???f?p???s? pa?

1
???f?p???s? pa?µ??
2
G?at? ??e???eta? ? µ??f?p???s? pa?µ??

• ??a? t??p?? e??tt?s?? t?? apa?t?se?? se fasµa
  ??a t?? ??f?a?? µetad?s? e??? a?a??????? s?µat??
  e??a? ? ???s? ap?d?t???? ?ßa?t?st?.
• ?? ? ???µ?? de??µat?????a? e??a? fs samples/sec,
  ?a?
• ?? e???µe ? 2n ep?peda ?ßa?t?sµ??, t?te
• ? ???µ?? pa?a????? d?ad???? s?µß???? e??a? R
  fs n bits/sec
• ?? apa?t??µe?? e???? fasµat?? ??a t?? µetad?s?
  e??a?
• BW CPS fs n Hz,
• ?p?? ? sta?e?a CPS e?a?tata? ap? t?? µ??f? t??
  pa?µ??
• ??a ded?µe?? ???sµ? t?? BW (s?????? 0.5 lt CPS
  lt1).
• ?a?ade??µa G?a tet?a?????? pa?µ? ?a? ???sµ? BW
  t?? s????t?ta p??t?? µ?de??sµ?? e??a? CPS 1 ?a?
  BW fs n Hz

3
???t???a s?ed?as?? µ??f?? pa?µ??

• S?????? p??sd???????µe d?? pa?aµet???? st? ped??
  s????t?t??
• ?? BW p??t?? µ?de??sµ?? (t? ?e???µe µ????)
• ? e?a??st? ap?sßes? t?? p?a???? ??ß?? se s?es?
  µe t? µe??st? t?µ? t?? ?????? ??ß?? se db down
  (?s? p?? µe?a?? t?s? ?a???te?a)
• ???spa???µe ?a st??????e???µe t?? a?µe? ?a? t??
  ????e? t?? pa?µ?? ??a ?a pe?????s??µe t? fasµa

P(f)2
db down
0 BW f (Hz)
4
?a?µ?? ?et?a??????? µ??f?? d?a??e?a? 1 µs

• BW p??t?? µ?de??sµ?? 1/? 1MHz
• ?e?e??? p?a???? ??ß?? 13.6 db down

1 MHz
5
?a?µ?? t????????? µ??f?? d?a??e?a? 1 µs

• BW p??t?? µ?de??sµ?? 2/? 2MHz
• ?e?e??? p?a???? ??ß?? 26 db down

2 ?Hz
6
?a?µ?? ?µ?t???e?d??? µ??f?? d?a??e?a? 1 µs

• BW p??t?? µ?de??sµ?? 1.5/? 1.5 MHz
• ?e?e??? p?a???? ??ß?? 22 db down

1.5 MHz
7
?a?µ?? Gaussian µ??f?? d?a??e?a? 1 µs

• BW p??t?? µ?de??sµ?? 1.5/? 1.5 MHz
• ?e?e??? p?a???? ??ß?? 31 db down

1.5 MHz
8
?p??a???? s?µß???? (InterSymbol Interference
ISI)

• Ta µp????saµe ?a ße?t??s??µe pe??ss?te?? t??
  µ??f? t?? pa?µ?? a??a ß?ep??µe ?t? e?µaste ???ta
  se ?ap??? ????.
• ??a? t??p?? ?a pet????µe µ???? e???? fasµat??
  e??a? ?a ???s?µ?p???s??µe pa?µ??? µe?a??te???
  d?a??e?a?.
• ?? ?µ?? ?? pa?µ?? e???? d?a??e?a µe?a??te?? t??
  T1/fs n t?te ?a e???µe ?pe??a???? t?? s?µß????
  (ISI InterSymbol Interference) ?a? p??ß??µa
  st?? ???? e?t?µ?s? t?? e?peµp?µe??? d?ad????
  s?µß????.

St??µe? de??µat?????a?
x(t) x(t-T)
-2T -T 0 T
t
9
????s? t?? d?a??e?a? t?? pa?µ??

• ?ta? e?a? pa?µ?? d?e??eta? ap? ?a?a?? µe e????
  fasµat?? µ???? se s?es? µe t? fasµa t?? pa?µ??,
  e???µe d?e????s? t?? d?a??e?a? t?? pa?µ??, ?p??
  p?? ?at?

10
??as?µß????? ?pe??a???? (ISI)

• ????????a pa?µ?? st?? e?s?d? t?? ?a?a????
• ?? pa?µ?? st?? e??d? t?? ?a?a????

11
??as?µß????? ?pe??a???? (ISI)

• ?? s?µa st?? e??d? e??a? ? ?pe??es? t?? pa?µ??

12
?e????e? Nyquist
13
??a?e??? ISI
14
???t???a t?? Nyquist ??a µ?de???? ISI

• ?? ep??a??pt??te? pa?µ?? de? ?a d?µ??????s???
  p??ß??µa st?? ???? e?t?µ?s? e??? d?ad????
  s?µß???? a? e???? µ?de???? t?µ? t?? st??µ? p??
  ?a???µe de??µat?????a t?? ?aµßa??µe??? s?µat??.
• ?e µa??µat????? ?????, ?e???µe ? pa?µ?? ?a
  ??a??p??e? t?? s?es?
• ?p?? k e??a? a?e?a??? ?a? ? ? ap?stas? µeta??
  s?µß????.
• ??a?? ?a? a?a??a?a s?????? ??a ?a ?s??e? ? p??
  pa?? s?es? e??a? ?
• ?? ? pa?µ?? e?e? ap???t? e???? fasµat?? ?W
  (d??ad? ?(f)0 ??a fgtBW) t?te ? µ???? t??p??
  ??a ?a ?s??e? ? p?? pa?? s?es? e??a? ?a e???µe
• (1/2?) ?W , ?p?te µ??? ? X(f)? ??a
  fltBW,?a? X(f) 0, a???? ??a??p??e? t?? s?es?,
  ?
• (1/2?) lt ?W ?p?te ?pa????? ?????e?e?e?
  s??a?t?se?? p?? ??a??p????? t? ???t????

15
S??epe?e? t?? ???t????? Nyquist ??a pa?µ??? µe
fasµa a?st??a pe?????sµe??

• ? pa?µ?? e?e? fasµa ?(f) µe a?st??a
  pe?????sµe?? ?W.
• ?? BW lt (1/2T) de? ?pa??e? pa?µ?? p?? ?a
  ??a??p??e? t? ???t????
• d??t?...
• ?? BW1/2T µ??? ? pa?µ?? µe fasµa X(f)sta?e?a
  ??a fltBW, ?a? X(f)0, a???? ??a??p??e? t??
  s?es?, d??t?...
• ???ad? ? pa?µ?? p?? ep?t?epe? µetad?s?
  s?µß???? µe ???µ? 1/? ????? ISI ?a? e?e? e?a??st?
  e???? fasµat?? e??a? ? x(t) sinc(t/T) . ?
  pa?µ?? a?t?? e??a? µ? p?a?µat?p???s?µ?? (d??t?
  e?e? µ? µ?de???? t?µ? ??a tlt0) a??a t??
  p??se??????µe µe µ?a ?a??ste??µe?? e?d??? t??,
  d?? t?? sinc(t-t)/T, ?p?? ? ?a??ste??s? t
  ep??e?eta? ets? ?ste ??a tlt0 ?a e???µe
  sinc(t-t)/T ? 0.

X(f)
S ?(fm/T)
...
...
-1/? -BW
BW 1/T f
S ?(fm/T)
...
...
-1/? -BW 0 BW 1/T f
16
S??epe?e? t?? ???t????? Nyquist ??a pa?µ??? µe
fasµa a?st??a pe?????sµe?? (2)

• 3. ?? BW gt (1/2T) ?pa????? ?????e?e?e? pa?µ??
  p?? ??a??p????? t? ???t????, d??t?...
• ?a?ade??µa pa?µ?? p?? ??a??p????? ta ???t???a
  t?? Nyquist e??a? ? ?????e?e?a pa?µ??
  ?pe????µe??? s???µ?t???? µe fasµa ?p?? st?
  s??µa. G?a f? 0 e???µe t?? p??????µe??
  pe??pt?s? BW1/2T.

S ?(fm/T)
...
...
-1/? -BW 0 BW
1/T f
1/2T


X(f)

?(f)
f0 1/2T

BW
17
?????e?e?a pa?µ?? ?pe????µe??? s???µ?t????

• ?e????af? st? ped?? s????t?t??
• ?p?? BW e??a? t? ap???t? e???? fasµat?? t??
  pa?µ??
• f0 1/2Ts, f? BW f0, f1 f0 f?,
• ? r f?/f0 e??a? ? roll-off factor
  (s??te?est?? a?ad?p??s??)

0, f
gt BW
r f?/f0 f00.5 fs 1/2Ts
r0 r0.5 r1
f0
18
S??a?t?s? µetaf??a? t?? pa?µ?? ?pe????µe???
s???µ?t????
r0 r0.5 r1
r f?/f0 f00.5 fs 1/2Ts
19
????? fasµat?? pa?µ?? ?pe????µe??? s???µ?t????

• G?a t? PCM s?st?µa µe s????t?ta de??µat?????a?
  fs ??d???p???s? µe n bits, e???µe
• BW (1r)/2 fs n Hz (1r)/2 R Hz
• r "rolloff factor", 0 ? r ? 1,
• ??d??e? pe??pt?se??
• r 0, e??a? ap?a ? pa?µ?? sinc(.)
• r 1, e??a? ? µe??st? d??at? t?µ? t?? pa?aµet???
  r ?a? t? fasµa pa???e? t?? µ??f? ?pe????µe???
  s???µ?t????
• r 0.35, e??a? ? t?µ? p?? ???s?µ?p??e?ta? sta
  ???e??-?µe???a???a ??f?a?a s?st?µata ????t??
  t??ef???a? NA-TDMA ?a? CDMA (p??t?p? IS-54/136)

r f?/f0 f00.5 fs 1/2Ts
20
?a?µ?? ?pe????µe??? s???µ?t???? - Fasµa

r f?/f0
21
?a?µ?? ?pe????µe??? s???µ?t????(Raised cosine)

• ?e????af? st? ped?? ??????

r0 r0.5 r1
22
?pe????µe?? s???µ?t??? µ??f? pa?µ??

r f?/f0
23
?a?µ?? ?pe????µe??? s???µ?t????
24
?a?µ?? ?pe????µe??? s???µ?t????
25
?a?µ?? ?pe????µe??? s???µ?t????Fasµat??? ap?d?s?
?
?
r0
2nd Nyquist (r1)
26
???p???s? t?? ?a?µ?? ?pe????µe??? S???µ?t????

• ?p??e? e????a ?a ???p????e? µe e?a ??f?a?? f??t??
  FIR (finite impulse response).
• ??a?????a f??t?a (p.?. f??t?a Butterworth)
  µp????? ( µe a??et? d?s????a) ?a p??se???s???
  t?? apa?t?t??? µ??f? t?? fasµat?? t??.
• ?? pa?µ?? st?? p?a?? ?a p?epe? ?a pe?????st??? ??
  p??? t?? d?a??e?a
• ??t?? ? ???????? pe?????sµ?? d?µ?????e? p?a?????
  ??ß???
• ?e???e? f??e?, ?a? ?????? ?ta? ta?t?s?µa f??t?a
  ???s?µ?p?????ta? st?? p?µp? ?a? st?? de?t?,
  ???s?µ?p??e?ta? e?a f??t?? µe fasµa "tet?a??????
  ???a" ?pe????µe??? s???µ?t????

27
??????a pe?????sµe??? pa?µ?? ?pe????µe???
s???µ?t????

• ? pe?????sµ?? t?? ???????? d?a??e?a? d?µ?????e?
  a???µe???? p?a????? ??ß???.

28
?a?ade??µa pa?µ?? ?pe????µe??? s???µ?t????.

• Data rate R 100 kbits/sec gt T 1/R 10 µs
• r 0.5 gt BW (1r)/2 R 0.75 R 75 kHz

BW ? 0.75(1/T) 0.75/10µs 75 kHz
29
Non-Nyquist te????e?Gaussian pa?µ??
30
?da????? pa?µ?? Nyquist
31
??d??e? G?aµµ?? Line Codes
32
??d??e? G?aµµ?? (Line coding)

• ???s?µ?p????µe pa?µ??? ??a µetad?s? e??? d?ad????
  s?µß???? (p?? s?????? µetafe?e? ?a? e?a bit
  p????f???a?).
• O s????este??? t??p? pa?astas?? t?? d?ad????
  s?µß???? µe pa?µ???, ???µa?eta? p?????? NRZ
• To "p??????" ?p???e? ?t? ste??eta? e?te e?a?
  pa?µ?? e?te ? a???t???? t??.
• ?? "NRZ" s?µa??e? "No Return to Zero" d??ad? ?
  d?a??e?a t?? pa?µ?? e??a? ? d?a??e?a t?? bit.
• p(t)
  p(t)
• 1 gt 0 T t 0 gt
  0 T t
• ???a? d??at?? ?a e???µe ?a? a??e? µ??fe? pa?µ?? ?
  "??d??e? ??aµµ??.

33
?????t?ta fasµat???? ?s???? t?? ??d??a ??aµµ?? "
??????? NRZ"

• G?a ?a?e µ??f? pa?µ?? e??a? e????? ?a ß?e?e? ?
  p????t?ta fasµat???? ?s????.
• SNRZ(f) P(f)2/T, P(f) Fp(t)

? SNRZ(f) ß??s?eta? µetas??µat????ta? t??
RNRZ(t) t?? a???????a? pa?µ??
T
SNRZ(f)

0.5T
R1/T
?p??et??µe tet?a?????? µ??f? pa?µ??
34
?a?ade??µa

• p(t) sinc(200.000t) sin(200.000 p t) /
  (200.000 p t)
• R 1/T 200.000 bits/sec
• G??eta? ???s? pa?µ?? ?pe????µe??? s???µ?t???? µe
• "rolloff factor" r 0.
• P(f) Fp(t) (1/200.000) ?(f/200.000)
• SNRZ(f) P(f)2/T (1/200.000)?(f/200.000)

1/200.000
-100.000 0 100.000
f
35
????? t?p?? ??d???? ??aµµ??

• ?? as??µate?, ?? ?ad??f????e? ?a? ?? d???f????e?
  t??ep????????e? ???s?µ?p????? ??d??a ??aµµ??
  t?p?? "p?????? NRZ" ??at? ets? e???????µe?ta?
  fasµa.
• Se a??a s?st?µata ??f?a??? t??ep??????????
  µe???e? f??e? ???s?µ?p?????ta? a???? ??d??e?
  ??aµµ?? ??a ?a ap??t?s??? ep???µ?ta
  ?a?a?t???st??a ta µetad?d?µe?a s?µata.
• ???µat?????a
• Polar (p??????) ste??eta? e?a? pa?µ?? ? ?
  a???t???? t??
• Unipolar (µ???p??????) ste??eta? e?a? pa?µ?? ? t?
  µ?de?
• Bipolar (d?p??????) t? e?a pa??sta?eta? µe
  e?a??a?? t?? p?????t?ta? t?? pa?µ??
• NRZ (?? Return to Zero) O pa?µ?? d?a??e? ?s? ?a?
  t? s?µß???
• RZ (Return to Zero) O pa?µ?? d?a??e? ?s? t? µ?s?
  s?µß???

36
????p?????? NRZ

• ??peµpeta? ? pa?µ?? ?ta? ste??eta? t? 1 ?a? de?
  e?peµpeta? t?p?te ?ta? ste??eta? t? 0.
• ???s?µ? ??a "µ? s?µf??e?" ep????????e? ?ta? ?
  de?t?? de? µp??e? ?a ap?fas?se? ??a t? p??s?µ?
  t?? pa?µ??.
• G??eta? e???tat? ???s? t?? st?? ep????????e? µes?
  ?pt???? ????.
• p(t)
  p(t)
• 1 gt 0 T t 0 gt
  0 T t

37
?????t?ta fasµat???? ?s???? t?? µ???p?????? NRZ
R1/T

• ?p??e? ?a ?e????e? sa? p????? s?µat?d?s?a µe
  p??s???? µ?a? s??e???? s???st?sa?.
• SUniNRZ(f) (T/4)sinc2(fT) 1 d(f)/T

T
O ßas???? pa?µ?? e?e? tet?a?????? µ??f?




0.5T
R1/T
38
????p?????? RZ

• H s?µat?d?s?a RZ e?e? t?s? t?? a?e???µe?? ?s?
  ?a? t?? ?ate???µe?? a?µ? t?? pa?µ?? µesa st??
  d?a??e?a e??? s?µß????
• ??t? µp??e? ?a fa?e? ???s?µ? ??a d?e??as?e?
  ?????sµ?? ?a? s???????sµ??. (?d??? a? t? s?µa
  e??a? µa??a a???????a 1)
• p(t)
  p(t)
• 1 gt 0 ?/2 ? t 0 gt
  0 T t
• 
  Spata?? ?s????
• SUniRZ(f) (T/16) sinc2(f T/2) 1 (1/T) S df
  (n/T)

?? fasµa e??a? s?ed?? d?p?as?? t?? NRZ
0.5T
39
??p?????? RZ

• ???a? µ???p????? s?µat?d?s?a µ??? p?? ed? t?
  1ste??eta? e?a??a? µe ?et????? ?a? a???t?????
  pa?µ???.
• ? e?a??a?? a?t? e???dete???e? t?? s???st?sa
  s??e???? t?? µ???p?????? s?µat??.
• ??t? e??a? ep???µ?t? se p???a ?a?a??a, p?? de?
  µp????? ?a µetad?s??? t?? s???st?sa s??e???? (?
  s??a?t?s? µetaf??a? ?(f) ? 0 ??a f?0).
• p(t) p(t)
  p(t)
• 1 gt ? T/2
  0 gt
• 0 T/2 T t 0
  T t 0 ? t

40
PSD t?? ??p?????? RZ

• ?? ?s??ata?eµ?µe??? ?et???? ?a? a???t???? pa?µ??
  e???dete?????? t?? s??e?? s???st?sa t??
  e?peµp?µe??? s?µat??
• SbiRZ(f) (T/4) sinc(fT/2) sin2(pfT)

0.5T
R1/T
R1/T
41
??d??a? ??aµµ?? Manchester

• Ste??eta? pa?µ?? d?? fase?? ??a t? "1" ( -) ?a?
  ??a t? "0" ( - )
• ?e???aµßa?eta? ?a? ? a?e???µe?? ?a? ? ?ate???µe??
  a?µ? t?? pa?µ?? µe ?a?e s?µß???.
• ?e? ?pa??e? s??e??? s???st?sa
• p(t)
  p(t)
• 1gt 0 T/2 T t 0 gt
  0 T/2 T t
• ???a? e?d?? p?????? s?µat?d?s?a?.
• Smanch(f) T sinc2(fT/2) sin2(ft/2)

0.5T

42
???f? pa?µ??
????e? µ??fe? ßas???? pa?µ??
43
?p?d?ase?? t?? d?af???? ßas???? pa?µ??

• ?? d?af???? ßas???? pa?µ?? ???s?µ?p?????ta? ??a
  t?? ??a??p???s? d?af???? apa?t?se??
• ??e??????s? s???????sµ?? ? RZ ?a? ? Manchester
  e?asfa?????? ?ap??a e?a??a?? ?atastas?? µe ?a?e
  s?µß???, a??µa ?a? a? e?peµpeta? µa??a a???????a
  0 ? 1.
• ???f?p???s? fasµat?? ?s?? ? p?? sp??da?a
  efa?µ???.
• ? µ??f? t?? fasµat?? e?a?tata? ?s???a ap? t??
  µ??f? t?? pa?µ??. ?ts? ep?t???a?eta?
• ????e??? s??e???? s???st?sa? st? e?peµp?µe??
  fasµa. ?e???a ?a?a??a (?p?? t? t??ef????? ?a?a??)
  de? ep?t?ep??? t?? d?e?e?s? t?? DC s???st?s?? t??
  s?µat??. St?? pe??pt?s? a?t? ???s?µ?p??e?ta? ?
  pa?µ?? Manchester
• ??e???? t?? e????? fasµat?? t?? e?peµp?µe???
  s?µat?? St? ep?µe?? slide fa??eta? ? s?es?
  µ??f?? pa?µ?? ?a? fasµat??

44
?a fasµata t?? ßas???? pa?µ?? 1/3

• NRZ
• S?µe?a µ?de??sµ?? NRZ
• RZ
• S?µe?a µ?de??sµ?? RZ

45
?a fasµata t?? ßas???? pa?µ?? 2/3

• Manchester
• S?µe?a µ?de??sµ??
• HS
• S?µe?a µ?de??sµ??

46
?a fasµata t?? ßas???? pa?µ?? 3/3
Ts d?a??e?a s?µß????