat?µ??f?? p??spa?e?a
  pa?astas?? t?? de??µat?? t?? ??µat?µ??f?? t??
  f???? st? ped?? t?? ??????.
• Fasµat??? ?e??d?? ??d???p???s?? p??spa?e?a
  pa?astas?? t?? fasµat???? ?a?a?t???st???? t??
  ??µat?µ??f?? t?? f????.
• ??d???p???s? ßas?sµe?? st? µ??te?? t?? f????.
  p??spa?e?a a?apa?a????? t?? µ??te??? t??
  d?ad??as?a? pa?a????? f????

53
????t?ta f???? vs ???µ?? ??d???p???s??

• ? ???µ?? ??d???p??s??
• µp??e? ?a e?att??e? µe
• a?ta??a?µa
• ??? a???s? t?? p???-
• p????t?ta? t?? ??d???-
• p???t?, ?
• ??? µe??s? t??
• p???t?ta? t?? f????

54
??d???p???s? t?? ??µat?µ??f?? t?? f??????af?????
PCM

• ?? s?µa t?? ?µ???a? e?e? µe?a?? s?s?et?s? ??a
  ?e?t????e? ??????e? st??µe?.
• ? d?af?????? pa?µ???d???p???t?? (DPCM-
  Differential PCM) ?ßa?t??e? t?? d?af??a µeta??
  e??? de??µat?? ?a? t?? p??ß?ep?µe??? t?µ?? t?? ?
  ?p??a p??ß?epeta? µe ??aµµ??? s??d?asµ?
  p??????µe??? de??µat??.
• S?????? ? d?af??a a?t? e??a? µ???? ?a? µe
  ????te?a bits ep?t???a?eta? µ???? pa?aµ??f?s?
• ? a?t???pt? p???t?ta f???? e?a?tata? ap? t??
  s?et??? t?µ? t?? sfa?µat?? ?ßa?t?sµ?? ?a? t??
  e?tase?? (?s????) t?? f????.
• ?? p??sa?µ???µe??? DPCM (ADPCM Adaptive DPCM)
  µeta-ßa????? t? ß?µa ?ßa?t?sµ?? a?a???a µe t??
  e?tas? t?? f????.
• ?? ADPCM µe 32kbits/sec e??a? p??? ????? ?a?
  e????? st?? ???p???s?, ???s?µ?p??e?ta? de e??tata
  (p.?. st? DECT)

55
??µ? t?? DPCM

xn
yn
rnrn-1ynqn


yn
Quantizer
S
S

ynqn

-
Delay T1
Delay T1
rn-1
xn-1
S?ss??e?s? t?? sfa?µat?? ?ßa?t?sµ??

yn
ynynqn
xn


yn
Quantizer

S
xn
-




yn

yn-1

Delay T1
Delay T1
S
S

xn-1





?e???a xn yn
??-s?ss??e?s? t?? sfa?µat?? ?ßa?t?sµ??
56
Predictive DPCM

• O predictor ???s?µ?p??e? ta p p??????µe?a
  ?ßa?t?sµe?a de??µata ??a ?a p??ß?e?e? t? pa???
  de??µa. ?ßa?t??eta? ? d?af??a t???.
• ?a ai ep??e???ta? ets? ?ste ?a e?a??st?p??e?ta?
  t? µes? tet?a?????? sfa?µa p??ß?e???
• Tet??µe

57
??aµ??f?s? DELTA (DM)

yn
yn1
xn

• ???a?a pe??pt?s? ??d???p???t? PCM st?? ?p??? t?
  s?µa ?f?stata? ?pe?-de??µat?????a ?a?
  ??d???p??e?ta? µe 1 bit/sample.
• ? ??aµ??f?t?? Delta µp??e? ?a ???p????e? µe e?a?
  e?a??et??a ap?? ?ßa?t?st? 1 ep?ped??.
• H Adaptive DM µe 16 kbits/sec µp??e? ?a pa?a?e?
  ??? ?a??? p???t?ta?

yn
1 bit Quantizer

S
xn
-
?
X
X


yn


yn-1

Delay T1
Delay T1
S
S


58
Fasµat??e? µe??d?? ??d???p???s??Subband Coding

• H a?t????? t?? a???st???? p???t?ta? e?a?tata? ap?
  t?? ???? s????t?t??. St?? p??? ?aµ??e? ? p???
  ????e? s????t?te? µp????? ?a ?????? a?e?ta
  µe?a??te?a MSE.
• ?? Subband Coders d?a???????? t? s?µa se p???e?
  ???e? µe ?ata????a f??t?a.
• ?a s?µata se ?a?e ???? µetat?ep??ta? se ??f?a?a
  µe t? standard PCM a??a µe d?af??et??? ???µ? R se
  ?a?e ????.

59
Fasµat??e? µe??d?? ??d???p???s??Adaptive
Transform Coding

• ?a de??µata t?? s?µat?? ?µad?p?????ta? se
  p?a?s?a.
• ?a s?s?et?sµe?a st?? ????? de??µata µetat?ep??ta?
  se as?s?et?sta (e?p????µe...) fasµat??a de??µata
  ?a???ta? FFT ? DCT (Discrete Cosine Transform).
• ?a fasµat??a de??µata pa??sta???ta? s?µf??a µe
  t?? ßa??? t??? st?? a?t????? t?? f????
• ? ße?t?st?? ??d???p???t?? f???? half-rate (4
  kbits/sec) ???s?µ?p??e? Adaptive Transform Coding
  ( µa?? µe d?a??sµat??? ?ßa?t?sµ? ?a? G?aµµ???
  p??ß?e??)

60
?e????e? ??d???p???s?? ßas???µe?e? se µ??te?a

• ??d???p???te? f???? G?aµµ???? p??ß?e??? Linear
  Predictive Speech Coders (LPC)
• ?? s?µa t?? f???? d?a??e?ta? se p?a?s?a d?a??e?a?
  20 ms.
• ? ?µ???a µ??te??p??e?ta? sa? ????ß?? (ae?a? ap?
  t??? p?e?µ??e?) p?? d?e?e??e? e?a ??aµµ??? f??t??
  (?a????a?, f???t??e? ???de?, ?a? st?µa ??????
  ?????t?ta).
• ? LPC ?ßa?t??e? t?? a???????a d?e?e?s??, t??
  pa?aµet???? t?? f??t???, ?a? t? ?e?d?? t??
  f??t???, ?a? µetad?de? ta d?ad??a ded?µe?a st??
  de?t?. S???a ???s?µ?p??e?ta? d?a??sµat????
  ?ßa?t?st??

????????a ??e?e?s??
???d?? F????
F??t?? ???ß?e???
?
?e?d?? F??t???
?a?aµet??? F??t???
61
Vector Sum Excited Linear Prediction (VSELP)

• ???s?µ?p??e?ta? st? ??f?a?? ????t? t??ef???a t??
  ?. ?µe????? (p??t?p? IS-136)
• ??a?s?a t?? 20 ms. ?a?e p?a?s?? pa??sta?eta? µe
  159 bits. ? ???µ?? ded?µe??? e??a? pe??p?? 8
  kbits/sec.
• ??a? d?a??sµat???? ?ßa?t?st?? d?? ßa?µ?d??
  ???s?µ?p??e?ta? ??a t?? ?ßa?t?sµ? t?? a???????a?
  d?e?e?s??.
• ?e???a bits (?p?? t? ?e?d?? t?? f??t???) e??a?
  p?? s?µa?t??a ??a t?? p???t?ta t?? f???? ap? ?t?
  a??a. ??ta p??state???ta? µe ??d???p???s?
  d?????s?? ?a???.

62
S?????s? µe??d?? ??d???p???s?? f????

• ??p?? ???µ?? (kb/s) ????p????t?ta(MIPS)
  ?a??ste??s? (ms) ????t?ta
• PCM 64
  0.01 0
  ?????
• ADPCM 32 0.1
  0
  ?????
• Delta Mod. 16 0.1
  0
  ?????
• Sub-Band 16 1
  25
  ?????
• VSELP 8
  100 35
  ?a??
• Te???a 1
  ?? ??
  ?????

63
??d???p???s? e????a? ?a? Video

• ?????a 1000 x 1000 pixels µe 8 bits ??a ?a?e e?a
  ap? ta t??a ???µata ??e?a?eta? 24 Mbits ??a ?a
  ??d???p????e?.
• ?? video ??e?a?eta? pe??p?? 20 frames/sec.
• ?a standards s?µp?es?? e??a? ßas??a ??a t??
  a?apt??? t?? ??f?a??? video.
• JPEG S?µp?es? e????a? ?ata 20 f??e? t???a??st??
• MPEG S?µp?es? video ?ata 100 f??e? ? pe??ss?te??