SlideShare a Scribd company logo
0RGXOH±6DPSOLQJ 4XDQWL]DWLRQ
 ,QWURGXFWLRQWR'LJLWDORPPXQLFDWLRQ6VWHP
RPPXQLFDWLRQ LV WKH SURFHVV FRQFHUQHG ZLWK WKH WUDQVPLVVLRQ RI LQIRUPDWLRQ WKURXJK
YDULRXVPHDQV,WFDQDOVREHGHILQHGDVWKHLQWHUWUDQVPLWWLQJWKHFRQWHQWRIGDWD VSHHFK
VLJQDOV SXOVHV HWF  IURP RQH QRGH WR DQRWKHU ([DPSOHV RI FRPPXQLFDWLRQ EHWZHHQ WZR
SRLQWV LQFOXGH D WHOHSKRQH FRQYHUVDWLRQ DFFHVVLQJ DQ ,QWHUQHW ZHEVLWH IURP RXU KRPH RU
RIILFHFRPSXWHURUWXQLQJLQWRD79RUUDGLRVWDWLRQ,QWKHSURFHVVRIFRPPXQLFDWLRQRQH
PD EH LQWHUHVWHG WR WUDQVPLW GLUHFWO WKH QDWXUDO VLJQDO DQDORJ VLJQDO  ZLWK RU ZLWKRXW
PRGXODWLRQ EDVHEDQGWUDQVPLVVLRQ 7KHUHDOOWKHSURFHVVRUVVVWHPVXVHGIRUWUDQVPLVVLRQ
SURFHVV DUH DQDORJ SURFHVVRUV GHVLJQHG XVLQJ GLVFUHWH DQDORJ HOHPHQWV OLNH RSDPSV
WUDQVLVWRUVUHVLVWRUVLQGXFWRUVFDSDFLWRUVHWF7KLVLVDQDORJFRPPXQLFDWLRQVVWHP
2QWKHRWKHUKDQGWKHVVWHPZKLFKVSHFLILFDOOGHDOVZLWKGLJLWDOGDWDDQGGLJLWDOO
SUHSURFHVVHG VLJQDOV LV D GLJLWDO FRPPXQLFDWLRQ VVWHP +HUH GLJLWDO SURFHVVRUV DQG
DFFHVVRULHVOLNHVWRUHGSURJUDP FRQWUROOHGSURFHVVRUVVRIWZDUHFRGHVGLJLWDOPHPRUHWF
WDNHVLPSRUWDQWUROHLQWKHSURFHVVRIVLJQDOWUDQVPLVVLRQDQGUHFHSWLRQ%XWDVZHNQRZDOO
WKH QDWXUDO XQGHUVWDQGDEOH VLJQDOV DUH DQDORJ RYHUKHDG KDUGZDUH IRU DQDORJ WR GLJLWDO
FRQYHUVLRQDQGGLJLWDOWRDQDORJFRQYHUVLRQDUHQHHGHGDWWKHWUDQVPLWWHUDQGUHFHLYHUHQG
UHVSHFWLYHO$OWKRXJKWKHQHFHVVLWRIH[WUDEORFNVIRUDQDORJWRGLJLWDOFRQYHUVLRQ $' 
DQG GLJLWDO WR DQDORJ FRQYHUVLRQ '$  GLJLWDO FRPPXQLFDWLRQ VVWHP LV SUHIHUUHG RYHU
DQDORJFRPPXQLFDWLRQVVWHPIRUVRPHSDUWLFXODUUHDVRQVDVIROORZV
Noise immunity:KLOHWUDQVPLWWLQJGLJLWDOLQIRUPDWLRQIRUPDWWLQJLVYHUHVVHQWLDOLHWZR
DQDORJ FRUUHVSRQGHQFH DPSOLWXGH YDOXHV DUH WR EH DVVLJQHG IRU ORJLF ]HUR DQG ORJLF RQH
UHVSHFWLYHO LQ FDVH RI ELQDU WUDQVPLVVLRQ 1RLVH LPPXQLW LQWR VXFK IRUPDWWHG GLJLWDO
LQIRUPDWLRQLVJUHDWHUWKDQWKDWRIDQDQDORJVLJQDO
Memory: $QDORJVLJQDOVDUHJHQHUDOOVWRUHGLQGHYLFHVOLNHPDJQHWLFWDSHVIORSSGLVNV
HWF,WUHTXLUHVPDQPDJQHWLFWDSHVWRVWRUHWKHDQDORJVLJQDOV0RUHRYHUWKHVHDUHHDVLO
DIIHFWHGEWKHPDJQHWLFDQGRWKHUPHFKDQLFDODQGSKVLFDOSKHQRPHQRQ2QWKHRWKHUKDQG
GLJLWDOLQIRUPDWLRQLVVWRUHGLQGHYLFHVOLNH'VDQGUHJLVWHUV)RUH[DPSOHLQD'IOLSIORS
WKHRXWSXWFDQEHUHWDLQHGIRUPDQHDUVZLWKRXWDQH[WHUQDOSRZHU:KHQWKHRXWSXWLV
QHHGHGWKHWULJJHUFORFNSXOVHLVVXSSOLHGWRWKHIOLSIORSDQGLWZLOOJLYHWKHRXWSXW/LIHWLPH
RIGLJLWDOPHPRULVDOVRKLJKHUWKDQWKDWRIDQDORJPHPRU
System Re-configurability: 2QHRIWKHPRVWVLJQLILFDQWDGYDQWDJHVRIGLJLWDOVVWHPVLVWKHLU
HDVHRIVVWHPUHFRQILJXUDELOLW$VIRUDQH[DPSOHOHWXVFRQVLGHUDQDQDORJORZSDVVILOWHU
7RFRQYHUWLWWRDKLJKSDVVILOWHUZHZLOOKDYHWRUHPRYHWKHFRPSRQHQWVIURPWKHFLUFXLW
DQGUHSODFHWKHPZLWKRWKHUDSSURSULDWHFRPSRQHQWV7KLVLVDWLUHVRPHMRELIWKHVVWHPLVD
FRPSOH[RQH2QWKHRWKHUKDQGWRFRQYHUWDGLJLWDOORZSDVVILOWHULQWRDKLJKSDVVILOWHUZH
FDQHDVLOFKDQJHWKHGLJLWDOILOWHUWUDQVIHUIXQFWLRQH z @MXVWEFKDQJLQJVRPHFRHIILFLHQWV
Aging: $JLQJVLJQLILHVJURZLQJROGHURIWKHVVWHP,WLVREYLRXVOOHVVHIIHFWLYHLQFDVHRI
GLJLWDOVVWHPV,QFDVHRIDQDORJVVWHPVWKHRXWSXWPDFKDQJHDIWHUDIHZHDUVGXHWR
DJLQJRIWKHGLVFUHWHDQDORJFRPSRQHQWVOLNHGLRGH$VWLPHJRHVWKHFXWLQYROWDJHRIWKH
GLRGHLQFUHDVHVVORZODQGXQVWHDGLO7KLVFDXVHVIOXFWXDWLRQLQWKHVVWHPSHUIRUPDQFH,Q
GLJLWDOVVWHPVWKHVVWHPHUURUGXHWRWKHSUREOHPRIDJLQJLVWRWDOODEVHQW
(OHPHQWVRI'LJLWDORPPXQLFDWLRQ6VWHP
RQVLGHUWKHEORFNGLDJUDPRIDGLJLWDOFRPPXQLFDWLRQOLQNGHSLFWHGLQ)LJXUH/HWXV
QRZEULHIOGLVFXVVWKHUROHVRIWKHEORFNVVKRZQLQWKHILJXUH

)LJXUH%ORFNGLDJUDPRIDGLJLWDOFRPPXQLFDWLRQVVWHP
,QDGLJLWDOFRPPXQLFDWLRQVVWHPWKHLQSXWVLJQDOVKRXOGEHLQGLJLWDOIRUPVRWKDWGLJLWDO
VLJQDOSURFHVVLQJWHFKQLTXHVFDQEHHPSORHGRQWKHVHVLJQDOV7KHHOHFWULFDOVLJQDODWWKH
RXWSXWRIWKHWUDQVGXFHUQHHGVWREHFRQYHUWHGLQWRDVHTXHQFHRIGLJLWDOVLJQDOV7KHEORFN
SHUIRUPLQJWKLVWDVNLVWSLFDOOWKHVHFRQGEORFNRIWKHGLJLWDOFRPPXQLFDWLRQVVWHPDQGLV
FRPPRQONQRZQDVIRUPDWWHU7KHRXWSXWVLJQDORIWKH)RUPDWWHULVLQGLJLWDOIRUP,IWKH
RXWSXWRIWKHLQIRUPDWLRQVRXUFHLVGLJLWDOWKHQZHQHHGQRWHPSORWKHIRUPDWWHU+HQFHWKH
GDWDFRPPXQLFDWLRQVVWHPEHWZHHQFRPSXWHUVGRHVQRWKDYHDIRUPDWWHU+RZHYHULIWKH
VRXUFHRILQIRUPDWLRQLQVXFKFDVHVLVNHERDUGRUWSHZULWHUFRQQHFWHGWRWKHFRPSXWHUWKHQ
WKHIRUPDWWLQJEORFNLVUHTXLUHGWRFRQYHUWFKDUDFWHUV ZKLFKDUHLQGLVFUHWHIRUPEXWQRWLQ
GLJLWDOIRUP WRGLJLWDOVLJQDOV
7R UHSUHVHQW WKHVH GLJLWDO VLJQDOV E DV IHZ GLJLWV DV SRVVLEOH GHSHQGLQJ RQ WKH
LQIRUPDWLRQFRQWHQWRIWKHPHVVDJHVDFRGLQJVVWHPFDQEHHPSORHGZKLFKPLQLPLVHVWKH
UHTXLUHPHQW RI QXPEHU RI GLJLWV 7KLV SURFHVV LV FDOOHG VRXUFH HQFRGLQJ DQG WKH EORFN
SHUIRUPLQJWKLVWDVNLVNQRZQDVVRXUFHHQFRGH7KLVVRXUFHHQFRGHUEORFNFRPSUHVVHVWKH
WRWDOGLJLWVRIDPHVVDJHVLJQDOIRUWUDQVPLVVLRQ
7R FRPEDW QRLVH LQ WKH FRPPXQLFDWLRQ FKDQQHO VRPH UHGXQGDQF LV GHOLEHUDWHO
LQWURGXFHGLQWKHPHVVDJH7KLVLVGRQHEWKHFKDQQHOHQFRGHUEORFN
,Q ORZ VSHHG ZLUHG WUDQVPLVVLRQ WKH FKDQQHO HQFRGHG VLJQDO LV JHQHUDOO QRW
PRGXODWHG7KHWUDQVPLVVLRQWDNHVSODFHLQEDVHEDQG+RZHYHUIRUSURSHUGHWHFWLRQLQWKH
UHFHLYHUDQGQRWWRFRPEDWQRLVHDQGLQWHUIHUHQFHOLQHFRGLQJLVXVHG6RPHSXOVHVKDSLQJLV
DORQHGRQHWRFRPEDWLQWHUIHUHQFH6RPHVSHFLDOILOWHUVDUHDOVRHPSORHGLQWKHUHFHLYHUWR
FRPEDWQRLVH$OOWKHVHDUHFROOHFWLYHOFDOOHGEDVHEDQGSURFHVVRU7KLVLVWKHFDVHLQIL[HG
WHOHSKRQDQGGDWDVWRUDJHVVWHP
 +RZHYHUIRUWUDQVPLVVLRQRIKLJKVSHHGGLJLWDOGDWD HJRPSXWHUFRPPXQLFDWLRQ
VVWHP  WKH GLJLWDO VLJQDO QHHGV WR EH PRGXODWHG LH IUHTXHQF WUDQVODWHG 7KH SULPDU
SXUSRVH RI WKH EDVHEDQG PRGXODWRU LV WR PDS WKH GLJLWDO VLJQDO WR KLJK IUHTXHQF DQDORJ
VLJQDOZDYHIRUPV$SHUIRUPDQFHPHDVXUHRIWKHPRGXODWRULVVSHFWUDOHIILFLHQFZKLFKLV
WKH QXPEHU RI ELWV VHQW SHU VHFRQG IRU HYHU +] RI FKDQQHO EDQGZLGWK 7KH SXUSRVH RI
,QIRUPDWLRQ6RXUFH
DQG,QSXW7UDQVGXFHU
2XWSXW7UDQVGXFHU
DQG2XWSXW6RXUFH
)RUPDWWHU
'HIRUPDWWHU
6RXUFH
(QFRGHU
6RXUFH
'HFRGHU
KDQQHO
(QFRGHU
KDQQHO
'HFRGHU
KDQQHO
%DVHEDQG3URFHVVRU 
%DQGSDVV0RGXODWRU
%DVHEDQG'HFRGHU 
%DQGSDVV'HPRGXODWRU
PRGXODWLRQLVWRLQFUHDVHWKHVSHFWUDOHIILFLHQFDVPXFKDVSRVVLEOH6RQHHGOHVVWRVDWKDW
LI WKH EDQGSDVV PRGXODWRU EORFN LV SUHVHQW WKH EDVHEDQG SURFHVVRU EORFN LV QRW UHTXLUHG
7KHUHIRUHWKHVHWZREORFNVDUHVKRZQDVPXWXDOOH[FOXVLYHEORFNV
 ,Q WKH FRPPXQLFDWLRQ FKDQQHO WKH WUDQVPLWWHG VLJQDO JHWV FRUUXSWHG E UDQGRP
QRLVH7KHQRLVHLVIURPYDULRXVVRXUFHVHLWKHUIURPHOHFWURQLFGHYLFHVLPSOHPHQWLQJWKH
FKDQQHO WKHUPDO QRLVH VKRUW QRLVH  RU IURP PDQPDGH GLVWXUEDQFHV DXWRPRELOH QRLVH
HOHFWURPDJQHWLFLQWHUIHUHQFHIURPRWKHUHOHFWURQLFHTXLSPHQWVHWF RUIURPQDWXUDOVRXUFHV
DWPRVSKHULFQRLVHHOHFWULFDOOLJKWLQJGLVFKDUJHVGXULQJWKXQGHUVWRUPUDGLDWLRQIURPVSDFH
IDOOLQJLQWKHHOHFWURPDJQHWLFVSHFWUXP 
 $WWKHUHFHLYHUWKHEDQGSDVVGHPRGXODWRUEORFNSURFHVVHVWKHFKDQQHOFRUUXSWHG
WUDQVPLWWHG ZDYHIRUP DQG PDSV WKHP EDFN WR D VHTXHQFH RI QXPEHU WKDW UHSUHVHQWV WKH
HVWLPDWHRIWUDQVPLWWHGGDWDVHTXHQFH,QFDVHRIEDVHEDQGWKHWDVNRIFRQYHUWLQJEDFNWKH
OLQH FRGHG SXOVH ZDYHIRUP WR WUDQVPLWWHG GDWD VHTXHQFH LV FDUULHG RXW E WKH EDVHEDQG
GHFRGHUEORFN
 7KLVVHTXHQFHRIQXPEHUVUHSUHVHQWLQJWKHGDWDVHTXHQFHLVSDVVHGWRWKHFKDQQHO
GHFRGHUZKLFKDWWHPSWVWRUHFRQVWUXFWWKHRULJLQDOLQIRUPDWLRQVHTXHQFH VRXUFHHQFRGHG 
IURPWKHNQRZOHGJHRIFKDQQHOHQFRGLQJDOJRULWKP
 7KHSHUIRUPDQFHPHDVXUHRIGHPRGXODWRUDQGGHFRGHULVWKHIUHTXHQFRIELWHUURU
%LW (UURU 5DWH %(5  LQ WKH GHFRGHG VHTXHQFH%(5 GHSHQGV RQ FKDQQHO FRGLQJ
FKDUDFWHULVWLFVWSHRIDQDORJVLJQDOXVHGLQWUDQVPLVVLRQDWPRGXODWRUWUDQVPLVVLRQSRZHU
FKDQQHO FKDUDFWHULVWLFV LH DPRXQW RI QRLVH QDWXUH RI LQWHUIHUHQFH  DQG WKH PHWKRG RI
GHPRGXODWLRQDQGGHFRGLQJ
 6RXUFH GHFRGHU HVWLPDWHV WKH GLJLWDO VLJQDO IURP WKH LQIRUPDWLRQ VHTXHQFH 7KH
GLIIHUHQFHRIWKHHVWLPDWHDQGWKHRULJLQDOGLJLWDOVLJQDOLVWKHGLVWRUWLRQLQWURGXFHGEWKH
GLJLWDOFRPPXQLFDWLRQVVWHP
 ,IWKHRULJLQDOLQIRUPDWLRQVRXUFHZDVQRWLQGLJLWDOGDWDIRUPDQGWKHRXWSXWRIWKH
UHFHLYHUQHHGVWREHLQWKHRULJLQDOIRUPRILQIRUPDWLRQDGHIRUPDWWHUEORFNLVQHHGHGWR
FRQYHUWEDFNWKHGLJLWDOGDWDWRHLWKHUGLVFUHWHIRUP OLNHNHERDUGFKDUDFWHU RUDQDORJIRUP
VDVSHHFKVLJQDO 
2XWSXWWUDQVGXFHUFRQYHUWVWKHHVWLPDWHRIGLJLWDOVLJQDO HLWKHULQGLVFUHWHIRUPRU
DQDORJIRUP WRDQDORJQRQHOHFWULFDOVLJQDOLIDQDQDORJRXWSXWLVQHHGHG+RZHYHULQGDWD
FRPPXQLFDWLRQVVWHPWKHLQSXWVLJQDODQGUHFRQVWUXFWLRQVLJQDOERWKDUHLQGLJLWDOIRUP6R
DQRXWSXWWUDQVGXFHUPDQRWEHDOZDVSUHVHQWLQGLJLWDOGDWDFRPPXQLFDWLRQVVWHP
 RPPXQLFDWLRQKDQQHO 0HGLXP FODVVLILFDWLRQ
RPPXQLFDWLRQFKDQQHOLVWKHSKVLFDOPHGLXPEHWZHHQWUDQVPLWWHUDQGUHFHLYHU7KHUHIRUH
DQ GHYLFH ZKLFK VHUYHV WKH SXUSRVH RI OLQNLQJ WUDQVPLWWHU ZLWK UHFHLYHU FDQ EH FDOOHG D
FKDQQHOKDQQHOPDEH³ZLUHG´FDUULQJHOHFWULFDOVLJQDODVLVWKHFDVHLQWHOHSKRQHZLUH
79 FDEOH RU (WKHUQHW FDEOH $ ZLUHG FKDQQHO PD DOVR FDUU RWKHU IRUPV RI VLJQDOV OLNH
RSWLFDO ILEHU FDUULQJ PRGXODWHG OLJKW EHDPV ³:LUHOHVVV ´FKDQQHO LV DOVR SRVVLEOH IRU
H[DPSOHXQGHUZDWHURFHDQFKDQQHOFDUULQJDFRXVWLFZDYHIRUVHDH[SORUDWLRQIUHHVSDFH
FDUULQJ HOHFWURPDJQHWLF ZDYH HWF $ FKDQQHO FDQ DOVR OLQN FR ORFDWHG WUDQVPLWWHU DQG
UHFHLYHUIRUH[DPSOHGDWDVWRUDJHPHGLXPVXFKDVPDJQHWLFWDSHPDJQHWLFGLVNRSWLFDOGLVN
ZKHUH GDWD LV VWRUHG DQG UHWULHYHG 6WRULQJ DQG UHWULHYLQJ GDWD UHTXLUHV WHFKQLTXHV OLNH
HQFRGLQJDQGVRXUFHFRGLQJZKLFKHPSORVDPHFRPPXQLFDWLRQSULQFLSOHVXVHGLQRWKHUWSH
RIFRPPXQLFDWLRQFKDQQHOV
$VGLIIHUHQWPHGLDLVPDGHRIGLIIHUHQWPDWHULDOVKDYLQJGLIIHUHQWHOHFWULFDOSURSHUWLHV
DQGGLIIHUHQWFRQILJXUDWLRQVWKHVXSSRUWGLIIHUHQWIUHTXHQFEDQGVRIRSHUDWLRQ,IWKHVLJQDO
EDQGZLGWK LV ZLWKLQ WKLV UDQJH RI IUHTXHQFLHV WKH FKDQQHO FDQ SDVV WKH VLJQDO ,Q DQDORJ
FRPPXQLFDWLRQGDVDIWHUGRLQJSUHSURFHVVLQJDWWKHWUDQVPLWWHU PDLQOPRGXODWLRQ WKH
PDLQZRUUZDVZKHWKHUWKHVLJQDOLVWUDQVIHUDEOHWKURXJKWKHFKDQQHO+RZHYHUWKHVFHQDULR
KDVFKDQJHGZLWKWKHDGYHQWRIGLJLWDOFRPPXQLFDWLRQ$PRUHLPSRUWDQWTXHVWLRQLVKRZIDVW
WKHVLJQDOFDQEHWUDQVPLWWHGEWKHFKDQQHO:HZRXOGVKRZWKURXJKRXWWKLVERRNWKDWWKH
MRERIDQHQFRGLQJDQGRUPRGXODWLQJVFKHPHLVWRVTXHH]HDVPXFKELWWUDQVPLVVLRQUDWH
IURPDFKDQQHOKDYLQJDILQLWHEDQGZLGWK7KHPRUHLWFDQH[WUDFWELWWUDQVPLVVLRQUDWHIURPD
JLYHQDPRXQWRIEDQGZLGWKWKHPRUHVSHFWUDOOHIILFLHQWWKHHQFRGLQJPRGXODWLRQSURFHVVLV
6RLWWXUQVRXWWKDWFKDQQHOVFDQEHFODVVLILHGDFFRUGLQJWRWKHPD[LPXPELWWUDQVPLVVLRQUDWH
LW FDQ KDQGOH +RZHYHU ZH ZDQW WR HPSKDVLVH KHUH WKDW ZLWK WKH LQYHQWLRQ RI QHZ
WHFKQRORJLHV WKLV FODVVLILFDWLRQ FDQ FKDQJH GUDPDWLFDOO DQG WKH ORZHU ELW UDWH VXSSRUWLQJ
FKDQQHORIWRGDFDQEHPRYHGXSZDUGLQWKHWUDQVPLVVLRQVSHHGWRPRUURZ$QH[DPSOHLV
WKHRUGLQDUFRSSHUWHOHSKRQHOLQH,QWKHJRRGROGGDVRIWHOHSKRQLWZDVFODVVLILHGDVD
FKDQQHOVXSSRUWLQJ.+]RIDQDORJVSHHFK:LWKWKHDGYHQWRI30LWVWDUWHGVXSSRUWLQJ
NESVVSHHFKWUDQVPLVVLRQ7KHQFDPH,6'1DQGLWVWDUWHGVXSSRUWLQJNESVVSHHFK
1RZDGDV ZLWK '6/ WHFKQRORJ SDUWLFXODUO ZLWK YHU KLJK VSHHG '6/ 96'/  LW FDQ
VXSSRUW0ESVRIGDWDUDWH
7DEOHODVVLILFDWLRQRIFRPPXQLFDWLRQFKDQQHOV
KDQQHO 7SH %LWUDWH%DQGZLGWK 5HSHDWHUGLVWDQFH $SSOLFDWLRQ
8QVKLHOGHG
WZLVWHGSDLU
:LUHOLQH NESV±*ESV )HZNP 6KRUWKDXO3671/$1
RD[LDOFDEOH :LUHOLQH )HZKXQGUHG0ESV )HZNP DEOH79/$1
2SWLFDOILEHU :LUHOLQH )HZ*ESV )HZWHQVRINP /RQJ+DXO3671/$1
)UHHVSDFH
EURDGFDVW
:LUHOHVV
)HZKXQGUHGN+]WR
)HZKXQGUHG0+]
1RUHSHDWHU %URDGFDVW5DGLR79
)UHHVSDFH
FHOOXODU
:LUHOHVV ±*+]
1RUHSHDWHUXSWR
EDVHVWDWLRQ
0RELOH7HOHSKRQ
606://
:LUHOHVV/$1 :LUHOHVV 8SWR0ESV
1RUHSHDWHUXSWR
DFFHVVSRLQW
:L)L%OXHWRRWK
7HUUHVWULDO
PLFURZDYH
OLQN
:LUHOHVV ±*+] (YHU±NP
/RQJKDXO36719LGHR
WUDQVPLVVLRQIURP
SODJURXQGWRVWXGLRLQ
DOLYHWHOHFDVW
6DWHOOLWH :LUHOHVV *+]*+]
6HYHUDO7KRXVDQG
NP
7UDQVFRQWLQHQWDO
WHOHSKRQDEOH79
EURDGFDVW'7+96$7
*36
,QIUDUHG :LUHOHVV )HZ7+] 1RUHSHDWHU
6KRUWGLVWDQFH/26OLNH
79UHPRWH
6LJQDODWWHQXDWLRQLQDFKDQQHOLVXVXDOODIXQFWLRQRIGLVWDQFHWKHVLJQDOWUDYHUVHVWKURXJK
WKHFKDQQHO7RNHHSWKHVLJQDOVWUHQJWKDWWKHUHFHLYHUVXIILFLHQWIRUGHWHFWLRQUHSHDWHUVDUH
XVHG LQ UHJXODU LQWHUYDOV DORQJ WKH FKDQQHO 7KH LQWHUUHSHDWHU GLVWDQFH LV DQ LPSRUWDQW
SDUDPHWHURIWKHFKDQQHO
 $SDUWIURPGDWDUDWHDQRWKHULQWHUHVWLQJIHDWXUHRIDFRPPXQLFDWLRQFKDQQHOLVLWV
FRPSDWLELOLWWRDSDUWLFXODUVLJQDORUDSSOLFDWLRQ7KHUHIRUHVRPHFKDQQHOVDUHPRUHVXLWDEOH
LQOLQNLQJDSDUWLFXODUWSHRIVLJQDOWRLWVUHFHLYHUWKDQWKHRWKHUV
 7DEOHJLYHVDFODVVLILFDWLRQRIFKDQQHOLQWHUPVRILWVSDUDPHWHUVGHVFULEHGDERYH
:KHUHWUDQVPLVVLRQPRGHLVVWLOOSULPDULODQDORJZHTXRWHWKHEDQGZLGWKLQVWHDGRIGDWD
UDWHDVWKHSHUIRUPDQFHPHDVXUHRIWKHFKDQQHO
 3HUIRUPDQFH0HDVXUH
:HKDYHDOUHDGVHHQWKDWDFRPPXQLFDWLRQFKDQQHOKDVDILQLWHEDQGZLGWK7KLVLVFDOOHGWKH
EDQGZLGWK FRQVWUDLQW RI WKH FRPPXQLFDWLRQ VVWHP 7KH VXFFHVV RI WHOHFRPPXQLFDWLRQ
VVWHPVLQWKHODVWFHQWXUJHQHUDWHGKXJHGHPDQGIURPXVHUFRPPXQLWIRUVXEVFULELQJWR
YDULRXV WHOHFRPPXQLFDWLRQ VHUYLFHV 7KLV UHTXLUHG DFFRPPRGDWLQJ PDQ XVHUV DQG KHQFH
PDQFKDQQHOVLQWKHILQLWHEDQGZLGWKRIWKHFKDQQHO)RUH[DPSOHDORQJGLVWDQFHWHOHSKRQH
SURYLGHU OLNH 961/ 9LGHVK 6DQFKDU 1LJDP /WG ,QGLD  ZRXOG DOZDV SUHIHU D GLJLWDO
VVWHP ZKLFK UHTXLUHV OHVV EDQGZLGWK WR VHQG RQH SHUVRQ¶V YRLFH RYHU RWKHU VVWHPV
UHTXLULQJPRUHWUDQVPLVVLRQEDQGZLGWK7KHVDPHREMHFWLYHLVWUXHIRUWKHZLUHOHVVVVWHPV
UDWKHUIRUZLUHOHVVVVWHPVGHFUHDVLQJWUDQVPLVVLRQEDQGZLGWKLVDTXHVWLRQRIVXUYLYDOLQ
WKH PDUNHWSODFH $OO ZLUHOHVV VVWHPV XWLOL]H WKH VDPH IUHH VSDFH IRU FRPPXQLFDWLRQ
SXUSRVHV 6R WKHUH ZRXOG KDYH EHHQ WUHPHQGRXV DPRXQW RI LQWHUIHUHQFH KDG LW QRW EHHQ
UHJXODWHG 7R IDFLOLWDWH ,QWHUQDWLRQDO 7HOHFRPPXQLFDWLRQ 8QLRQ ,78  DOORFDWH YDULRXV
SRUWLRQVRIWKHXVDEOHHOHFWURPDJQHWLFIUHTXHQFEDQG 8VXDOOFDOOHG6SHFWUXP WRGLIIHUHQW
FRPPXQLFDWLRQDSSOLFDWLRQV XVXDOOFDOOHG6HUYLFHV :KHQVSHFWUXPLVOLPLWHGLW¶VFRVWV
KXJH PRQH WR EX WKDW )RU H[DPSOH WKH FHOOXODU VHUYLFH SURYLGHUV VSHQW DV PXFK DV 
ELOOLRQIRUHYHU0+]RI36 3HUVRQDORPPXQLFDWLRQ6VWHP EDQGZLGWK1DWXUDOOWKH
FRPPXQLFDWLRQ WHFKQLTXHV GHOLYHULQJ PRUH GDWD SHU EDQGZLGWK KHOSV VVWHPV LQ WKH
PDUNHWSODFH WR FDWHU WR PRUH WR PRUH QXPEHU RI VXEVFULEHUV 6R WKH ILUVW SHUIRUPDQFH
PHDVXUHRIDGLJLWDOFRPPXQLFDWLRQVVWHPLVVSHFWUDOHIILFLHQFWKDWLVKRZPXFKGDWDUDWH
LVVXSSRUWHGEDXQLWRIEDQGZLGWKDJDLQVWWKHEDQGZLGWKFRQVWUDLQWVRIWKHVVWHP8VXDOO
FRGLQJ DQG DQG PRGXODWLRQ WHFKQLTXHV DUH HPSORHG WR JR RQ LPSURYLQJ WKH VSHFWUDO
HIILFLHQF XQWLO RWKHU FRQVWUDLQWV IRUFH WKH GHVLJQHU WR VHWWOH IRU D SDUWLFXODU YDOXH RI WKH
VSHFWUDOHIILFLHQF
 KDQQHOLVWKHILUVWEORFNLQWKHFRPPXQLFDWLRQVVWHPZKHUHDVLJQDOJHWVH[SRVHGWR
RWKHUVLJQDOVIURPYDULHGVRXUFHV,WLVKHUHWKDWLWJHWVFRQWDPLQDWHGEVHYHUDOXQGHVLUHG
ZDYHIRUPVHJQRLVHDQGLQWHUIHUHQFHZKLFKDUHQRWKLQJEXWVLJQDOVIURPYDULHGVRXUFHV
7KH FKDQQHO EHKDYHV OLNH DQ HOHFWULFDO GHYLFH WR WKH WUDQVPLWWHG VLJQDO 6R LW LQWURGXFHV
DPSOLWXGHDQG RU SKDVHGLVWRUWLRQWRWKHVLJQDO,IWKHFKDQQHOLVVXFKWKDWWKHVLJQDOJHWV
PRUHWKDQRQHSDWKWRUHDFKWKHUHFHLYHUDGLVWRUWLRQFDOOHGPXOWLSDWKGLVWRUWLRQPDFUHHSLQ
7KH QHW HIIHFW RI DOO WKHVH GHJUDGDWLRQV LV WR FDXVH HUURUV LQ GHWHFWLRQ ,Q GLJLWDO
FRPPXQLFDWLRQ VVWHPV WKH SHUIRUPDQFH PHDVXUH RI WKLV HUURU LV %(5 %(5 FDQ EH
LPSURYHGEUHVRUWLQJWRWKHIROORZLQJIRXUWHFKQLTXHV
x ,QFUHDVLQJWUDQVPLWWHGVLJQDOSRZHU
x ,PSURYLQJIUHTXHQFILOWHULQJWHFKQLTXHV
x 0RGXODWLRQDQG'HPRGXODWLRQWHFKQLTXHV
x RGLQJDQG'HFRGLQJWHFKQLTXHV
$OO WKHVH IRXU WHFKQLTXHV KDYH VRPH SKVLFDO FRQVWUDLQW OLPLWLQJ WKHLU SHUIRUPDQFH (DFK
HOHFWURQLFHTXLSPHQWKDVDSRZHUKDQGOLQJFDSDELOLWZKLFKOLPLWVWKHVLJQDOSRZHUWKDWFDQ
EHWUDQVPLWWHG7KLVLVFDOOHG³SRZHUFRQVWUDLQWRIWKHVVWHP´$OVRGXHWRWKHEDQGZLGWK
FRQVWUDLQWVRIWKHFRPPXQLFDWLRQVVWHPILOWHULQJFDQQRWEHLPSURYHGLQGHILQLWHO+HQFH
WKHEDQGZLGWKFRQVWUDLQWWRJHWKHUZLWKWKHSRZHUFRQVWUDLQWGHWHUPLQHVWKHPD[LPXPGDWD
WUDQVPLVVLRQUDWHWKDWFDQEHDFKLHYHGEDFKDQQHO,WLVWKHMRERIDQSDUWLFXODUPRGXODWLRQ
DQGRU FRGLQJ VFKHPH WR RSWLPLVH WKH %(5 SHUIRUPDQFH LH 3RZHU RQVWUDLQW  WKDW LV
DFKLHYDEOHEWKHVVWHPIRUDJLYHQWUDQVPLVVLRQEDQGZLGWKLH %DQGZLGWKRQVWUDLQW 
 %DQGZLGWK
0DQ LPSRUWDQW WKHRUHPV RI FRPPXQLFDWLRQ DQG LQIRUPDWLRQ WKHRU DUH EDVHG RQ WKH
DVVXPSWLRQRIVWULFWOEDQGOLPLWHGFKDQQHOVZKLFKPHDQVWKDWQRVLJQDOSRZHUZKDWHYHULV
DOORZHGRXWVLGHWKHGHILQHGEDQG+RZHYHURXUNQRZOHGJHRI)RXULHUDQDOVLVWHOOVXVWKDW
VWULFWO EDQGOLPLWHG VLJQDOV DUH QRW UHDOLVDEOH EHFDXVH WKH LPSO VLJQDOV ZLWK LQILQLWH
GXUDWLRQ 2Q WKH RWKHU KDQG WLPHOLPLWHG VLJQDOV DUH UHDOLVDEOH EXW WKH )RXULHU WUDQVIRUP
FRQWDLQVVLJQLILFDQWHQHUJLHVDWTXLWHKLJKKDUPRQLFV6RWKHGHILQLWLRQLVQRWJHQHUDODQGLW
GHSHQGVRQWKHDSSOLFDWLRQ
 $OOEDQGZLGWKFULWHULDKDYHLQFRPPRQWKHDWWHPSWWRVSHFLIDPHDVXUHRIWKHZLGWK
WRIDQRQQHJDWLYHUHDOYDOXHGVSHFWUDOGHQVLWGHILQHGIRUDOOSRVVLEOHIUHTXHQFLHV7KH
ILJXUHVKRZVGLIIHUHQWGHILQLWLRQVRIEDQGZLGWK$WSLFDOUHFWDQJXODUEDQGSDVVGLJLWDOSXOVH
ZLWKWLPHGXUDWLRQTFDUULHUIUHTXHQFfc KDVDVSHFWUXP

VLQ c
x
c
f f T
G f T
f f T
S
S
ª º

« »

¬ ¼
  
,QFDVHRIGLJLWDOGDWDVHTXHQFHZHWDONRI36'RIWKHGDWDZKLFKLVWKH36'RID
UDQGRPVHTXHQFHRIWKHUHFWDQJXODUSXOVHMXVWGHILQHGDERYH7KHSORWFRQVLVWVRIDPDLQOREH
DQGVPDOOHUVLGHOREHV7KHJHQHUDOVKDSHRIWKHSORWLVYDOLGIRUPRVWGLJLWDOIRUPDWVVRPH
IRUPDWV KRZHYHU GR QRW KDYH ZHOO GHILQHG OREHV 7KH YDULRXV GHILQLWLRQV RI EDQGZLGWK
UHOHYDQWIURPWKHGLJLWDOFRPPXQLFDWLRQVVWHPVDUH
+DOISRZHU%DQGZLGWK7KLVLVWKHLQWHUYDOEHWZHHQIUHTXHQFLHVDWZKLFKGx(f)KDVGURSSHG
KDOISRZHURUG%EHORZWKHSHDNYDOXH
1RLVHHTXLYDOHQW%DQGZLGWKWNLVGHILQHGDVWN Px/Gx fc ZKHUHPxLVWKHWRWDOVLJQDO
SRZHURYHUDOOIUHTXHQFLHVDQGGx fc LVWKHYDOXHRIWKHPD[LPXPVSHFWUDOFRPSRQHQW)RU
EDQGSDVVVLJQDOWKHPD[LPXPVSHFWUDOFRQWHQWPD[LPXPRFFXUVDWWKHFDUULHUIUHTXHQF
)UDFWLRQDO3RZHURQWDLQPHQW%DQGZLGWK7KHSRZHUFRQWDLQHGZLWKLQWKHEDQGLV
DERYHDQGEHORZWKHEDQGLVH[DFWORIWKHWRWDOVLJQDOSRZHUUHVLGHV7KHGHILQLWLRQLV
DFFHSWHGE)
%RXQGHG 3RZHU 6SHFWUDO'HQVLW$SRSXODUPHWKRGRIVSHFLILQJSRZHULVWRVWDWHWKDW
HYHUZKHUHRXWVLGHWKHVSHFLILHGEDQG Gx(f)PXVWKDYHIDOOHQDWOHDVWWRFHUWDLQVWDWHGOHYHO
EHORZWKDWIRXQGDWWKHEDQGFHQWUH7SLFDOODWWHQXDWLRQOHYHOPLJKWEHRUG%
$EVROXWHEDQGZLGWK7KLVLVLQWHUYDOEHWZHHQIUHTXHQFLHVRXWVLGHRIZKLFKWKHVSHFWUXPLV
]HUR,WLVXVHIXOZDWRGHILQHDQ,GHDOVVWHP+RZHYHUIRUDOOUHDOLVDEOHZDYHIRUPVWKH
DEVROXWHEDQGZLGWKLVLQILQLWH

)LJXUH9DULRXVEDQGZLGWKGHILQLWLRQVRIGLJLWDOVLJQDO D +DOI±3RZHU E 1XOO±WR±QXOO F RI
SRZHU G G%
 6DPSOLQJ
7KH VDPSOLQJ SURFHVV LV DQ RSHUDWLRQ WKDW LV EDVLF WR GLJLWDO VLJQDO SURFHVVLQJ DQG GLJLWDO
FRPPXQLFDWLRQV7KURXJKXVHRIWKHVDPSOLQJSURFHVVHVDQDQDORJVLJQDOLVFRQYHUWHGLQWRD
FRUUHVSRQGLQJVHTXHQFHRIVDPSOHVWKDWDUHXVXDOOVSDFHGXQLIRUPOLQWKHWLPHOHDUOIRU
VXFKDSURFHGXUHWRKDYHSUDFWLFDOXWLOLWLWLVQHFHVVDUWKDWZHFKRRVHWKHVDPSOLQJUDWH
SURSHUOVRWKDWWKHVHTXHQFHRIVDPSOHVXQLTXHOGHILQHGWKHRULJLQDODQDORJVLJQDO

 D  E 
)LJXUH7KHVDPSOLQJSURFHVV D $QDORJVLJQDO E ,QVWDQWDQHRXVOVDPSOHGYHUVLRQRIWKHDQDORJ
VLJQDO
/HW g t
G GHQRWH WKH VLJQDO REWDLQHG E LQGLYLGXDOO ZHLJKWLQJ WKH HOHPHQWV RI D
SHULRGLF VHTXHQFH RI GHOWD IXQFWLRQV VSDFHG Ts VHFRQGV DSDUW E WKH VHTXHQFH RI QXPEHUV
^g nTs `DVVKRZQ VHH)LJXUH E 
g t
 
t t
s
T
g t
G
s s
n
g t g nT t nT
G G
f
f

¦   
)URPWKHGHILQLWLRQRIDGHOWDIXQFWLRQZHKDYH
s s s
g nT t nT g t t nT
G G
  
+HQFHZHPDUHZULWH(T  LQWKHHTXLYDOHQWIRUP
s
s T
n
g t g t t nT g t t
G G G
f
f

¦ 
:KHUH s
T t
G LVWKH'LUDFRULGHDOVDPSOLQJIXQFWLRQ/HWG f DQGGį f GHQRWHWKH)RXULHU
WUDQVIRUPVRIg t DQGgį t UHVSHFWLYHO7KH)RXULHUWUDQVIRUPRI s
T t
G LV
 s
T s s
m
F t f f mf
G G
f
f
ª º 
¬ ¼ ¦ 
:KHUH F@ VLJQLILHV WKH )RXULHU WUDQVIRUP RSHUDWLRQ DQG fs LV WKH VDPSOLQJ UDWH 7KXV
WUDQVIRUPLQJ(T  LQWRWKHIUHTXHQFGRPDLQZHREWDLQ
s s
m
G f G f f f mf
G G
f
f
ª º

« »
¬ ¼
¦ 
ZKHUH LQGLFDWHVFRQYROXWLRQ,QWHUFKDQJLQJWKHRUGHURIWKHVXPPDWLRQWKHQ
s s
m
G f f G f f mf
G G
f
f
ª º

« »
¬ ¼
¦ 
)URPWKHSURSHUWLHVRIWKHGHOWDIXQFWLRQZHILQGWKDWWKHFRQYROXWLRQRIG f DQGį f±mfs 
HTXDOVG f±mfs +HQFHZHPDVLPSOLIDERYHHTXDWLRQVDV
s s
m
G f f G f mf
G
f
f
ª º

« »
¬ ¼
¦ 
,QWKHDERYHHTXDWLRQWKHGį f PDDOVREHH[SUHVVHGDV
s s s
m
G f f G f f G f mf
G
f
f
 
¦   
/HWXVFRQVLGHUWKHDQDORJVLJQDOg t LVVWULFWOEDQGOLPLWHGWKDWPHDQV
G f  IRU_f_•W
)RUWKLVVLJQDOZHWUWRSORWVSHFWUXPRIGį f IRUWKUHHFDVHVZKHUHLQWKHDVH±,
fs WWKHQWKHVSHFWUXPRIGį f

FDQEHVKRZQDV

)LJXUH D 6SHFWUXPRIDVWULFWOEDQG±OLPLWHGVLJQDOg t  E 6SHFWUXPRIWKHVDPSOHGYHUVLRQRIg t 
IRUDVDPSOLQJSHULRGTs W
7KHVDPSOLQJUDWHRIWVDPSOHVSHUVHFRQGIRUDVLJQDOEDQGZLGWKRIWKHUW]LVFDOOHGWKH
1TXLVWUDWHDQGLWVUHFLSURFDOW PHDVXUHGLQVHFRQGV LVFDOOHGWKH1TXLVWLQWHUYDO
DVH±,,fsWWKHQWKHVSHFWUXPRIGį f

FDQEHVKRZQDV

)LJXUH D 6SHFWUXPRIDVLJQDO E 6SHFWUXPRIDQXQGHUVDPSOHGYHUVLRQRIWKHVLJQDOH[KLELWLQJWKH
DOLDVLQJSKHQRPHQRQ
7KLV FDVH LV FDOOHG DV XQGHUVDPSOLQJ ZKLFK UHVXOWV DOLDVLQJ $OLDVLQJ UHIHUV WR WKH
SKHQRPHQRQRIDKLJKIUHTXHQFFRPSRQHQWLQWKHVSHFWUXPRIWKHVLJQDOVHHPLQJOWDFNLQJ
RQWKHLGHQWLWRIDORZHUIUHTXHQFLQWKHVSHFWUXPRILWVVDPSOHGYHUVLRQDVLOOXVWUDWHGLQ
)LJXUH
7RFRPEDWWKHHIIHFWRIDOLDVLQJLQSUDFWLFHZHPDXVHWZRFRUUHFWLYHPHDVXUHVDV
GHVFULEHGKHUH
 3ULRU WR VDPSOLQJ D ORZ SDVV DQWLDOLDVLQJ ILOWHU LV XVHG WR DWWHQXDWH WKRVH KLJK
IUHTXHQF FRPSRQHQWV RI WKH VLJQDO WKDW DUH QRW HVVHQWLDO WR WKH LQIRUPDWLRQ EHLQJ
FRQYHHGEWKHVLJQDO
7KHILOWHUHGVLJQDOLVVDPSOHGDWDUDWHVOLJKWOKLJKHUWKDWWKH1TXLVWUDWHWRUHFRYHU
WKHRULJLQDOVLJQDOIURPLWVVDPSOHGYHUVLRQ
DVH±,,,fsWWKHQWKHVSHFWUXPRIGį f

FDQEHVKRZQDVRQVLGHUWKHH[DPSOHRID
PHVVDJHVLJQDOWKDWKDVEHHQDQWLDOLDV ORZSDVV ILOWHUHGUHVXOWLQJLQWKHVSHFWUXPVKRZQLQ
)LJXUH  D  7KH FRUUHVSRQGLQJ VSHFWUXP RI WKH LQVWDQWDQHRXVO VDPSOHG YHUVLRQ RI WKH
VLJQDO LV VKRZQ LQ )LJXUH  E  DVVXPLQJ D VDPSOLQJ UDWH KLJKHU WKDQ WKH 1TXLVW UDWH
$FFRUGLQJWR)LJXUH E ZHUHDGLOVHHWKDWWKHGHVLJQRIWKHUHFRQVWUXFWLRQILOWHUPDEH
VSHFLILHGDVIROORZV VHH)LJXUH F 

)LJXUH D $QWLDOLDVILOWHUHGVSHFWUXPRIDQLQIRUPDWLRQEHDULQJVLJQDO E 6SHFWUXPRI
LQVWDQWDQHRXVOVDPSOHGYHUVLRQRIWKHVLJQDODVVXPLQJWKHXVHRIDVDPSOLQJUDWHJUHDWHUWKDQ
WKH1TXLVWUDWH F PDJQLWXGHUHVSRQVHRIUHFRQVWUXFWLRQILOWHU
%DVHGRQQDWXUHWKHVDPSOLQJWHFKQLTXHVDUHFODVVLILHGDV,PSXOVHVDPSOLQJ1DWXUDO
VDPSOLQJDQG)ODW7RSVDPSOLQJ
Impulse Sampling,PSXOVHVDPSOLQJFDQEHSHUIRUPHGEPXOWLSOLQJLQSXWVLJQDOg t ZLWK
LPSXOVH WUDLQ s
n
t nT
G
f
f

¦ RI SHULRG µTs¶ +HUH WKH DPSOLWXGH RI LPSXOVH FKDQJHV ZLWK
UHVSHFWWRDPSOLWXGHRILQSXWVLJQDOg t 7KHRXWSXWRIVDPSOHULVJLYHQE
s s s
n n
g t g t t nT g nT t nT
G G G
f f
f f
u  
¦ ¦   
7KLVNLQGRIVDPSOLQJLVDOUHDGVKRZQLQ)LJXUH E 
Natural Sampling /HW DQ DUELWUDU DQDORJ VLJQDO g t  EH DSSOLHG WR D VZLWFKLQJ FLUFXLW
VKRZQ LQ )LJXUH   FRQWUROOHG E D VDPSOLQJ IXQFWLRQ c t  WKDW FRQVLVWV RI DQ LQILQLWH
VXFFHVVLRQRIUHFWDQJXODUIXQFWLRQVRIDPSOLWXGHAGXUDWLRQTDQGRFFXUULQJZLWKSHULRGTs
7KH RXWSXW RI VZLWFKLQJ FLUFXLW LV VKRZQ E s t  7KH ZDYHIRUPV RI g t  c t  DQG s t  DUH
LOOXVWUDWHG LQ SDUW D  E  DQG F  RI )LJXUH  UHVSHFWLYHO :H VHH WKDW WKH VZLWFKLQJ
RSHUDWLRQ PHUHO H[WUDFWV IURP DQ DQDORJ VLJQDO g t  VXFFHVVLYH SRUWLRQ RI SUHGHWHUPLQHG
GXUDWLRQTWDNHQUHJXODUODWWKHUDWHfs Ts$FFRUGLQJOWKHVDPSOHGVLJQDOFRQVLVWVRID
VHTXHQFHRISRVLWLYHDQGQHJDWLYHSXOVHVDVLQ)LJXUH F 6RPDWKHPDWLFDOOWKHVDPSOHG
VLJQDOg t LVREWDLQHGEPXOWLSOLFDWLRQRIVDPSOLQJIXQFWLRQ SXOVHWUDLQ c t DQGWKHLQSXW
VLJQDOg t 

)LJXUH6ZLWFKLQJFLUFXLW

)LJXUH D $QDORJVLJQDO E 6DPSOHGIXQFWLRQ F 6DPSOHGVLJQDO
Flat-top Sampling RQVLGHU QH[W VLWXDWLRQ ZKHUH WKH DQDORJ VLJQDO g t  LV VDPSOHG
LQVWDQWDQHRXVODWWKHUDWHfs TsDQGWKDWWKHGXUDWLRQRIHDFKVDPSOHLVOHQJWKHQHGWRTDV
LOOXVWUDWHGLQ)LJXUH F  $SUDFWLFDOUHDVRQIRULQWHQWLRQDOOOHQJWKHQLQJWKHGXUDWLRQRI
HDFKSXOVHLVWRUHGXFHEDQGZLGWK $VLPSOH)ODWWRSVDPSOHGVLJQDOFDQEHJHQHUDWHGEWKH
XVHRIVDPSOHDQGKROGFLUFXLW8VLQJs t WRGHQRWHWKHVHTXHQFHRIIODWWRSSXOVHVJHQHUDWHG
LQWKLVZDZHPDZULWH
s s
n
s t g nT h t nT
f
f

¦   
ZKHUHh t LVDUHFWDQJXODUSXOVHRIXQLWDPSOLWXGHDQGGXUDWLRQTDVVKRZQLQ)LJXUH E 

)LJXUH D ,QVWDQWDQHRXVOVDPSOHGVLJQDO E 5HFWDQJXODU3XOVH F )ODWWRSVDPSOHGVLJQDO
4XDQWL]DWLRQ
$FRQWLQXRXVVLJQDOVXFKDVYRLFHKDVDFRQWLQXRXVUDQJHRIDPSOLWXGHVDQGWKHUHIRUHLWV
VDPSOHVKDYHDFRQWLQXRXVDPSOLWXGHUDQJH,QRWKHUZRUGZLWKLQWKHILQLWHDPSOLWXGHUDQJH
RI VLJQDOV ZH ILQG DQ LQILQLWH QXPEHU RI DPSOLWXGH OHYHOV ,W LV QRW QHFHVVDU LQ IDFW WR
WUDQVPLW WKH H[DFW DPSOLWXGHV RI WKH VDPSOHV $Q KXPDQ VHQVH WKH HH RU WKH HDU  DV
XOWLPDWH UHFHLYHU FDQ GHWHFW RQO ILQLWH LQWHQVLW GLIIHUHQFHV 7KLV PHDQV WKDW WKH RULJLQDO
FRQWLQXRXV VLJQDO PD EH DSSUR[LPDWHG E D VLJQDO FRQVWUXFWHG RI GLVFUHWH DPSOLWXGHV
VHOHFWHGRQPLQLPXPHUURUEDVLVIURPDQDYDLODEOHVHW7KHH[LVWHQFHRIDILQLWHQXPEHURI
GLVFUHWHDPSOLWXGHOHYHOVLVDEDVLFFRQGLWLRQRISXOVHFRGHPRGXODWLRQOHDUOLIZHDVVLJQ
WKHGLVFUHWHDPSOLWXGHOHYHOVZLWKVXIILFLHQWOFORVHVSDFLQJZHPDPDNHWKHDSSUR[LPDWHG
VLJQDOSUDFWLFDOOLQGLVWLQJXLVKDEOHIURPWKHRULJLQDOFRQWLQXRXVVLJQDO
$PSOLWXGH TXDQWL]DWLRQ LV GHILQHG DV WKH SURFHVV RI WUDQVIRUPLQJ WKH VDPSOH
DPSOLWXGHVm nTs RIDPHVVDJHVLJQDOm t DWWLPHt nTsLQWRDGLVFUHWHDPSOLWXGHv nTs 
WDNHQIURPDILQLWHVHWRISRVVLEOHDPSOLWXGHV:HDVVXPHWKDWWKHTXDQWL]DWLRQSURFHVVLV
PHPRUOHVVDQGLQVWDQWDQHRXVZKLFKPHDQVWKDWWKHWUDQVIRUPDWLRQDWWLPHt nTsLVQRW
DIIHFWHGEHDUOLHURUODWHUVDPSOHVRIWKHPHVVDJHVLJQDO

)LJXUH'HVFULSWLRQRIDPHPRUOHVVTXDQWL]HU
:KHQGHDOLQJZLWKDPHPRUOHVVTXDQWL]HUZHPDVLPSOLIWKHQRWDWLRQEGURSSLQJWKH
WLPH LQGH[ :H PD WKXV XVH WKH VPERO P LQ SODFH RIm nTs  DV LQGLFDWHG LQ WKH EORFN
GLDJUDPRIDTXDQWL]HUVKRZQLQ)LJXUH D 7KHQDVVKRZQLQ)LJXUH E WKHVLJQDO
DPSOLWXGHPLVVSHFLILHGEWKHLQGH[kLILWOLHVLQVLGHWKHSDUWLWLRQFHOO
^ `

  
k k k
I m m m k L

 d   
ZKHUHLLVWKHWRWDOQXPEHURIDPSOLWXGHOHYHOVXVHGLQWKHTXDQWL]HU7KHGLVFUHWHDPSOLWXGHV
mkk «LDWWKHTXDQWL]HULQSXWDUHFDOOHGGHFLVLRQOHYHOVRUGHFLVLRQWKUHVKROGV$W
WKH TXDQWL]HU RXWSXW WKH LQGH[ k LV WUDQVIRUPHG LQWR DQ DPSOLWXGH vk WKDW UHSUHVHQWV DOO
DPSOLWXGHV RI WKH FHOO Ik 7KHVH GLVFUHWH DPSOLWXGHV vk k    « L DUH FDOOHG
UHSUHVHQWDWLRQ OHYHOV RU UHFRQVWUXFWLRQ OHYHOV DQG WKH VSDFLQJ EHWZHHQ WZR DGMDFHQW
UHSUHVHQWDWLRQOHYHOVLVFDOOHGDTXDQWXPRUVWHSVL]H7KXVWKHTXDQWL]HURXWSXWvHTXDOVvkLI
WKHLQSXWVLJQDOmEHORQJVWRWKHLQWHUYDOIk7KHPDSSLQJ VHH)LJXUH D v g m LVWKH
TXDQWL]HUFKDUDFWHULVWLFZKLFKLVDVWDLUFDVHIXQFWLRQEGHILQLWLRQ
4XDQWL]HUV FDQ EH RI XQLIRUP RU QRQXQLIRUP WSH ,Q D XQLIRUP TXDQWL]HU WKH
UHSUHVHQWDWLRQ OHYHOV DUH XQLIRUPO VSDFHG RWKHUZLVH WKH TXDQWL]HU LV QRQXQLIRUP 7KH
TXDQWL]HUFKDUDFWHULVWLFFDQDOVREHRIPLGWUHDGRUPLGULVHWSH)LJXUH D VKRZVWKH
LQSXWRXWSXWFKDUDFWHULVWLFRIDXQLIRUPTXDQWL]HURIWKHPLGWUHDGWSHZKLFKLVVRFDOOHG
EHFDXVHWKHRULJLQOLHVLQWKHPLGGOHRIDWKUHDGRIDVWDLUFDVHOLNHJUDSK)LJXUH E 
VKRZVWKHFRUUHVSRQGLQJLQSXWRXWSXWFKDUDFWHULVWLFRIWKHVWDLUFDVHOLNHJUDSK1RWHWKDWERWK
WKHPLGWUHDGDQGPLGULVHWSHVRIXQLIRUPTXDQWL]HUVLOOXVWUDWHGLQ)LJXUHDUHVPPHWULF
DERXWWKHRULJLQ

 D  E 
)LJXUH7ZRWSHVRITXDQWL]DWLRQ D PLGWKUHDGDQG E PLGULVH
 6LJQDOWRTXDQWL]DWLRQQRLVHUDWLR
7KHXVHRITXDQWL]DWLRQLQWURGXFHVDQHUURUGHILQHGDVWKHGLIIHUHQFHEHWZHHQWKHLQSXWVLJQDO
P DQG WKH RXWSXW VLJQDO v WKH HUURU LV FDOOHG TXDQWL]DWLRQ QRLVH )LJXUH  LOOXVWUDWHV D
WSLFDO YDULDWLRQ RI WKH TXDQWL]DWLRQ DV D IXQFWLRQ RI WLPH DVVXPLQJ WKH XVH RI D XQLIRUP
TXDQWL]HURIWKHPLGWUHDGWSH
)LJXUH,OOXVWUDWLRQRIWKHTXDQWL]DWLRQSURFHVV
/HWWKHTXDQWL]HULQSXWPEHWKHVDPSOHYDOXHRID]HURPHDQUDQGRPYDULDEOHM ,I
WKHLQSXWKDVDQRQ]HURPHDQZHFDQDOZDVUHPRYHLWEVXEWUDFWLQJWKHPHDQIURPWKH
LQSXWDQGWKHQDGGLQJLWEDFNDIWHUTXDQWL]DWLRQ $TXDQWL]HUg  PDSVWKHLQSXWUDQGRP
YDULDEOHMRIFRQWLQXRXVDPSOLWXGHLQWRDGLVFUHWHUDQGRPYDULDEOHVWKHLUUHVSHFWLYHVDPSOH
YDOXHVmDQGvDUHUHODWHGEv g m /HWWKHTXDQWL]DWLRQHUURUEHGHQRWHGEWKHUDQGRP
YDULDEOHQRIVDPSOHYDOXHq:HPDWKXVZULWH
q m±v  
RUFRUUHVSRQGLQJO
Q M±V  
:LWKWKHLQSXWMKDYLQJ]HURPHDQDQGWKHTXDQWL]HUDVVXPHGWREHVPPHWULFDVLQ)LJXUH
LWIROORZVWKDWWKHTXDQWL]HURXWSXWVDQGWKHUHIRUHWKHTXDQWL]DWLRQHUURUQZLOODOVR
KDYH ]HUR PHDQ 7KXV IRU D SDUWLFXODU VWDWLVWLFDO FKDUDFWHUL]DWLRQ RI TXDQWL]HU LQ WHUPV RI
RXWSXWVLJQDOWR TXDQWL]DWLRQ QRLVHUDWLRZHQHHGRQOILQGWKHPHDQVTXDUHYDOXHRIWKH
TXDQWL]DWLRQHUURUQ
RQVLGHU WKHQ DQ LQSXW m RI FRQWLQXRXV DPSOLWXGH LQ WKH UDQJH ±VPD[ VPD[ 
$VVXPLQJDXQLIRUPTXDQWL]HURIWKHPLGULVHWSHLOOXVWUDWHGLQ)LJXUH E ZHILQGWKDW
WKHVWHSVL]HRIWKHTXDQWL]HULVJLYHQE
PD[
V
L
'   
ZKHUHLLVWKHWRWDOQXPEHURIUHSUHVHQWDWLRQOHYHOV)RUDXQLIRUPTXDQWL]HUWKHTXDQWL]DWLRQ
HUURUQZLOOKDYHLWVVDPSOHVYDOXHVERXQGHGE±ǻ”q”ǻ,IWKHVWHSVL]HLVVXIILFLHQWO
VPDOO LH WKH QXPEHU RI UHSUHVHQWDWLRQ OHYHOV L LV VXIILFLHQWO ODUJH  LW LV UHDVRQDEOH WR
DVVXPH WKDW WKH TXDQWL]DWLRQ HUURU Q LV D XQLIRUPO GLVWULEXWHG UDQGRP YDULDEOH DQG WKH
LQWHUIHULQJHIIHFWRIWKHTXDQWL]DWLRQQRLVHRQWKHTXDQWL]HULQSXWLVVLPLODUWRWKDWRIWKHUPDO
QRLVH:HPDWKXVH[SUHVVWKHSUREDELOLWGHQVLWIXQFWLRQRIWKHTXDQWL]DWLRQHUURUQDV
IROORZV


 
 RWKHUZLVH
Q
q
f q
' '
­
  d
°
'
®
°̄
  
)RUWKLVWREHWUXHZHPXVWHQVXUHWKDWWKHLQFRPLQJVLJQDOGRHVQRWRYHUORDGWKHTXDQWL]HU
7KH DUHD XQGHU SUREDELOLW GHQVLW IXQFWLRQ RI D XQLIRUPO GLVWULEXWHG UDQGRP
YDULDEOHLVHTXDOWRXQLWEHFDXVHVXPRISUREDELOLWLHVRIHDFKVDPSOHVKRXOGEHXQLW6R
WKH PDJQLWXGH RI SUREDELOLW GHQVLW IXQFWLRQ RI WKH TXDQWL]DWLRQ HUURU Q LV ǻ RYHU DQ
LQWHUYDO±ǻWRǻDVVKRZQLQ)LJXUH
)LJXUH3UREDELOLWGHQVLWIXQFWLRQRI4XDQWL]DWLRQHUURUQ
7KHQZLWKWKHPHDQRIWKHTXDQWL]DWLRQHUURUEHLQJ]HURLWVYDULDQFH 
Q
V LVWKHVDPHDVWKH
PHDQVTXDUHYDOXH

  

Q Q
E Q q f q dq
V
'
'
ª º
¬ ¼ ³   




Q
q f q dq
'
'
³ 
1RWH7KHSRZHURIDUDQGRPYDULDEOH OHWx HTXDOVWRLWVPHDQVTXDUHGYDOXHLHEx
@
8VXDOOWKHQRLVHKDV]HURPHDQ μ DQG 
n
V YDULDQFHZKHUH   
n E n E n
V P
ª º ª º

¬ ¼ ¬ ¼ 6R
QRLVHSRZHUHTXDOWRLWVYDULDQFH 6XEVWLWXWLQJ(T  LQWR(T  ZHJHW


 



Q q dq
V
'
'
'
' ³   
/HWnGHQRWHWKHQXPEHURIELWVSHUVDPSOHXVHGLQWKHFRQVWUXFWLRQRIELQDUFRGHWKHQWKH
QXPEHURITXDQWL]DWLRQOHYHOVFDQEHL n
RUHTXLYDOHQWO

ORJ
n L   
+HQFHWKHVWHSVL]HJLYHQLQ(T  LV
PD[

n
V
'   
7KXVWKHXVHRI(T  LQ(T  LHOGV
  
PD[



n
Q V
V 
  
/HWPGHQRWHWKHDYHUDJHSRZHURIWKHPHVVDJHVLJQDOm t :HPDWKHQH[SUHVVWKHRXWSXW
VLJQDOWRQRLVHUDWLRRIDXQLIRUPTXDQWL]HUDV

 
PD[

 n
O
Q
P P
SNR
V
V
§ ·
¨ ¸
© ¹
  
q
Q
f q

'
 '

'
(T  VKRZVWKDWWKHRXWSXWVLJQDOWRQRLVHUDWLRRIWKHTXDQWL]HULQFUHDVHVH[SRQHQWLDOO
ZLWKLQFUHDVLQJQXPEHURIELWVSHUVDPSOHn5HFRJQL]LQJWKDWDQLQFUHDVHLQQUHTXLUHVD
SURSRUWLRQDWHLQFUHDVHLQWKHFKDQQHO WUDQVPLVVLRQ EDQGZLGWKBTZHWKXVVHHWKDWXVHRID
ELQDUFRGHIRUWKHUHSUHVHQWDWLRQRIDPHVVDJHVLJQDO DVLQSXOVHFRGHPRGXODWLRQ SURYLGHV
DPRUHHIILFLHQWPHWKRGWKDQHLWKHUIUHTXHQFPRGXODWLRQ )0 RUSXOVHSRVLWLRQPRGXODWLRQ
330 IRUWKHWUDGHRIIRILQFUHDVHGFKDQQHOEDQGZLGWKIRULPSURYHGQRLVHSHUIRUPDQFH,Q
PDNLQJWKLVVWDWHPHQWZHSUHVXPHWKDWWKH)0DQG330VVWHPVDUHOLPLWHGEUHFHLYHU
QRLVHZKHUHDVWKHELQDUFRGHGPRGXODWLRQVVWHPLVOLPLWHGETXDQWL]DWLRQQRLVH
RQVLGHUWKHVSHFLDOFDVHRIDIXOOORDGVLQXVRLGDOPRGXODWLQJVLJQDORIDPSOLWXGHAm
ZKLFKXWLOL]HVDOOWKHUHSUHVHQWDWLRQOHYHOVSURYLGHG7KHDYHUDJHVLJQDOSRZHULV DVVXPLQJD
ORDGRIRKP 

 
 

m
rms m
A
A A
P
R R
  
7KHWRWDOUDQJHRIWKHTXDQWL]HULQSXWLV AmEHFDXVHWKHPRGXODWLQJVLJQDOVZLQJVEHWZHHQ
± AmDQGAm:HPDWKHUHIRUHVHWVPD[ AmLQZKLFKFDVHWKHXVHRI(T  LHOGVWKH
DYHUDJHSRZHU YDULDQFH RIWKHTXDQWL]DWLRQQRLVHDV
  



n
Q m
A
V 
  
7KHRXWSXWVLJQDOWRQRLVHUDWLRRIDXQLIRUPTXDQWL]HUIRUDIXOOORDGWHVWWRQHLV


 
 

  
n
m
O n
m
A
SNR
A 
  
([SUHVVLQJVLJQDOWRQRLVHUDWLRLQGHFLEHOVZHJHW

ORJ  
O
SNR n
   
,In  615 G%UHTXLUHGLVLIn  615 G%UHTXLUHGLVDQGLIn  615 G%
UHTXLUHGLV6RIRULQFUHPHQWRIRQHELWWRUHSUHVHQWHDFKVDPSOHZHUHTXLUHG%RI
DGGLWLRQWUDQVPLWWLQJSRZHU
 1RQXQLIRUP4XDQWL]DWLRQ
6SHHFKFRPPXQLFDWLRQLVDYHULPSRUWDQWDQGVSHFLDOL]HGDUHDRIGLJLWDOFRPPXQLFDWLRQV
+XPDQVSHHFKLVFKDUDFWHUL]HGEXQLTXHVWDWLVWLFDOSURSHUWDVLOOXVWUDWHGLQ)LJXUH7KH
DEVFLVVD UHSUHVHQWV VSHHFK VLJQDO PDJQLWXGHV QRUPDOL]HG WR WKH URRWPHDQVTXDUH UPV 
YDOXHVDQGWKHRUGLQDWHLVSUREDELOLW)RUPRVWYRLFHFRPPXQLFDWLRQFKDQQHOVYHUORZ
VSHHFKYROXPHVSUHGRPLQDWHDQGODUJHDPSOLWXGHYDOXHVDUHUHODWLYHOUDUH7KDWPHDQV
RIWKHWLPHWKHYROWDJHFKDUDFWHUL]LQJGHWHFWHGVSHHFKHQHUJLVOHVVWKDQRQHIRXUWKRIWKH
UPV YDOXH DQG RQO  RI WKH WLPH GRHV WKH YROWDJH H[FHHG WKH UPV YDOXH $V WKH
TXDQWL]DWLRQQRLVHGHSHQGVRQVWHSVL]HDXQLIRUPTXDQWL]HUZRXOGEHZDVWHIXOIRUVSHHFK
VLJQDOVEHFDXVHPDQRIWKHTXDQWL]LQJVWHSVZRXOGUDUHOEHXVHG
,QDVVWHPWKDWXVHVHTXDOOVSDFHGTXDQWL]DWLRQOHYHOVWKHTXDQWL]DWLRQQRLVHLVWKH
VDPHIRUDOOVLJQDOPDJQLWXGHV7KHUHIRUHZLWKXQLIRUPTXDQWL]DWLRQWKH615LVZRUVWIRU
ORZOHYHOVLJQDOVWKDQIRUKLJKOHYHOVLJQDOV+RZHYHUQRQXQLIRUPTXDQWL]DWLRQFDQSURYLGH
ILQHTXDQWL]DWLRQRIZHDNVLJQDOVDQGFRDUVHTXDQWL]DWLRQIRUWKHVWURQJVLJQDOV7KXVLQWKH
FDVHRIQRQXQLIRUPTXDQWL]DWLRQTXDQWL]DWLRQQRLVHFDQEHPDGHSURSRUWLRQDOWRVLJQDOVL]H
7KHHIIHFWLVWRLPSURYHWKHRYHUDOO615EUHGXFLQJWKHQRLVHIRUWKHSUHGRPLQDQWZHDN
VLJQDOVDWWKHH[SHQVHRIDQLQFUHDVHLQQRLVHIRUWKHUDUHORFFXUULQJVWURQJVLJQDOV

)LJXUH6WDWLVWLFDOGLVWULEXWLRQRIVLQJOHWDONHUVSHHFKVLJQDOPDJQLWXGHV
2QH ZD RI DFKLHYLQJ QRQXQLIRUP TXDQWL]DWLRQ LV WR XVH D QRQXQLIRUP TXDQWL]HU
FKDUDFWHULVWLFVKRZQLQ)LJXUH D %XWWKLVWSHRITXDQWL]HUZLWKYDULQJVWHSVL]HLV
GLIILFXOWWRLPSOHPHQW0RUHRIWHQQRQXQLIRUPTXDQWL]DWLRQLVDFKLHYHGEILUVWGLVWRUWLQJ
WKHRULJLQDOVLJQDOZLWKDORJDULWKPLFFRPSUHVVLRQFKDUDFWHULVWLFDVVKRZQLQ)LJXUH E 
DQG WKHQ XVLQJ D XQLIRUP TXDQWL]HU )RU VPDOO PDJQLWXGH VLJQDOV WKH FRPSUHVVLRQ
FKDUDFWHULVWLFKDVDPXFKVWHHSHUVORSWKDQIRUODUJHPDJQLWXGHVLJQDOV7KXVDJLYHQVLJQDO
FKDQJH DW VPDOO PDJQLWXGHV ZLOO FDUU WKH XQLIRUP TXDQWL]HU WKURXJK PRUH VWHSV WKDQ WKH
VDPH FKDQJH DW ODUJH PDJQLWXGHV 7KH FRPSUHVVLRQ FKDUDFWHULVWLF HIIHFWLYHO FKDQJHV WKH
GLVWRUWLRQ RI WKH LQSXW VLJQDO PDJQLWXGHV VR WKDW WKHUH LV QRW D SUHSRQGHUDQFH RI ORZ
PDJQLWXGHVLJQDOVDWWKHRXWSXWRIWKHFRPSUHVVRU$IWHUFRPSUHVVLRQWKHGLVWRUWHGVLJQDOLV
XVHGDVWKHLQSXWWRDXQLIRUP OLQHDU TXDQWL]HUFKDUDFWHULVWLFVKRZQLQ)LJXUH F $W
UHFHLYHU DQ LQYHUVH FRPSUHVVLRQ FKDUDFWHULVWLF FDOOHG H[SDQVLRQ LV DSSOLHG VR WKDW WKH
RYHUDOO WUDQVPLVVLRQ LV QRW GLVWRUWHG 7KH SURFHVVLQJ SDLU FRPSUHVVLRQ DQG H[SDQVLRQ  LV
XVXDOOUHIHUUHGWRDVFRPSDQGLQJ
D  E  F 
)LJXUH D 1RQXQLIRUPTXDQWL]HUFKDUDFWHULVWLF E RPSUHVVLRQFKDUDFWHULVWLF F 8QLIRUP
TXDQWL]HUFKDUDFWHULVWLF
7KH HDUO 30 VVWHPV LPSOHPHQWHG D VPRRWK ORJDULWKPLF FRPSUHVVLRQ IXQFWLRQ
7RGD PRVW 30 VVWHPV XVH D SLHFHZLVH OLQHDU DSSUR[LPDWLRQ WR WKH ORJDULWKPLF
FRPSUHVVLRQFKDUDFWHULVWLFV$PHULFDDQG(XURSHERWKDJUHHGRQWKHQHHGIRUFRPSDQGHULQ
YRLFH WHOHSKRQ VVWHPV EXW FRXOG QRW DJUHH RQ WKH GHWDLOV  +HQFH WZR ORJDULWKPLF
FRPSUHVVLRQ ODZV KDYH EHHQ VWDQGDUGLVHG $PHULFD DQG -DSDQ XVH μODZ FRPSDQGHU DQG
(XURSHDQGUHVWRIWKHZRUOG¶VQDWLRQDOVVWHPVDQGLQWHUQDWLRQDOVVWHPVXVH$ODZ)LJXUH
 VKRZV WKDW ERWK WKH μODZ DQG $ODZ WUDQVIHU IXQFWLRQV DUH ORJDULWKPLF μODZ
FKDUDFWHULVWLFVFDQEHGHILQHGE
PD[
PD[ PD[

OQ    
OQ 
x x
y y
x x
P
P
§ ·
  
¨ ¸
 © ¹
  
ZKHUHμLVDSRVLWLYHFRQVWDQWxDQGyUHSUHVHQWVLQSXWDQGRXWSXWYROWDJHVDQGxPD[DQGyPD[
DUH WKH PD[LPXP SRVLWLYH H[FXUVLRQ RI WKH LQSXW DQG RXWSXW YROWDJHV UHVSHFWLYHO 7KH
FRPSUHVVLRQ FKDUDFWHULVWLF LV VKRZQ LQ )LJXUH  D  IRU VHYHUDO YDOXHV RI μ ,Q 1RUWK
$PHULFD WKH VWDQGDUG YDOXH IRU μ LV  1RWLFH WKDW μ =  FRUUHVSRQGV WR XQLIRUP
TXDQWL]DWLRQ6LPLODUOWKH$ODZFKDUDFWHULVWLFGHILQHGDV
PD[
PD[ PD[
PD[
PD[ PD[

 
 OQ
 
 OQ  
 OQ
A x x
y
A x x A
y
x x
y A
A x A x
­ § ·
 
° ¨ ¸
 © ¹
°
®
§ ·
§ ·
°   
¨ ¸
¨ ¸
°  © ¹
© ¹
¯
  
ZKHUH A LV D SRVLWLYH FRQVWDQW DQG x DQG y DUH DV GHILQHG LQ (T   7KH AODZ
FRPSUHVVLRQFKDUDFWHULVWLFLVVKRZQLQ)LJXUH E IRUVHYHUDOYDOXHVRIA$VWDQGDUG
YDOXHIRUALV
D  E 
)LJXUHRPSUHVVLRQFKDUDFWHULVWLFV D —ODZFKDUDFWHULVWLFV E $ODZFKDUDFWHULVWLFV

More Related Content

Similar to Module 1.pdf

Remedies lecture 2
Remedies lecture 2Remedies lecture 2
Remedies lecture 2FAROUQ
 
Balzac et la petite tailleuse chinoise
Balzac et la petite tailleuse chinoiseBalzac et la petite tailleuse chinoise
Balzac et la petite tailleuse chinoisedreamytang
 
Conditions and System of Government/Official Information in some NATO Countries
Conditions and System of Government/Official Information in some NATO Countries Conditions and System of Government/Official Information in some NATO Countries
Conditions and System of Government/Official Information in some NATO Countries Ivan Zary
 
Material On The Authenticity Of The Quran
Material On The Authenticity Of The QuranMaterial On The Authenticity Of The Quran
Material On The Authenticity Of The Quranzakir2012
 
A Note On Phillips Curve (The Phillips Curve Was Simply A Set of Observations...
A Note On Phillips Curve (The Phillips Curve Was Simply A Set of Observations...A Note On Phillips Curve (The Phillips Curve Was Simply A Set of Observations...
A Note On Phillips Curve (The Phillips Curve Was Simply A Set of Observations...ayshaayyoob2003
 
En contemporary issues
En contemporary issuesEn contemporary issues
En contemporary issuesLoveofpeople
 
Discharge lecture
Discharge lectureDischarge lecture
Discharge lectureFAROUQ
 
Sfantul Nectarie, Sfantul Iubirii, Iosif D Agapitos
Sfantul Nectarie, Sfantul Iubirii, Iosif D  AgapitosSfantul Nectarie, Sfantul Iubirii, Iosif D  Agapitos
Sfantul Nectarie, Sfantul Iubirii, Iosif D Agapitossokoban
 
Sfantul nectarie sfintul iubirii, minuni necunoscute
Sfantul nectarie   sfintul iubirii, minuni necunoscuteSfantul nectarie   sfintul iubirii, minuni necunoscute
Sfantul nectarie sfintul iubirii, minuni necunoscutegedeona19
 
Los derechos de los animales - Hector Hidalgo (2xhoja36).pdf
Los derechos de los animales - Hector Hidalgo (2xhoja36).pdfLos derechos de los animales - Hector Hidalgo (2xhoja36).pdf
Los derechos de los animales - Hector Hidalgo (2xhoja36).pdfyenifferdenisseoband1
 
La guerra de las plantas alelopatia
La guerra de las plantas alelopatiaLa guerra de las plantas alelopatia
La guerra de las plantas alelopatiaunellezvipi
 
Seneca -de_la_brevedad_de_la_vida[1]
Seneca  -de_la_brevedad_de_la_vida[1]Seneca  -de_la_brevedad_de_la_vida[1]
Seneca -de_la_brevedad_de_la_vida[1]Rafael
 

Similar to Module 1.pdf (20)

Remedies lecture 2
Remedies lecture 2Remedies lecture 2
Remedies lecture 2
 
Balzac et la petite tailleuse chinoise
Balzac et la petite tailleuse chinoiseBalzac et la petite tailleuse chinoise
Balzac et la petite tailleuse chinoise
 
Conditions and System of Government/Official Information in some NATO Countries
Conditions and System of Government/Official Information in some NATO Countries Conditions and System of Government/Official Information in some NATO Countries
Conditions and System of Government/Official Information in some NATO Countries
 
Material On The Authenticity Of The Quran
Material On The Authenticity Of The QuranMaterial On The Authenticity Of The Quran
Material On The Authenticity Of The Quran
 
Module 3.pdf
Module 3.pdfModule 3.pdf
Module 3.pdf
 
A Note On Phillips Curve (The Phillips Curve Was Simply A Set of Observations...
A Note On Phillips Curve (The Phillips Curve Was Simply A Set of Observations...A Note On Phillips Curve (The Phillips Curve Was Simply A Set of Observations...
A Note On Phillips Curve (The Phillips Curve Was Simply A Set of Observations...
 
En contemporary issues
En contemporary issuesEn contemporary issues
En contemporary issues
 
Contemporary Issues
Contemporary IssuesContemporary Issues
Contemporary Issues
 
Module 2.pdf
Module 2.pdfModule 2.pdf
Module 2.pdf
 
Discharge lecture
Discharge lectureDischarge lecture
Discharge lecture
 
Fiqh-us-Sunnah: Essentials of Everyday Worship
Fiqh-us-Sunnah: Essentials of Everyday WorshipFiqh-us-Sunnah: Essentials of Everyday Worship
Fiqh-us-Sunnah: Essentials of Everyday Worship
 
Twitter Traffic
Twitter TrafficTwitter Traffic
Twitter Traffic
 
Sfantul Nectarie, Sfantul Iubirii, Iosif D Agapitos
Sfantul Nectarie, Sfantul Iubirii, Iosif D  AgapitosSfantul Nectarie, Sfantul Iubirii, Iosif D  Agapitos
Sfantul Nectarie, Sfantul Iubirii, Iosif D Agapitos
 
Sfantul nectarie sfintul iubirii, minuni necunoscute
Sfantul nectarie   sfintul iubirii, minuni necunoscuteSfantul nectarie   sfintul iubirii, minuni necunoscute
Sfantul nectarie sfintul iubirii, minuni necunoscute
 
Los derechos de los animales - Hector Hidalgo (2xhoja36).pdf
Los derechos de los animales - Hector Hidalgo (2xhoja36).pdfLos derechos de los animales - Hector Hidalgo (2xhoja36).pdf
Los derechos de los animales - Hector Hidalgo (2xhoja36).pdf
 
Fiqh us-sunnah
Fiqh us-sunnahFiqh us-sunnah
Fiqh us-sunnah
 
Razonamientomatematico
RazonamientomatematicoRazonamientomatematico
Razonamientomatematico
 
La guerra de las plantas alelopatia
La guerra de las plantas alelopatiaLa guerra de las plantas alelopatia
La guerra de las plantas alelopatia
 
Seneca -de_la_brevedad_de_la_vida[1]
Seneca  -de_la_brevedad_de_la_vida[1]Seneca  -de_la_brevedad_de_la_vida[1]
Seneca -de_la_brevedad_de_la_vida[1]
 
Islam Perfectly Complete
Islam Perfectly CompleteIslam Perfectly Complete
Islam Perfectly Complete
 

More from Mohamedshabana38

1 Sampling and Signal Reconstruction.pdf
1 Sampling and Signal Reconstruction.pdf1 Sampling and Signal Reconstruction.pdf
1 Sampling and Signal Reconstruction.pdfMohamedshabana38
 
dsl-advances-0130938106-9780130938107.pdf
dsl-advances-0130938106-9780130938107.pdfdsl-advances-0130938106-9780130938107.pdf
dsl-advances-0130938106-9780130938107.pdfMohamedshabana38
 
419907669-Linear-Algebra-by-Gilbert-Strang.pdf
419907669-Linear-Algebra-by-Gilbert-Strang.pdf419907669-Linear-Algebra-by-Gilbert-Strang.pdf
419907669-Linear-Algebra-by-Gilbert-Strang.pdfMohamedshabana38
 
Cable Engineering for Local Area Networks (Barry J. Elliott) (Z-Library).pdf
Cable Engineering for Local Area Networks (Barry J. Elliott) (Z-Library).pdfCable Engineering for Local Area Networks (Barry J. Elliott) (Z-Library).pdf
Cable Engineering for Local Area Networks (Barry J. Elliott) (Z-Library).pdfMohamedshabana38
 
exfo_spec-sheet_maxtester-635_v16_en.pdf
exfo_spec-sheet_maxtester-635_v16_en.pdfexfo_spec-sheet_maxtester-635_v16_en.pdf
exfo_spec-sheet_maxtester-635_v16_en.pdfMohamedshabana38
 
454022781-ODN-Planning-and-Design-Suggestions-TLF.pdf
454022781-ODN-Planning-and-Design-Suggestions-TLF.pdf454022781-ODN-Planning-and-Design-Suggestions-TLF.pdf
454022781-ODN-Planning-and-Design-Suggestions-TLF.pdfMohamedshabana38
 
383934148-DWDM-101-Introduction-to-DWDM-2-pdf.pdf
383934148-DWDM-101-Introduction-to-DWDM-2-pdf.pdf383934148-DWDM-101-Introduction-to-DWDM-2-pdf.pdf
383934148-DWDM-101-Introduction-to-DWDM-2-pdf.pdfMohamedshabana38
 
Applications of Operational Amplifiers 3rd generation techniques (Jerald G. G...
Applications of Operational Amplifiers 3rd generation techniques (Jerald G. G...Applications of Operational Amplifiers 3rd generation techniques (Jerald G. G...
Applications of Operational Amplifiers 3rd generation techniques (Jerald G. G...Mohamedshabana38
 
Exfo-CABLESHARK-P3-Specifications-11A67.pdf
Exfo-CABLESHARK-P3-Specifications-11A67.pdfExfo-CABLESHARK-P3-Specifications-11A67.pdf
Exfo-CABLESHARK-P3-Specifications-11A67.pdfMohamedshabana38
 
101483423-Fiber-Characterization-Training.pdf
101483423-Fiber-Characterization-Training.pdf101483423-Fiber-Characterization-Training.pdf
101483423-Fiber-Characterization-Training.pdfMohamedshabana38
 
424185963-Introduction-to-VoLTE.pdf
424185963-Introduction-to-VoLTE.pdf424185963-Introduction-to-VoLTE.pdf
424185963-Introduction-to-VoLTE.pdfMohamedshabana38
 
exfo_reference-guide_otn.pdf
exfo_reference-guide_otn.pdfexfo_reference-guide_otn.pdf
exfo_reference-guide_otn.pdfMohamedshabana38
 
388865344-990dsl-Manu-copper-loop-tester.pdf
388865344-990dsl-Manu-copper-loop-tester.pdf388865344-990dsl-Manu-copper-loop-tester.pdf
388865344-990dsl-Manu-copper-loop-tester.pdfMohamedshabana38
 

More from Mohamedshabana38 (20)

1 Sampling and Signal Reconstruction.pdf
1 Sampling and Signal Reconstruction.pdf1 Sampling and Signal Reconstruction.pdf
1 Sampling and Signal Reconstruction.pdf
 
2 Aliasing (1).pdf
2 Aliasing (1).pdf2 Aliasing (1).pdf
2 Aliasing (1).pdf
 
1.pdf
1.pdf1.pdf
1.pdf
 
dsl-advances-0130938106-9780130938107.pdf
dsl-advances-0130938106-9780130938107.pdfdsl-advances-0130938106-9780130938107.pdf
dsl-advances-0130938106-9780130938107.pdf
 
419907669-Linear-Algebra-by-Gilbert-Strang.pdf
419907669-Linear-Algebra-by-Gilbert-Strang.pdf419907669-Linear-Algebra-by-Gilbert-Strang.pdf
419907669-Linear-Algebra-by-Gilbert-Strang.pdf
 
Cable Engineering for Local Area Networks (Barry J. Elliott) (Z-Library).pdf
Cable Engineering for Local Area Networks (Barry J. Elliott) (Z-Library).pdfCable Engineering for Local Area Networks (Barry J. Elliott) (Z-Library).pdf
Cable Engineering for Local Area Networks (Barry J. Elliott) (Z-Library).pdf
 
Module 1 (1).pdf
Module 1 (1).pdfModule 1 (1).pdf
Module 1 (1).pdf
 
exfo_spec-sheet_maxtester-635_v16_en.pdf
exfo_spec-sheet_maxtester-635_v16_en.pdfexfo_spec-sheet_maxtester-635_v16_en.pdf
exfo_spec-sheet_maxtester-635_v16_en.pdf
 
mod_2.pdf
mod_2.pdfmod_2.pdf
mod_2.pdf
 
454022781-ODN-Planning-and-Design-Suggestions-TLF.pdf
454022781-ODN-Planning-and-Design-Suggestions-TLF.pdf454022781-ODN-Planning-and-Design-Suggestions-TLF.pdf
454022781-ODN-Planning-and-Design-Suggestions-TLF.pdf
 
mod_3.pdf
mod_3.pdfmod_3.pdf
mod_3.pdf
 
383934148-DWDM-101-Introduction-to-DWDM-2-pdf.pdf
383934148-DWDM-101-Introduction-to-DWDM-2-pdf.pdf383934148-DWDM-101-Introduction-to-DWDM-2-pdf.pdf
383934148-DWDM-101-Introduction-to-DWDM-2-pdf.pdf
 
mod_4.pdf
mod_4.pdfmod_4.pdf
mod_4.pdf
 
Applications of Operational Amplifiers 3rd generation techniques (Jerald G. G...
Applications of Operational Amplifiers 3rd generation techniques (Jerald G. G...Applications of Operational Amplifiers 3rd generation techniques (Jerald G. G...
Applications of Operational Amplifiers 3rd generation techniques (Jerald G. G...
 
408375669-XDSL.pdf
408375669-XDSL.pdf408375669-XDSL.pdf
408375669-XDSL.pdf
 
Exfo-CABLESHARK-P3-Specifications-11A67.pdf
Exfo-CABLESHARK-P3-Specifications-11A67.pdfExfo-CABLESHARK-P3-Specifications-11A67.pdf
Exfo-CABLESHARK-P3-Specifications-11A67.pdf
 
101483423-Fiber-Characterization-Training.pdf
101483423-Fiber-Characterization-Training.pdf101483423-Fiber-Characterization-Training.pdf
101483423-Fiber-Characterization-Training.pdf
 
424185963-Introduction-to-VoLTE.pdf
424185963-Introduction-to-VoLTE.pdf424185963-Introduction-to-VoLTE.pdf
424185963-Introduction-to-VoLTE.pdf
 
exfo_reference-guide_otn.pdf
exfo_reference-guide_otn.pdfexfo_reference-guide_otn.pdf
exfo_reference-guide_otn.pdf
 
388865344-990dsl-Manu-copper-loop-tester.pdf
388865344-990dsl-Manu-copper-loop-tester.pdf388865344-990dsl-Manu-copper-loop-tester.pdf
388865344-990dsl-Manu-copper-loop-tester.pdf
 

Module 1.pdf

  • 1. 0RGXOH±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oise immunity:KLOHWUDQVPLWWLQJGLJLWDOLQIRUPDWLRQIRUPDWWLQJLVYHUHVVHQWLDOLHWZR DQDORJ FRUUHVSRQGHQFH DPSOLWXGH YDOXHV DUH WR EH DVVLJQHG IRU ORJLF ]HUR DQG ORJLF RQH UHVSHFWLYHO LQ FDVH RI ELQDU WUDQVPLVVLRQ 1RLVH LPPXQLW LQWR VXFK IRUPDWWHG GLJLWDO LQIRUPDWLRQLVJUHDWHUWKDQWKDWRIDQDQDORJVLJQDO Memory: $QDORJVLJQDOVDUHJHQHUDOOVWRUHGLQGHYLFHVOLNHPDJQHWLFWDSHVIORSSGLVNV HWF,WUHTXLUHVPDQPDJQHWLFWDSHVWRVWRUHWKHDQDORJVLJQDOV0RUHRYHUWKHVHDUHHDVLO DIIHFWHGEWKHPDJQHWLFDQGRWKHUPHFKDQLFDODQGSKVLFDOSKHQRPHQRQ2QWKHRWKHUKDQG GLJLWDOLQIRUPDWLRQLVVWRUHGLQGHYLFHVOLNH'VDQGUHJLVWHUV)RUH[DPSOHLQD'IOLSIORS WKHRXWSXWFDQEHUHWDLQHGIRUPDQHDUVZLWKRXWDQH[WHUQDOSRZHU:KHQWKHRXWSXWLV QHHGHGWKHWULJJHUFORFNSXOVHLVVXSSOLHGWRWKHIOLSIORSDQGLWZLOOJLYHWKHRXWSXW/LIHWLPH RIGLJLWDOPHPRULVDOVRKLJKHUWKDQWKDWRIDQDORJPHPRU System Re-configurability: 2QHRIWKHPRVWVLJQLILFDQWDGYDQWDJHVRIGLJLWDOVVWHPVLVWKHLU HDVHRIVVWHPUHFRQILJXUDELOLW$VIRUDQH[DPSOHOHWXVFRQVLGHUDQDQDORJORZSDVVILOWHU 7RFRQYHUWLWWRDKLJKSDVVILOWHUZHZLOOKDYHWRUHPRYHWKHFRPSRQHQWVIURPWKHFLUFXLW DQGUHSODFHWKHPZLWKRWKHUDSSURSULDWHFRPSRQHQWV7KLVLVDWLUHVRPHMRELIWKHVVWHPLVD FRPSOH[RQH2QWKHRWKHUKDQGWRFRQYHUWDGLJLWDOORZSDVVILOWHULQWRDKLJKSDVVILOWHUZH FDQHDVLOFKDQJHWKHGLJLWDOILOWHUWUDQVIHUIXQFWLRQH z @MXVWEFKDQJLQJVRPHFRHIILFLHQWV Aging: $JLQJVLJQLILHVJURZLQJROGHURIWKHVVWHP,WLVREYLRXVOOHVVHIIHFWLYHLQFDVHRI GLJLWDOVVWHPV,QFDVHRIDQDORJVVWHPVWKHRXWSXWPDFKDQJHDIWHUDIHZHDUVGXHWR DJLQJRIWKHGLVFUHWHDQDORJFRPSRQHQWVOLNHGLRGH$VWLPHJRHVWKHFXWLQYROWDJHRIWKH GLRGHLQFUHDVHVVORZODQGXQVWHDGLO7KLVFDXVHVIOXFWXDWLRQLQWKHVVWHPSHUIRUPDQFH,Q GLJLWDOVVWHPVWKHVVWHPHUURUGXHWRWKHSUREOHPRIDJLQJLVWRWDOODEVHQW
  • 2. (OHPHQWVRI'LJLWDORPPXQLFDWLRQ6VWHP RQVLGHUWKHEORFNGLDJUDPRIDGLJLWDOFRPPXQLFDWLRQOLQNGHSLFWHGLQ)LJXUH/HWXV QRZEULHIOGLVFXVVWKHUROHVRIWKHEORFNVVKRZQLQWKHILJXUH )LJXUH%ORFNGLDJUDPRIDGLJLWDOFRPPXQLFDWLRQVVWHP ,QDGLJLWDOFRPPXQLFDWLRQVVWHPWKHLQSXWVLJQDOVKRXOGEHLQGLJLWDOIRUPVRWKDWGLJLWDO VLJQDOSURFHVVLQJWHFKQLTXHVFDQEHHPSORHGRQWKHVHVLJQDOV7KHHOHFWULFDOVLJQDODWWKH RXWSXWRIWKHWUDQVGXFHUQHHGVWREHFRQYHUWHGLQWRDVHTXHQFHRIGLJLWDOVLJQDOV7KHEORFN SHUIRUPLQJWKLVWDVNLVWSLFDOOWKHVHFRQGEORFNRIWKHGLJLWDOFRPPXQLFDWLRQVVWHPDQGLV FRPPRQONQRZQDVIRUPDWWHU7KHRXWSXWVLJQDORIWKH)RUPDWWHULVLQGLJLWDOIRUP,IWKH RXWSXWRIWKHLQIRUPDWLRQVRXUFHLVGLJLWDOWKHQZHQHHGQRWHPSORWKHIRUPDWWHU+HQFHWKH GDWDFRPPXQLFDWLRQVVWHPEHWZHHQFRPSXWHUVGRHVQRWKDYHDIRUPDWWHU+RZHYHULIWKH VRXUFHRILQIRUPDWLRQLQVXFKFDVHVLVNHERDUGRUWSHZULWHUFRQQHFWHGWRWKHFRPSXWHUWKHQ WKHIRUPDWWLQJEORFNLVUHTXLUHGWRFRQYHUWFKDUDFWHUV ZKLFKDUHLQGLVFUHWHIRUPEXWQRWLQ GLJLWDOIRUP WRGLJLWDOVLJQDOV 7R UHSUHVHQW WKHVH GLJLWDO VLJQDOV E DV IHZ GLJLWV DV SRVVLEOH GHSHQGLQJ RQ WKH LQIRUPDWLRQFRQWHQWRIWKHPHVVDJHVDFRGLQJVVWHPFDQEHHPSORHGZKLFKPLQLPLVHVWKH UHTXLUHPHQW RI QXPEHU RI GLJLWV 7KLV SURFHVV LV FDOOHG VRXUFH HQFRGLQJ DQG WKH EORFN SHUIRUPLQJWKLVWDVNLVNQRZQDVVRXUFHHQFRGH7KLVVRXUFHHQFRGHUEORFNFRPSUHVVHVWKH WRWDOGLJLWVRIDPHVVDJHVLJQDOIRUWUDQVPLVVLRQ 7R FRPEDW QRLVH LQ WKH FRPPXQLFDWLRQ FKDQQHO VRPH UHGXQGDQF LV GHOLEHUDWHO LQWURGXFHGLQWKHPHVVDJH7KLVLVGRQHEWKHFKDQQHOHQFRGHUEORFN ,Q ORZ VSHHG ZLUHG WUDQVPLVVLRQ WKH FKDQQHO HQFRGHG VLJQDO LV JHQHUDOO QRW PRGXODWHG7KHWUDQVPLVVLRQWDNHVSODFHLQEDVHEDQG+RZHYHUIRUSURSHUGHWHFWLRQLQWKH UHFHLYHUDQGQRWWRFRPEDWQRLVHDQGLQWHUIHUHQFHOLQHFRGLQJLVXVHG6RPHSXOVHVKDSLQJLV DORQHGRQHWRFRPEDWLQWHUIHUHQFH6RPHVSHFLDOILOWHUVDUHDOVRHPSORHGLQWKHUHFHLYHUWR FRPEDWQRLVH$OOWKHVHDUHFROOHFWLYHOFDOOHGEDVHEDQGSURFHVVRU7KLVLVWKHFDVHLQIL[HG WHOHSKRQDQGGDWDVWRUDJHVVWHP +RZHYHUIRUWUDQVPLVVLRQRIKLJKVSHHGGLJLWDOGDWD HJRPSXWHUFRPPXQLFDWLRQ VVWHP WKH GLJLWDO VLJQDO QHHGV WR EH PRGXODWHG LH IUHTXHQF WUDQVODWHG 7KH SULPDU SXUSRVH RI WKH EDVHEDQG PRGXODWRU LV WR PDS WKH GLJLWDO VLJQDO WR KLJK IUHTXHQF DQDORJ VLJQDOZDYHIRUPV$SHUIRUPDQFHPHDVXUHRIWKHPRGXODWRULVVSHFWUDOHIILFLHQFZKLFKLV WKH QXPEHU RI ELWV VHQW SHU VHFRQG IRU HYHU +] RI FKDQQHO EDQGZLGWK 7KH SXUSRVH RI ,QIRUPDWLRQ6RXUFH DQG,QSXW7UDQVGXFHU 2XWSXW7UDQVGXFHU DQG2XWSXW6RXUFH )RUPDWWHU 'HIRUPDWWHU 6RXUFH (QFRGHU 6RXUFH 'HFRGHU KDQQHO (QFRGHU KDQQHO 'HFRGHU KDQQHO %DVHEDQG3URFHVVRU %DQGSDVV0RGXODWRU %DVHEDQG'HFRGHU %DQGSDVV'HPRGXODWRU
  •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³ZLUHG´FDUULQJHOHFWULFDOVLJQDODVLVWKHFDVHLQWHOHSKRQHZLUH 79 FDEOH RU (WKHUQHW FDEOH $ ZLUHG FKDQQHO PD DOVR FDUU RWKHU IRUPV RI VLJQDOV OLNH RSWLFDO ILEHU FDUULQJ PRGXODWHG OLJKW EHDPV ³:LUHOHVVV ´FKDQQHO LV DOVR SRVVLEOH IRU H[DPSOHXQGHUZDWHURFHDQFKDQQHOFDUULQJDFRXVWLFZDYHIRUVHDH[SORUDWLRQIUHHVSDFH FDUULQJ HOHFWURPDJQHWLF ZDYH HWF $ FKDQQHO FDQ DOVR OLQN FR ORFDWHG WUDQVPLWWHU DQG UHFHLYHUIRUH[DPSOHGDWDVWRUDJHPHGLXPVXFKDVPDJQHWLFWDSHPDJQHWLFGLVNRSWLFDOGLVN
  •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±*ESV )HZNP 6KRUWKDXO3671/$1 RD[LDOFDEOH :LUHOLQH )HZKXQGUHG0ESV )HZNP DEOH79/$1 2SWLFDOILEHU :LUHOLQH )HZ*ESV )HZWHQVRINP /RQJ+DXO3671/$1 )UHHVSDFH EURDGFDVW :LUHOHVV )HZKXQGUHGN+]WR )HZKXQGUHG0+] 1RUHSHDWHU %URDGFDVW5DGLR79 )UHHVSDFH FHOOXODU :LUHOHVV ±*+] 1RUHSHDWHUXSWR EDVHVWDWLRQ 0RELOH7HOHSKRQ 606:// :LUHOHVV/$1 :LUHOHVV 8SWR0ESV 1RUHSHDWHUXSWR DFFHVVSRLQW :L)L%OXHWRRWK 7HUUHVWULDO PLFURZDYH OLQN :LUHOHVV ±*+] (YHU±NP /RQJKDXO36719LGHR WUDQVPLVVLRQIURP SODJURXQGWRVWXGLRLQ DOLYHWHOHFDVW 6DWHOOLWH :LUHOHVV *+]*+] 6HYHUDO7KRXVDQG NP 7UDQVFRQWLQHQWDO WHOHSKRQDEOH79 EURDGFDVW'7+96$7 *36 ,QIUDUHG :LUHOHVV )HZ7+] 1RUHSHDWHU 6KRUWGLVWDQFH/26OLNH 79UHPRWH
  •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¶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¶VFRVWV KXJH PRQH WR EX WKDW )RU H[DPSOH WKH FHOOXODU VHUYLFH SURYLGHUV VSHQW DV PXFK DV ELOOLRQIRUHYHU0+]RI36 3HUVRQDORPPXQLFDWLRQ6VWHP EDQGZLGWK1DWXUDOOWKH FRPPXQLFDWLRQ WHFKQLTXHV GHOLYHULQJ PRUH GDWD SHU EDQGZLGWK KHOSV VVWHPV LQ WKH PDUNHWSODFH WR FDWHU WR PRUH WR PRUH QXPEHU RI VXEVFULEHUV 6R WKH ILUVW SHUIRUPDQFH PHDVXUHRIDGLJLWDOFRPPXQLFDWLRQVVWHPLVVSHFWUDOHIILFLHQFWKDWLVKRZPXFKGDWDUDWH LVVXSSRUWHGEDXQLWRIEDQGZLGWKDJDLQVWWKHEDQGZLGWKFRQVWUDLQWVRIWKHVVWHP8VXDOO FRGLQJ DQG DQG PRGXODWLRQ WHFKQLTXHV DUH HPSORHG WR JR RQ LPSURYLQJ WKH VSHFWUDO HIILFLHQF XQWLO RWKHU FRQVWUDLQWV IRUFH WKH GHVLJQHU WR VHWWOH IRU D SDUWLFXODU YDOXH RI WKH VSHFWUDOHIILFLHQF KDQQHOLVWKHILUVWEORFNLQWKHFRPPXQLFDWLRQVVWHPZKHUHDVLJQDOJHWVH[SRVHGWR RWKHUVLJQDOVIURPYDULHGVRXUFHV,WLVKHUHWKDWLWJHWVFRQWDPLQDWHGEVHYHUDOXQGHVLUHG ZDYHIRUPVHJQRLVHDQGLQWHUIHUHQFHZKLFKDUHQRWKLQJEXWVLJQDOVIURPYDULHGVRXUFHV 7KH FKDQQHO EHKDYHV OLNH DQ HOHFWULFDO GHYLFH WR WKH WUDQVPLWWHG VLJQDO 6R LW LQWURGXFHV DPSOLWXGHDQG RU SKDVHGLVWRUWLRQWRWKHVLJQDO,IWKHFKDQQHOLVVXFKWKDWWKHVLJQDOJHWV PRUHWKDQRQHSDWKWRUHDFKWKHUHFHLYHUDGLVWRUWLRQFDOOHGPXOWLSDWKGLVWRUWLRQPDFUHHSLQ 7KH QHW HIIHFW RI DOO WKHVH GHJUDGDWLRQV LV WR FDXVH HUURUV LQ GHWHFWLRQ ,Q GLJLWDO FRPPXQLFDWLRQ VVWHPV WKH SHUIRUPDQFH PHDVXUH RI WKLV HUURU LV %(5 %(5 FDQ EH LPSURYHGEUHVRUWLQJWRWKHIROORZLQJIRXUWHFKQLTXHV
  • 6. x ,QFUHDVLQJWUDQVPLWWHGVLJQDOSRZHU x ,PSURYLQJIUHTXHQFILOWHULQJWHFKQLTXHV x 0RGXODWLRQDQG'HPRGXODWLRQWHFKQLTXHV x RGLQJDQG'HFRGLQJWHFKQLTXHV $OO WKHVH IRXU WHFKQLTXHV KDYH VRPH SKVLFDO FRQVWUDLQW OLPLWLQJ WKHLU SHUIRUPDQFH (DFK HOHFWURQLFHTXLSPHQWKDVDSRZHUKDQGOLQJFDSDELOLWZKLFKOLPLWVWKHVLJQDOSRZHUWKDWFDQ EHWUDQVPLWWHG7KLVLVFDOOHG³SRZHUFRQVWUDLQWRIWKHVVWHP´$OVRGXHWRWKHEDQGZLGWK FRQVWUDLQWVRIWKHFRPPXQLFDWLRQVVWHPILOWHULQJFDQQRWEHLPSURYHGLQGHILQLWHO+HQFH WKHEDQGZLGWKFRQVWUDLQWWRJHWKHUZLWKWKHSRZHUFRQVWUDLQWGHWHUPLQHVWKHPD[LPXPGDWD WUDQVPLVVLRQUDWHWKDWFDQEHDFKLHYHGEDFKDQQHO,WLVWKHMRERIDQSDUWLFXODUPRGXODWLRQ DQGRU FRGLQJ VFKHPH WR RSWLPLVH WKH %(5 SHUIRUPDQFH LH 3RZHU RQVWUDLQW WKDW LV DFKLHYDEOHEWKHVVWHPIRUDJLYHQWUDQVPLVVLRQEDQGZLGWKLH %DQGZLGWKRQVWUDLQW %DQGZLGWK 0DQ LPSRUWDQW WKHRUHPV RI FRPPXQLFDWLRQ DQG LQIRUPDWLRQ WKHRU DUH EDVHG RQ WKH DVVXPSWLRQRIVWULFWOEDQGOLPLWHGFKDQQHOVZKLFKPHDQVWKDWQRVLJQDOSRZHUZKDWHYHULV DOORZHGRXWVLGHWKHGHILQHGEDQG+RZHYHURXUNQRZOHGJHRI)RXULHUDQDOVLVWHOOVXVWKDW VWULFWO EDQGOLPLWHG VLJQDOV DUH QRW UHDOLVDEOH EHFDXVH WKH LPSO VLJQDOV ZLWK LQILQLWH GXUDWLRQ 2Q WKH RWKHU KDQG WLPHOLPLWHG VLJQDOV DUH UHDOLVDEOH EXW WKH )RXULHU WUDQVIRUP FRQWDLQVVLJQLILFDQWHQHUJLHVDWTXLWHKLJKKDUPRQLFV6RWKHGHILQLWLRQLVQRWJHQHUDODQGLW GHSHQGVRQWKHDSSOLFDWLRQ $OOEDQGZLGWKFULWHULDKDYHLQFRPPRQWKHDWWHPSWWRVSHFLIDPHDVXUHRIWKHZLGWK WRIDQRQQHJDWLYHUHDOYDOXHGVSHFWUDOGHQVLWGHILQHGIRUDOOSRVVLEOHIUHTXHQFLHV7KH ILJXUHVKRZVGLIIHUHQWGHILQLWLRQVRIEDQGZLGWK$WSLFDOUHFWDQJXODUEDQGSDVVGLJLWDOSXOVH ZLWKWLPHGXUDWLRQTFDUULHUIUHTXHQFfc KDVDVSHFWUXP VLQ c x c f f T G f T f f T S S ª º « » ¬ ¼ ,QFDVHRIGLJLWDOGDWDVHTXHQFHZHWDONRI36'RIWKHGDWDZKLFKLVWKH36'RID UDQGRPVHTXHQFHRIWKHUHFWDQJXODUSXOVHMXVWGHILQHGDERYH7KHSORWFRQVLVWVRIDPDLQOREH DQGVPDOOHUVLGHOREHV7KHJHQHUDOVKDSHRIWKHSORWLVYDOLGIRUPRVWGLJLWDOIRUPDWVVRPH IRUPDWV KRZHYHU GR QRW KDYH ZHOO GHILQHG OREHV 7KH YDULRXV GHILQLWLRQV RI EDQGZLGWK UHOHYDQWIURPWKHGLJLWDOFRPPXQLFDWLRQVVWHPVDUH +DOISRZHU%DQGZLGWK7KLVLVWKHLQWHUYDOEHWZHHQIUHTXHQFLHVDWZKLFKGx(f)KDVGURSSHG KDOISRZHURUG%EHORZWKHSHDNYDOXH 1RLVHHTXLYDOHQW%DQGZLGWKWNLVGHILQHGDVWN Px/Gx fc ZKHUHPxLVWKHWRWDOVLJQDO SRZHURYHUDOOIUHTXHQFLHVDQGGx fc LVWKHYDOXHRIWKHPD[LPXPVSHFWUDOFRPSRQHQW)RU EDQGSDVVVLJQDOWKHPD[LPXPVSHFWUDOFRQWHQWPD[LPXPRFFXUVDWWKHFDUULHUIUHTXHQF )UDFWLRQDO3RZHURQWDLQPHQW%DQGZLGWK7KHSRZHUFRQWDLQHGZLWKLQWKHEDQGLV DERYHDQGEHORZWKHEDQGLVH[DFWORIWKHWRWDOVLJQDOSRZHUUHVLGHV7KHGHILQLWLRQLV DFFHSWHGE)
  • 7. %RXQGHG 3RZHU 6SHFWUDO'HQVLW$SRSXODUPHWKRGRIVSHFLILQJSRZHULVWRVWDWHWKDW HYHUZKHUHRXWVLGHWKHVSHFLILHGEDQG Gx(f)PXVWKDYHIDOOHQDWOHDVWWRFHUWDLQVWDWHGOHYHO EHORZWKDWIRXQGDWWKHEDQGFHQWUH7SLFDOODWWHQXDWLRQOHYHOPLJKWEHRUG% $EVROXWHEDQGZLGWK7KLVLVLQWHUYDOEHWZHHQIUHTXHQFLHVRXWVLGHRIZKLFKWKHVSHFWUXPLV ]HUR,WLVXVHIXOZDWRGHILQHDQ,GHDOVVWHP+RZHYHUIRUDOOUHDOLVDEOHZDYHIRUPVWKH DEVROXWHEDQGZLGWKLVLQILQLWH )LJXUH9DULRXVEDQGZLGWKGHILQLWLRQVRIGLJLWDOVLJQDO D +DOI±3RZHU E 1XOO±WR±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g t G GHQRWH WKH VLJQDO REWDLQHG E LQGLYLGXDOO ZHLJKWLQJ WKH HOHPHQWV RI D SHULRGLF VHTXHQFH RI GHOWD IXQFWLRQV VSDFHG Ts VHFRQGV DSDUW E WKH VHTXHQFH RI QXPEHUV ^g nTs `DVVKRZQ VHH)LJXUH E g t t t s T g t G
  • 8. s s n g t g nT t nT G G f f ¦ )URPWKHGHILQLWLRQRIDGHOWDIXQFWLRQZHKDYH s s s g nT t nT g t t nT G G +HQFHZHPDUHZULWH(T LQWKHHTXLYDOHQWIRUP s s T n g t g t t nT g t t G G G f f ¦ :KHUH s T t G LVWKH'LUDFRULGHDOVDPSOLQJIXQFWLRQ/HWG f DQGGį f GHQRWHWKH)RXULHU WUDQVIRUPVRIg t DQGgį t UHVSHFWLYHO7KH)RXULHUWUDQVIRUPRI s T t G LV s T s s m F t f f mf G G f f ª º ¬ ¼ ¦ :KHUH F@ VLJQLILHV WKH )RXULHU WUDQVIRUP RSHUDWLRQ DQG fs LV WKH VDPSOLQJ UDWH 7KXV WUDQVIRUPLQJ(T LQWRWKHIUHTXHQFGRPDLQZHREWDLQ s s m G f G f f f mf G G f f ª º « » ¬ ¼ ¦ ZKHUH LQGLFDWHVFRQYROXWLRQ,QWHUFKDQJLQJWKHRUGHURIWKHVXPPDWLRQWKHQ s s m G f f G f f mf G G f f ª º « » ¬ ¼ ¦ )URPWKHSURSHUWLHVRIWKHGHOWDIXQFWLRQZHILQGWKDWWKHFRQYROXWLRQRIG f DQGį f±mfs HTXDOVG f±mfs +HQFHZHPDVLPSOLIDERYHHTXDWLRQVDV s s m G f f G f mf G f f ª º « » ¬ ¼ ¦ ,QWKHDERYHHTXDWLRQWKHGį f PDDOVREHH[SUHVVHGDV s s s m G f f G f f G f mf G f f ¦ /HWXVFRQVLGHUWKHDQDORJVLJQDOg t LVVWULFWOEDQGOLPLWHGWKDWPHDQV G f IRU_f_•W )RUWKLVVLJQDOZHWUWRSORWVSHFWUXPRIGį f IRUWKUHHFDVHVZKHUHLQWKHDVH±,
  • 9. fs WWKHQWKHVSHFWUXPRIGį f FDQEHVKRZQDV )LJXUH D 6SHFWUXPRIDVWULFWOEDQG±OLPLWHGVLJQDOg t E 6SHFWUXPRIWKHVDPSOHGYHUVLRQRIg t IRUDVDPSOLQJSHULRGTs W 7KHVDPSOLQJUDWHRIWVDPSOHVSHUVHFRQGIRUDVLJQDOEDQGZLGWKRIWKHUW]LVFDOOHGWKH 1TXLVWUDWHDQGLWVUHFLSURFDOW PHDVXUHGLQVHFRQGV LVFDOOHGWKH1TXLVWLQWHUYDO DVH±,,fsWWKHQWKHVSHFWUXPRIGį f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
  • 10. 7KHILOWHUHGVLJQDOLVVDPSOHGDWDUDWHVOLJKWOKLJKHUWKDWWKH1TXLVWUDWHWRUHFRYHU WKHRULJLQDOVLJQDOIURPLWVVDPSOHGYHUVLRQ DVH±,,,fsWWKHQWKHVSHFWUXPRIGį f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mpulse Sampling,PSXOVHVDPSOLQJFDQEHSHUIRUPHGEPXOWLSOLQJLQSXWVLJQDOg t ZLWK LPSXOVH WUDLQ s n t nT G f f ¦ RI SHULRG µTs¶ +HUH WKH DPSOLWXGH RI LPSXOVH FKDQJHV ZLWK UHVSHFWWRDPSOLWXGHRILQSXWVLJQDOg t 7KHRXWSXWRIVDPSOHULVJLYHQE
  • 11. s s s n n g t g t t nT g nT t nT G G G f f f f u ¦ ¦ 7KLVNLQGRIVDPSOLQJLVDOUHDGVKRZQLQ)LJXUH E Natural Sampling /HW DQ DUELWUDU DQDORJ VLJQDO g t EH DSSOLHG WR D VZLWFKLQJ FLUFXLW VKRZQ LQ )LJXUH FRQWUROOHG E D VDPSOLQJ IXQFWLRQ c t WKDW FRQVLVWV RI DQ LQILQLWH VXFFHVVLRQRIUHFWDQJXODUIXQFWLRQVRIDPSOLWXGHAGXUDWLRQTDQGRFFXUULQJZLWKSHULRGTs 7KH RXWSXW RI VZLWFKLQJ FLUFXLW LV VKRZQ E s t 7KH ZDYHIRUPV RI g t c t DQG s t DUH LOOXVWUDWHG LQ SDUW D E DQG F RI )LJXUH UHVSHFWLYHO :H VHH WKDW WKH VZLWFKLQJ RSHUDWLRQ PHUHO H[WUDFWV IURP DQ DQDORJ VLJQDO g t VXFFHVVLYH SRUWLRQ RI SUHGHWHUPLQHG GXUDWLRQTWDNHQUHJXODUODWWKHUDWHfs Ts$FFRUGLQJOWKHVDPSOHGVLJQDOFRQVLVWVRID VHTXHQFHRISRVLWLYHDQGQHJDWLYHSXOVHVDVLQ)LJXUH F 6RPDWKHPDWLFDOOWKHVDPSOHG VLJQDOg t LVREWDLQHGEPXOWLSOLFDWLRQRIVDPSOLQJIXQFWLRQ SXOVHWUDLQ c t DQGWKHLQSXW VLJQDOg t )LJXUH6ZLWFKLQJFLUFXLW )LJXUH D $QDORJVLJQDO E 6DPSOHGIXQFWLRQ F 6DPSOHGVLJQDO
  • 12. Flat-top Sampling RQVLGHU QH[W VLWXDWLRQ ZKHUH WKH DQDORJ VLJQDO g t LV VDPSOHG LQVWDQWDQHRXVODWWKHUDWHfs TsDQGWKDWWKHGXUDWLRQRIHDFKVDPSOHLVOHQJWKHQHGWRTDV LOOXVWUDWHGLQ)LJXUH F $SUDFWLFDOUHDVRQIRULQWHQWLRQDOOOHQJWKHQLQJWKHGXUDWLRQRI HDFKSXOVHLVWRUHGXFHEDQGZLGWK $VLPSOH)ODWWRSVDPSOHGVLJQDOFDQEHJHQHUDWHGEWKH XVHRIVDPSOHDQGKROGFLUFXLW8VLQJs t WRGHQRWHWKHVHTXHQFHRIIODWWRSSXOVHVJHQHUDWHG LQWKLVZDZHPDZULWH s s n s t g nT h t nT f f ¦ ZKHUHh t LVDUHFWDQJXODUSXOVHRIXQLWDPSOLWXGHDQGGXUDWLRQTDVVKRZQLQ)LJXUH E )LJXUH D ,QVWDQWDQHRXVOVDPSOHGVLJQDO E 5HFWDQJXODU3XOVH F )ODWWRSVDPSOHGVLJQDO
  •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m nTs RIDPHVVDJHVLJQDOm t DWWLPHt nTsLQWRDGLVFUHWHDPSOLWXGHv nTs WDNHQIURPDILQLWHVHWRISRVVLEOHDPSOLWXGHV:HDVVXPHWKDWWKHTXDQWL]DWLRQSURFHVVLV PHPRUOHVVDQGLQVWDQWDQHRXVZKLFKPHDQVWKDWWKHWUDQVIRUPDWLRQDWWLPHt nTsLVQRW DIIHFWHGEHDUOLHURUODWHUVDPSOHVRIWKHPHVVDJHVLJQDO )LJXUH'HVFULSWLRQRIDPHPRUOHVVTXDQWL]HU :KHQGHDOLQJZLWKDPHPRUOHVVTXDQWL]HUZHPDVLPSOLIWKHQRWDWLRQEGURSSLQJWKH WLPH LQGH[ :H PD WKXV XVH WKH VPERO P LQ SODFH RIm nTs DV LQGLFDWHG LQ WKH EORFN GLDJUDPRIDTXDQWL]HUVKRZQLQ)LJXUH D 7KHQDVVKRZQLQ)LJXUH E WKHVLJQDO DPSOLWXGHPLVVSHFLILHGEWKHLQGH[kLILWOLHVLQVLGHWKHSDUWLWLRQFHOO ^ ` k k k I m m m k L d ZKHUHLLVWKHWRWDOQXPEHURIDPSOLWXGHOHYHOVXVHGLQWKHTXDQWL]HU7KHGLVFUHWHDPSOLWXGHV mkk «LDWWKHTXDQWL]HULQSXWDUHFDOOHGGHFLVLRQOHYHOVRUGHFLVLRQWKUHVKROGV$W WKH TXDQWL]HU RXWSXW WKH LQGH[ k LV WUDQVIRUPHG LQWR DQ DPSOLWXGH vk WKDW UHSUHVHQWV DOO DPSOLWXGHV RI WKH FHOO Ik 7KHVH GLVFUHWH DPSOLWXGHV vk k « L DUH FDOOHG UHSUHVHQWDWLRQ OHYHOV RU UHFRQVWUXFWLRQ OHYHOV DQG WKH VSDFLQJ EHWZHHQ WZR DGMDFHQW UHSUHVHQWDWLRQOHYHOVLVFDOOHGDTXDQWXPRUVWHSVL]H7KXVWKHTXDQWL]HURXWSXWvHTXDOVvkLI WKHLQSXWVLJQDOmEHORQJVWRWKHLQWHUYDOIk7KHPDSSLQJ VHH)LJXUH D v g m LVWKH TXDQWL]HUFKDUDFWHULVWLFZKLFKLVDVWDLUFDVHIXQFWLRQEGHILQLWLRQ 4XDQWL]HUV FDQ EH RI XQLIRUP RU QRQXQLIRUP WSH ,Q D XQLIRUP TXDQWL]HU WKH UHSUHVHQWDWLRQ OHYHOV DUH XQLIRUPO VSDFHG RWKHUZLVH WKH TXDQWL]HU LV QRQXQLIRUP 7KH TXDQWL]HUFKDUDFWHULVWLFFDQDOVREHRIPLGWUHDGRUPLGULVHWSH)LJXUH D VKRZVWKH LQSXWRXWSXWFKDUDFWHULVWLFRIDXQLIRUPTXDQWL]HURIWKHPLGWUHDGWSHZKLFKLVVRFDOOHG
  • 14. EHFDXVHWKHRULJLQOLHVLQWKHPLGGOHRIDWKUHDGRIDVWDLUFDVHOLNHJUDSK)LJXUH E VKRZVWKHFRUUHVSRQGLQJLQSXWRXWSXWFKDUDFWHULVWLFRIWKHVWDLUFDVHOLNHJUDSK1RWHWKDWERWK WKHPLGWUHDGDQGPLGULVHWSHVRIXQLIRUPTXDQWL]HUVLOOXVWUDWHGLQ)LJXUHDUHVPPHWULF DERXWWKHRULJLQ D E )LJXUH7ZRWSHVRITXDQWL]DWLRQ D PLGWKUHDGDQG E PLGULVH 6LJQDOWRTXDQWL]DWLRQQRLVHUDWLR 7KHXVHRITXDQWL]DWLRQLQWURGXFHVDQHUURUGHILQHGDVWKHGLIIHUHQFHEHWZHHQWKHLQSXWVLJQDO P DQG WKH RXWSXW VLJQDO v WKH HUURU LV FDOOHG TXDQWL]DWLRQ QRLVH )LJXUH LOOXVWUDWHV D WSLFDO YDULDWLRQ RI WKH TXDQWL]DWLRQ DV D IXQFWLRQ RI WLPH DVVXPLQJ WKH XVH RI D XQLIRUP TXDQWL]HURIWKHPLGWUHDGWSH )LJXUH,OOXVWUDWLRQRIWKHTXDQWL]DWLRQSURFHVV
  • 15. /HWWKHTXDQWL]HULQSXWPEHWKHVDPSOHYDOXHRID]HURPHDQUDQGRPYDULDEOHM ,I WKHLQSXWKDVDQRQ]HURPHDQZHFDQDOZDVUHPRYHLWEVXEWUDFWLQJWKHPHDQIURPWKH LQSXWDQGWKHQDGGLQJLWEDFNDIWHUTXDQWL]DWLRQ $TXDQWL]HUg PDSVWKHLQSXWUDQGRP YDULDEOHMRIFRQWLQXRXVDPSOLWXGHLQWRDGLVFUHWHUDQGRPYDULDEOHVWKHLUUHVSHFWLYHVDPSOH YDOXHVmDQGvDUHUHODWHGEv g m /HWWKHTXDQWL]DWLRQHUURUEHGHQRWHGEWKHUDQGRP YDULDEOHQRIVDPSOHYDOXHq:HPDWKXVZULWH q m±v RUFRUUHVSRQGLQJO Q M±V :LWKWKHLQSXWMKDYLQJ]HURPHDQDQGWKHTXDQWL]HUDVVXPHGWREHVPPHWULFDVLQ)LJXUH LWIROORZVWKDWWKHTXDQWL]HURXWSXWVDQGWKHUHIRUHWKHTXDQWL]DWLRQHUURUQZLOODOVR KDYH ]HUR PHDQ 7KXV IRU D SDUWLFXODU VWDWLVWLFDO FKDUDFWHUL]DWLRQ RI TXDQWL]HU LQ WHUPV RI RXWSXWVLJQDOWR TXDQWL]DWLRQ QRLVHUDWLRZHQHHGRQOILQGWKHPHDQVTXDUHYDOXHRIWKH TXDQWL]DWLRQHUURUQ RQVLGHU WKHQ DQ LQSXW m RI FRQWLQXRXV DPSOLWXGH LQ WKH UDQJH ±VPD[ VPD[ $VVXPLQJDXQLIRUPTXDQWL]HURIWKHPLGULVHWSHLOOXVWUDWHGLQ)LJXUH E ZHILQGWKDW WKHVWHSVL]HRIWKHTXDQWL]HULVJLYHQE PD[ V L ' ZKHUHLLVWKHWRWDOQXPEHURIUHSUHVHQWDWLRQOHYHOV)RUDXQLIRUPTXDQWL]HUWKHTXDQWL]DWLRQ HUURUQZLOOKDYHLWVVDPSOHVYDOXHVERXQGHGE±ǻ”q”ǻ,IWKHVWHSVL]HLVVXIILFLHQWO VPDOO LH WKH QXPEHU RI UHSUHVHQWDWLRQ OHYHOV L LV VXIILFLHQWO ODUJH LW LV UHDVRQDEOH WR DVVXPH WKDW WKH TXDQWL]DWLRQ HUURU Q LV D XQLIRUPO GLVWULEXWHG UDQGRP YDULDEOH DQG WKH LQWHUIHULQJHIIHFWRIWKHTXDQWL]DWLRQQRLVHRQWKHTXDQWL]HULQSXWLVVLPLODUWRWKDWRIWKHUPDO QRLVH:HPDWKXVH[SUHVVWKHSUREDELOLWGHQVLWIXQFWLRQRIWKHTXDQWL]DWLRQHUURUQDV IROORZV RWKHUZLVH Q q f q ' ' ­ d ° ' ® °̄ )RUWKLVWREHWUXHZHPXVWHQVXUHWKDWWKHLQFRPLQJVLJQDOGRHVQRWRYHUORDGWKHTXDQWL]HU 7KH DUHD XQGHU SUREDELOLW GHQVLW IXQFWLRQ RI D XQLIRUPO GLVWULEXWHG UDQGRP YDULDEOHLVHTXDOWRXQLWEHFDXVHVXPRISUREDELOLWLHVRIHDFKVDPSOHVKRXOGEHXQLW6R WKH PDJQLWXGH RI SUREDELOLW GHQVLW IXQFWLRQ RI WKH TXDQWL]DWLRQ HUURU Q LV ǻ RYHU DQ LQWHUYDO±ǻWRǻDVVKRZQLQ)LJXUH
  • 16. )LJXUH3UREDELOLWGHQVLWIXQFWLRQRI4XDQWL]DWLRQHUURUQ 7KHQZLWKWKHPHDQRIWKHTXDQWL]DWLRQHUURUEHLQJ]HURLWVYDULDQFH Q V LVWKHVDPHDVWKH PHDQVTXDUHYDOXH Q Q E Q q f q dq V ' ' ª º ¬ ¼ ³ Q q f q dq ' ' ³ 1RWH7KHSRZHURIDUDQGRPYDULDEOH OHWx HTXDOVWRLWVPHDQVTXDUHGYDOXHLHEx @ 8VXDOOWKHQRLVHKDV]HURPHDQ μ DQG n V YDULDQFHZKHUH n E n E n V P ª º ª º ¬ ¼ ¬ ¼ 6R QRLVHSRZHUHTXDOWRLWVYDULDQFH 6XEVWLWXWLQJ(T LQWR(T ZHJHW Q q dq V ' ' ' ' ³ /HWnGHQRWHWKHQXPEHURIELWVSHUVDPSOHXVHGLQWKHFRQVWUXFWLRQRIELQDUFRGHWKHQWKH QXPEHURITXDQWL]DWLRQOHYHOVFDQEHL n RUHTXLYDOHQWO ORJ n L +HQFHWKHVWHSVL]HJLYHQLQ(T LV PD[ n V ' 7KXVWKHXVHRI(T LQ(T LHOGV PD[ n Q V V /HWPGHQRWHWKHDYHUDJHSRZHURIWKHPHVVDJHVLJQDOm t :HPDWKHQH[SUHVVWKHRXWSXW VLJQDOWRQRLVHUDWLRRIDXQLIRUPTXDQWL]HUDV PD[ n O Q P P SNR V V § · ¨ ¸ © ¹ q Q f q ' ' '
  • 17. (T VKRZVWKDWWKHRXWSXWVLJQDOWRQRLVHUDWLRRIWKHTXDQWL]HULQFUHDVHVH[SRQHQWLDOO ZLWKLQFUHDVLQJQXPEHURIELWVSHUVDPSOHn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m ZKLFKXWLOL]HVDOOWKHUHSUHVHQWDWLRQOHYHOVSURYLGHG7KHDYHUDJHVLJQDOSRZHULV DVVXPLQJD ORDGRIRKP m rms m A A A P R R 7KHWRWDOUDQJHRIWKHTXDQWL]HULQSXWLV AmEHFDXVHWKHPRGXODWLQJVLJQDOVZLQJVEHWZHHQ ± AmDQGAm:HPDWKHUHIRUHVHWVPD[ AmLQZKLFKFDVHWKHXVHRI(T LHOGVWKH DYHUDJHSRZHU YDULDQFH RIWKHTXDQWL]DWLRQQRLVHDV n Q m A V 7KHRXWSXWVLJQDOWRQRLVHUDWLRRIDXQLIRUPTXDQWL]HUIRUDIXOOORDGWHVWWRQHLV n m O n m A SNR A ([SUHVVLQJVLJQDOWRQRLVHUDWLRLQGHFLEHOVZHJHW ORJ O SNR n ,In 615 G%UHTXLUHGLVLIn 615 G%UHTXLUHGLVDQGLIn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
  •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
  • 19. D E F )LJXUH D 1RQXQLIRUPTXDQWL]HUFKDUDFWHULVWLF E RPSUHVVLRQFKDUDFWHULVWLF F 8QLIRUP TXDQWL]HUFKDUDFWHULVWLF 7KH HDUO 30 VVWHPV LPSOHPHQWHG D VPRRWK ORJDULWKPLF FRPSUHVVLRQ IXQFWLRQ 7RGD PRVW 30 VVWHPV XVH D SLHFHZLVH OLQHDU DSSUR[LPDWLRQ WR WKH ORJDULWKPLF FRPSUHVVLRQFKDUDFWHULVWLFV$PHULFDDQG(XURSHERWKDJUHHGRQWKHQHHGIRUFRPSDQGHULQ YRLFH WHOHSKRQ VVWHPV EXW FRXOG QRW DJUHH RQ WKH GHWDLOV +HQFH WZR ORJDULWKPLF FRPSUHVVLRQ ODZV KDYH EHHQ VWDQGDUGLVHG $PHULFD DQG -DSDQ XVH μODZ FRPSDQGHU DQG (XURSHDQGUHVWRIWKHZRUOG¶VQDWLRQDOVVWHPVDQGLQWHUQDWLRQDOVVWHPVXVH$ODZ)LJXUH VKRZV WKDW ERWK WKH μODZ DQG $ODZ WUDQVIHU IXQFWLRQV DUH ORJDULWKPLF μODZ FKDUDFWHULVWLFVFDQEHGHILQHGE PD[ PD[ PD[ OQ OQ x x y y x x P P § · ¨ ¸ © ¹ ZKHUHμLVDSRVLWLYHFRQVWDQWxDQGyUHSUHVHQWVLQSXWDQGRXWSXWYROWDJHVDQGxPD[DQGyPD[ DUH WKH PD[LPXP SRVLWLYH H[FXUVLRQ RI WKH LQSXW DQG RXWSXW YROWDJHV UHVSHFWLYHO 7KH FRPSUHVVLRQ FKDUDFWHULVWLF LV VKRZQ LQ )LJXUH D IRU VHYHUDO YDOXHV RI μ ,Q 1RUWK $PHULFD WKH VWDQGDUG YDOXH IRU μ LV 1RWLFH WKDW μ = FRUUHVSRQGV WR XQLIRUP TXDQWL]DWLRQ6LPLODUOWKH$ODZFKDUDFWHULVWLFGHILQHGDV PD[ PD[ PD[ PD[ PD[ PD[ OQ OQ OQ A x x y A x x A y x x y A A x A x ­ § · ° ¨ ¸ © ¹ ° ® § · § · ° ¨ ¸ ¨ ¸ ° © ¹ © ¹ ¯ ZKHUH A LV D SRVLWLYH FRQVWDQW DQG x DQG y DUH DV GHILQHG LQ (T 7KH AODZ FRPSUHVVLRQFKDUDFWHULVWLFLVVKRZQLQ)LJXUH E IRUVHYHUDOYDOXHVRIA$VWDQGDUG YDOXHIRUALV
  • 20. D E )LJXUHRPSUHVVLRQFKDUDFWHULVWLFV D —ODZFKDUDFWHULVWLFV E $ODZFKDUDFWHULVWLFV