Signal compression techniques may be useful in reducing the data size of .... Differential pulse code modulation (DPCM) (Jayant & Noll, 1984) refers to signal.
%QORTGUUKQPQH5WTHCEG'NGEVTQO[QITCRJKE5KIPCNU7UKPI6YQ&KOGPUKQPCN6GEJPKSWGU
:
%QORTGUUKQPQH5WTHCEG'NGEVTQO[QITCRJKE 5KIPCNU7UKPI6YQ&KOGPUKQPCN6GEJPKSWGU
0DUFXV9&&RVWD-RmR/$&DUYDOKR3HGUR$%HUJHU $GVRQ)GD5RFKDDQG)UDQFLVFR$21DVFLPHQWR 'HSDUWPHQWRI(OHFWULFDO(QJLQHHULQJ
'HSDUWPHQWRI&RPSXWHU6FLHQFH
8QLYHUVLW\RI%UDVtOLD %UD]LO
+PVTQFWEVKQP
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wW$OL &DYDUR0p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ð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³QDPHO\WKH-3(*DQGWKH+$9&LQWUDDOJRULWKPV³PD\EHXVHGIRU HIILFLHQWFRPSUHVVLRQRI6(0*VLJQDOV)LQDOO\ZHTXDQWLWDWLYHO\FRPSDUHWKHSHUIRUPDQFH
4GEGPV#FXCPEGUKP$KQOGFKECN'PIKPGGTKPI
RI WKHVH WZR DOJRULWKPV ZLWK WKH 6(0* HQFRGHUV SURSRVHG E\ 1RUULV HW DO DQG %HUJHUHWDO
'NGEVTQO[QITCRJKE5KIPCNU
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
5WTHCEGXUKPVTCOWUEWNCTGNGEVTQO[QITCRJ[ (OHFWURP\RJUDSK\ LV EDVHG RQ H[WUDFHOOXODU DVVHVVPHQW RI WKH HYHQWV GHVFULEHG DERYH ,QWUDPXVFXODU DQG VXUIDFH HOHFWURP\RJUDSKLF WHFKQLTXHV DUH VXSSOHPHQWDU\ WR HDFK RWKHU DQG ERWK DUH UHOHYDQW LQVWUXPHQWV IRU SK\VLRORJLFDO LQYHVWLJDWLRQ ,QWUDPXVFXODU
%QORTGUUKQPQH5WTHCEG'NGEVTQO[QITCRJKE5KIPCNU7UKPI6YQ&KOGPUKQPCN6GEJPKSWGU
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
)LJ6(0*VLJQDOPHDVXUHGRQWKHELFHSVEUDFKLLGXULQJDQLVRPHWULFFRQWUDFWLRQ
5KIPCN%QORTGUUKQP6GEJPKSWGU
'LJLWL]DWLRQ RI ELRPHGLFDO VLJQDOV KDV EHHQ XVHG IRU PDQ\ GLIIHUHQW DSSOLFDWLRQV VXFK DV DPEXODWRU\PRQLWRULQJSKRQHOLQHWUDQVPLVVLRQGDWDEDVHVWRUDJHDQGVHYHUDORWKHUXVHVLQ KHDOWK DQG ELRPHGLFDO HQJLQHHULQJ 7KHVH DSSOLFDWLRQV KDYH KHOSHG LQ GLDJQRVWLFV SDWLHQW FDUH DQG UHPRWH WUHDWPHQW 2QH H[DPSOH LV WKH GLJLWDO WUDQVPLVVLRQ RI (&* VLJQDOV IURP WKH SDWLHQW·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´WKH UDWLR RI WKH HQWURS\ RI D VRXUFH WR WKH PD[LPXP YDOXHLWFRXOGKDYHZKLOHVWLOOUHVWULFWHGWRWKHVDPHV\PEROVµ
4GEGPV#FXCPEGUKP$KQOGFKECN'PIKPGGTKPI
6LJQDO FRPSUHVVLRQ KDV EHHQ ZLGHO\ VWXGLHG LQ WKH SDVW GHFDGHV *HUVKR *UD\ -D\DQW 1ROO 6D\RRG 6DORPRQ 6LJQDO FRPSUHVVLRQ WHFKQLTXHV DUH FRPPRQO\ FODVVLILHG LQWR WZR FDWHJRULHV ORVVOHVV DQG ORVV\ FRPSUHVVLRQ /RVVOHVV FRPSUHVVLRQ PHDQV WKDW WKH GHFRGHG VLJQDO LV LGHQWLFDO WR WKH RULJLQDO VLJQDO ,Q ORVV\ FRPSUHVVLRQ D FRQWUROOHG DPRXQW RI GLVWRUWLRQ LV DOORZHG /RVV\ VLJQDO FRPSUHVVLRQ WHFKQLTXHVJHQHUDOO\DFKLHYHKLJKHUFRPSUHVVLRQUDWHVWKDQORVVOHVVWHFKQLTXHV
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
)LJ([DPSOHRIUXQOHQJWKHQFRGLQJD RULJLQDOVLJQDOE HQFRGHGVLJQDO
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
%QORTGUUKQPQH5WTHCEG'NGEVTQO[QITCRJKE5KIPCNU7UKPI6YQ&KOGPUKQPCN6GEJPKSWGU
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
)LJ+XIIPDQFRGHFRQVWUXFWLRQH[DPSOH
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´%$&$'($µ ZLWK SUREDELOLW\ PRGHO S$ S% S& S' DQGS(
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
4GEGPV#FXCPEGUKP$KQOGFKECN'PIKPGGTKPI
)LJ 6WHSE\VWHS DULWKPHWLF HQFRGLQJ SURFHVV IRU WKH PHVVDJH ´%$&$'($µ ZLWK SUREDELOLW\PRGHOS$ S% S& S' DQGS(
)LJ'LIIHUHQWLDOHQFRGLQJH[DPSOHD RULJLQDOVLJQDOE HQFRGHGVLJQDO
.QUU[EQORTGUUKQP 7KHUH DUH WZR PDLQ FDWHJRULHV RI ORVV\ FRPSUHVVLRQ WHFKQLTXHV XVHG ZLWK ELRPHGLFDO VLJQDOVGLUHFWPHWKRGVDQGWUDQVIRUPFRPSUHVVLRQ
&KTGEVOGVJQFU 'LUHFW PHWKRGV HQFRGH VLJQDOV LQ WLPH GRPDLQ 7KHVH DOJRULWKPV GHSHQG RQ WKH PRUSKRORJ\ RI WKH LQSXW VLJQDO ,Q PRVW FDVHV WKHVH PHWKRGV DUH FRPSOH[ DQG SURYLGH ORZHUFRPSUHVVLRQHIILFLHQF\WKDQWUDQVIRUPHQFRGHUVGLVFXVVHGLQWKHQH[WVHFWLRQ 'LUHFWFRPSUHVVLRQPHWKRGVXVHVRSKLVWLFDWHGSURFHVVHVDQG´LQWHOOLJHQWµVLJQDOGHFLPDWLRQ DQG LQWHUSRODWLRQ ,Q RWKHU ZRUGV WKHVH PHWKRGV H[WUDFW . ´VLJQLILFDQWµ VDPSOHV RI WKH RULJLQDOOHQJWK1VLJQDO[Q LH
%QORTGUUKQPQH5WTHCEG'NGEVTQO[QITCRJKE5KIPCNU7UKPI6YQ&KOGPUKQPCN6GEJPKSWGU
Q [Q Q
1 o QN [QN N
.
ZKHUH.17KHSURFHVVRIVHOHFWLQJVLJQLILFDQWVDPSOHVLVEDVHGRQWKHFKDUDFWHULVWLFVRIWKH VLJQDODQGRQDWROHUDQFHLQWHUYDOFULWHULRQIRUWKHUHFRQVWUXFWLRQHUURU 7KH UHFRQVWUXFWLRQ RI YDOXHV EHWZHHQ VLJQLILFDQW VDPSOHV LV SHUIRUPHG E\ LQWHUSRODWLRQ XVLQJWKHJHQHULFH[SUHVVLRQ6|UQPR /DJXQD Q Q Q. [Q °I Q Q Q Q ° Q Q [ Q ® # °# ° I Q Q Q Q Q. Q. ¯ . .
7KH LQWHUSRODWLRQ IXQFWLRQ I QN QN Q LV JHQHUDOO\ D ILUVWRUGHU SRO\QRPLDO DQG FRQQHFWV SDLUVRIFRQVHFXWLYHVLJQLILFDQWVDPSOHV2QO\.VDPSOHVDUHVWRUHGLQVWHDGRI1UHVXOWLQJ LQDUHGXFWLRQRIWKHDPRXQWRIVWRUHGRUWUDQVPLWWHGGDWD
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ĀHYLþ 6WUDQJ 1JX\HQ ,Q WKLV WUDQVIRUP D VLJQDO FRQWDLQLQJ 1 VDPSOHV LV ILOWHUHG XVLQJ D SDLU RI ILOWHUVWKDWGHFRPSRVHWKHVLJQDOLQWRORZ/ DQGDKLJK+ IUHTXHQF\EDQGV(DFKEDQGLV XQGHUVDPSOHG E\ D IDFWRU RI WZR WKDW LV HDFK EDQG FRQWDLQV 1 VDPSOHV :LWK WKH DSSURSULDWHILOWHUGHVLJQWKLVSURFHVVLVUHYHUVLEOH7KLVSURFHGXUHFDQEHH[WHQGHGWRWZR GLPHQVLRQDO VLJQDOV VXFK DV LPDJHV ,Q )LJXUH ZH VKRZ DQ H[DPSOH RI ZDYHOHW GHFRPSRVLWLRQIRUDJUD\VFDOHLPDJHZLWKðSL[HOV6LPLODUO\WRZKDWZDVREVHUYHG
4GEGPV#FXCPEGUKP$KQOGFKECN'PIKPGGTKPI
XVLQJ WKH '&7 PDQ\ RI WKH FRHIILFLHQWV LQ WKH KLJKIUHTXHQF\ VXEEDQGV KDYH DPSOLWXGHV FORVHWR]HURGDUNSL[HOV DQGLWLVSRVVLEOHWRFRPSUHVVWKHLPDJHE\GLVFDUGLQJWKHP
)LJ([DPSOHRI'&7EDVHGLPDJHFRPSUHVVLRQDSSOLHGLQEORFNVRIðSL[HOV4GHQRWHV TXDQWL]DWLRQ
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
%QORTGUUKQPQH5WTHCEG'NGEVTQO[QITCRJKE5KIPCNU7UKPI6YQ&KOGPUKQPCN6GEJPKSWGU
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
%QORTGUUKQPQH5'/)5KIPCNU
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
4GEGPV#FXCPEGUKP$KQOGFKECN'PIKPGGTKPI
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
6YQ&KOGPUKQPCN5'/)%QORTGUUKQP
2QHGLPHQVLRQDO VLJQDOV PD\ EH FRPSUHVVHG XVLQJ LPDJH HQFRGLQJ DOJRULWKPV VLPSO\ E\ UHDUUDQJLQJWKHVLJQDOVDPSOHVLQWRDWZRGLPHQVLRQDOPDWUL[ZKLFKPD\EHSURFHVVHGDV DQ LPDJH 7KLV DSSURDFK KDV EHHQ SUHYLRXVO\ GHPRQVWUDWHG LQ WKH ILHOG RI HOHFWURFDUGLRJUDSK\ )RU H[DPSOH WKH -3(* LPDJH HQFRGLQJ DOJRULWKP KDV EHHQ HIILFLHQWO\ DSSOLHG WR (&* VLJQDO FRPSUHVVLRQ %LOJLQ HW DO &KRX HW DO 6LPLODUO\ WKH +$9&LQWUD HQFRGHU KDV DOVR EHHQ XVHG )LOKR HW DO E 7ZR GLPHQVLRQDOHQFRGLQJPHWKRGVEDVHGRQWKHGLVFUHWHZDYHOHWWUDQVIRUPIROORZHGE\63,+7 FRHIILFLHQWHQFRGLQJKDYHDOVREHHQSURSRVHG/XHWDO3RR\DQHWDO0LDRX &KDR 0RD]DPL*RXGDU]L HW DO 5H]D]DGHK HW DO 7DL HW DO 6KDULIDKPDGLDQ HW DO 6DKUDHLDQ )DWHPL]DGHK 7KLV VHFWLRQ LQYHVWLJDWHV WKH XVHRILPDJHHQFRGLQJDOJRULWKPVIRUFRPSUHVVLRQRI6(0*VLJQDOV
%QORTGUUKQPQH5WTHCEG'NGEVTQO[QITCRJKE5KIPCNU7UKPI6YQ&KOGPUKQPCN6GEJPKSWGU
)LJ,OOXVWUDWLRQRIWKHTXDQWL]DWLRQDOJRULWKPXVHGLQWKHHQFRGHUSURSRVHGE\%HUJHUHW DO (DFK EORFN RI ZDYHOHW FRHIILFLHQWV LV GLYLGHG LQWR VXEEDQGV ZLWK VSHFWUDO OLQHV 7KH LGHDO ELW DOORFDWLRQ YHFWRU LV FRQVWUXFWHG XVLQJ WKH QXPEHU RI ELWV QHFHVVDU\ WR TXDQWL]H WKH ODUJHVW FRHIILFLHQW LQ HDFK VXEEDQG 7KLV LV XVHG DV LQSXW RI D .RKRQHQQHXUDOQHWZRUNZKLFKRXWSXWVWKHDSSUR[LPDWHGELWDOORFDWLRQYHFWRU
6YQFKOGPUKQPCN5'/)OQFGNKPI 6(0* VLJQDOV RI LVRPHWULF FRQWUDFWLRQV DUH XVXDOO\ PRGHOHG DV VWRFKDVWLF SURFHVVHV 7KH W\SLFDODXWRFRUUHODWLRQIXQFWLRQDVVRFLDWHGZLWK6(0*VLJQDOVLQGLFDWHVDVWDWLRQDU\RUDW OHDVWORFDOO\VWDWLRQDU\SURFHVV ,Q WZRGLPHQVLRQDO FRPSUHVVLRQ RI 6(0* VLJQDOV WKH RQHGLPHQVLRQDO YHFWRU LV VHJPHQWHG LQ 0 ZLQGRZV RI OHQJWK 1 DQG DUUDQJHG LQWR D 1ð0 PDWUL[ )LJXUH 7KLV OHDGVXVWRDWZRGLPHQVLRQDOUHDOUDQGRPILHOG[V >QP@ZKHUHQ «1ïP «0ï V : DQG : ^ !` LVWKHVDPSOHVSDFH)LJXUH 7KH'PDWUL[DVVRFLDWHG
ZLWK HDFK SRVVLEOH UHDOL]DWLRQ FRUUHVSRQGV WR D GLIIHUHQW WZRGLPHQVLRQDOO\ UHDUUDQJHG 6 (0*VLJQDO 7KHWZRGLPHQVLRQDOO\DUUDQJHGGDWDFDQEHVHHQDVDKRPRJHQHRXVUDQGRPILHOGEHFDXVH LW LV DVVXPHG WKDW RQHGLPHQVLRQDO 6(0* VLJQDO LV D VWDWLRQDU\ VWRFKDVWLF SURFHVV $ UDQGRP ILHOG LV FDOOHG KRPRJHQHRXV LI LWV H[SHFWHG YDOXH RI [>QP@ P [ LV LQGHSHQGHQW RI G G SRVLWLRQ Y LH P [ Y P [ )RUUHDUUDQJHG6(0*GDWD P [
4GEGPV#FXCPEGUKP$KQOGFKECN'PIKPGGTKPI
)LJ2QHGLPHQVLRQDO6(0*VLJQDOUHDUUDQJHGLQWRDWZRGLPHQVLRQDOPDWUL[
)LJ7ZRGLPHQVLRQDOUHDOUDQGRPILHOG[V >QP@VKRZLQJPXOWLSOHUHDOL]DWLRQVRIWZR GLPHQVLRQDOO\DUUDQJHG6(0*VLJQDOV +RPRJHQHRXVUDQGRPILHOGVSUHVHQWWUDQVODWLRQLQYDULDQWDXWRFRUUHODWLRQIXQFWLRQVLH G G G G G G G G 5[ Y Y 5[ ^[ Y [ Y ` { 5[ Y Y { 5[ Y Y
%QORTGUUKQPQH5WTHCEG'NGEVTQO[QITCRJKE5KIPCNU7UKPI6YQ&KOGPUKQPCN6GEJPKSWGU
G G ,IZHGHQRWHWKHSRVLWLRQYHFWRUV Y DQG Y E\WKHLUUHVSHFWLYHSDLURIGLVFUHWHFRRUGLQDWHV
PQDQGMLUHVSHFWLYHO\WKHQWKHDXWRFRUUHODWLRQIXQFWLRQFDQEHH[SUHVVHGDV 5[ Q P L M 5[ > Q L P M @ 5[ > L Q M P@
,I ZH XVH WKH GLVFUHWH YDULDEOHV N DQG U WR GHQRWH WKH FRRUGLQDWH GLIIHUHQFHV QïL DQG PïM UHVSHFWLYHO\WKHDERYHHTXDWLRQFDQEHUHZULWWHQDV 5[ Q P L M 5[ > N U @ 5[ > N U @ ,Q JHQHUDO WKH DXWRFRUUHODWLRQ IXQFWLRQ RI D UDQGRP ILHOG LV D IXQFWLRQ RI IRXU YDULDEOHV +RZHYHUWKHDXWRFRUUHODWLRQIXQFWLRQRIDKRPRJHQHRXVUDQGRPILHOGHJ6(0*GDWD LV DIXQFWLRQRIRQO\WZRYDULDEOHVNDQGU 5[ > N U @ ( ^[ > Q P@ [ > Q N P U @`
1 0
¦ ¦ [ >Q P@ [ >Q N P U @
Q P
7KHDXWRFRYDULDQFHIXQFWLRQ&[>NU@LVGHILQHGDV & [ > N U @ ( ^[ > Q P @ [ > Q N P U @ P `
1 0
¦ ¦ [ >Q P@ [ >Q N P U @ P
Q P
8QGHUWKHDVVXPSWLRQWKDWDFODVVRIUHDUUDQJHG6(0*GDWDIRUPVDKRPRJHQHRXVUDQGRP ILHOGWKHDXWRFRUUHODWLRQIXQFWLRQ5[>NU@PD\EHDVVXPHGWREHRIWKHIRUP 5[ > N U @ 5[ > @ P H D N E U P ZKHUHǂDQGǃDUHSRVLWLYHFRQVWDQWV5RVHQIHOG .DN DQGZKHUHE\GHILQLWLRQ
^
5[ > @ ( [ > Q P@
`
1 0
¦ ¦ [ >Q P@ DQG
Q P
P
(^[ > Q P@`
)RUUHDUUDQJHG6(0*GDWD P
1 0 ¦ ¦ [ >Q P@ 10 Q P
DQGWKHDXWRFRUUHODWLRQIXQFWLRQLVUHGXFHGWR
5[ > N U @
& [ > N U @ &RQVWDQWV ǂDQG ǃFDQEHGLVWLQFWGXHWRWKHQDWXUHRIUHDUUDQJHG6(0*GDWD7KLVPHDQV WKDWWKHDXWRFRUUHODWLRQIXQFWLRQFDQEHXVHGWRPRGHOWZRGLPHQVLRQDOGDWDZLWKGLIIHUHQW GHJUHHVRIFRUUHODWLRQLQWKHKRUL]RQWDODQGYHUWLFDOGLUHFWLRQVE\VSHFLI\LQJWKHYDOXHVRI ǂ DQG ǃ,QRXUPHWKRGRQHGLUHFWLRQFRUUHVSRQGVWROLQHDUWLPHGDWDVDPSOLQJZLWKVWURQJ
5[ > @ H D N E U
4GEGPV#FXCPEGUKP$KQOGFKECN'PIKPGGTKPI
FRUUHODWLRQDQGWKHRWKHUFRUUHVSRQGVWRZLQGRZVWHSDQGOHDGVWRZHDNFRUUHODWLRQ7KH FRUUHODWLRQ DORQJ WKH ZLQGRZ VWHS GLUHFWLRQ PD\ EH LQFUHDVHG XVLQJ FROXPQ UHRUGHULQJ EDVHGRQLQWHUFROXPQFRUUHODWLRQDVGLVFXVVHGLQWKHQH[WVHFWLRQ )LJXUHDSUHVHQWVWKHWKHRUHWLFDODXWRFRUUHODWLRQIXQFWLRQFDOFXODWHGXVLQJHTXDWLRQ ZLWK ǂ DQG ǃ )LJXUH E SUHVHQWV WKH DXWRFRUUHODWLRQ IXQFWLRQ DVVRFLDWHG ZLWK WKH 6(0* VKRZQ LQ )LJXUH DIWHU FROXPQ UHRUGHULQJ 7KHVH UHVXOWV GHPRQVWUDWH WKDW WZRGLPHQVLRQDOO\ DUUDQJHG 6(0* GDWD SUHVHQWV WZRGLUHFWLRQDO FRUUHODWLRQ DQG WZR GLPHQVLRQDO UHGXQGDQF\ 7KHUHIRUH WKLV W\SH RI GDWD PD\ EH FRPSUHVVHG XVLQJ LPDJH FRPSUHVVLRQ WHFKQLTXHV ,Q WKH QH[W VHFWLRQ ZH SUHVHQW D WHFKQLTXH IRU PD[LPL]LQJ WZR GLPHQVLRQDO6(0*FRUUHODWLRQDQGWKXVLPSURYLQJFRPSUHVVLRQHIILFLHQF\
)LJ $XWRFRUUHODWLRQ IXQFWLRQV D FRPSXWHG IURP WKH WKHRUHWLFDO PRGHO XVLQJ ǂ DQGǃ E FRPSXWHGIURPWKHGDWDVKRZQLQ)LJXUH
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
7KHQWKHSDLU RIFROXPQVWKDWSUHVHQWWKHKLJKHVWFURVVFRUUHODWLRQFRHIILFLHQWLVSODFHGDV WKH ILUVW WZR FROXPQV RI D QHZ PDWUL[ 7KH FROXPQ WKDW SUHVHQWV WKH KLJKHVW FURVV FRUUHODWLRQZLWKWKHVHFRQGFROXPQRIWKHQHZPDWUL[LVSODFHGDVWKHWKLUGFROXPQRIWKH QHZPDWUL[DQGVRIRUWK$OLVWRIFROXPQSRVLWLRQVLQDQQRWDWHG7KLVSURFHGXUHLVVLPLODU
%QORTGUUKQPQH5WTHCEG'NGEVTQO[QITCRJKE5KIPCNU7UKPI6YQ&KOGPUKQPCN6GEJPKSWGU
WRWKDWXVHGE\)LOKRHWDOE IRUUHRUGHULQJVHJPHQWVRI(&*VLJQDOVEXWWKHVLPLODULW\ PHWULF XVHG LQ WKDW VWXG\ ZDV WKH PHDQ VTXDUHG HUURU )LJXUH LOOXVWUDWHV WKH UHVXOW RI DSSO\LQJWKHSURSRVHGFROXPQFRUUHODWLRQVRUWLQJVFKHPHWRD6(0*VLJQDODUUDQJHGLQ' UHSUHVHQWDWLRQ
)LJ 7ZRGLPHQVLRQDOO\ DUUDQJHG 6(0* VLJQDO OHIW DQG DVVRFLDWHG DXWRFRUUHODWLRQ IXQFWLRQULJKW D ZLWKRXWFRUUHODWLRQVRUWLQJE ZLWKFRUUHODWLRQVRUWLQJ
+OCIGEQORTGUUKQPVGEJPKSWGUCRRNKGFVQ&CTTCPIGF5'/) )LJXUHVKRZVDEORFNGLDJUDPRIWKHSURSRVHGHQFRGLQJVFKHPH7KHPHWKRGFRQVLVWVLQ VHJPHQWLQJ HDFK 6(0* VLJQDO LQWR VDPSOH ZLQGRZV DQG WKHQ DUUDQJLQJ WKHVH VHJPHQWVDVGLIIHUHQWFROXPQVRIDWZRGLPHQVLRQDOPDWUL[ZKLFKFDQWKHQEHFRPSUHVVHG XVLQJ ' DOJRULWKPV ,Q WKLV ZRUN ZH LQYHVWLJDWHG WKH XVH RI WZR RIIWKHVKHOI LPDJH HQFRGHUVWKH-3(*DOJRULWKPDQGWKH+$9&HQFRGHU
4GEGPV#FXCPEGUKP$KQOGFKECN'PIKPGGTKPI
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
'ZRGTKOGPVCNOGVJQFU $ FRPPHUFLDO HOHFWURP\RJUDSK 'HOV\V %DJQROL %RVWRQ 86$ ZDV XVHG IRU VLJQDO DFTXLVLWLRQ7KLVHTXLSPHQWXVHVDFWLYHHOHFWURGHVZLWKDSUHDPSOLILFDWLRQRI99DQGD SDVVEDQG RI ²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
%QORTGUUKQPQH5WTHCEG'NGEVTQO[QITCRJKE5KIPCNU7UKPI6YQ&KOGPUKQPCN6GEJPKSWGU
&)
2V &V 2V
ZKHUH 2VLVWKHQXPEHURIELWVUHTXLUHGIRUVWRULQJWKHRULJLQDOGDWDDQG &VLVWKHQXPEHU RIELWVUHTXLUHGIRUVWRULQJWKHFRPSUHVVHGGDWDLQFOXGLQJRYHUKHDGLQIRUPDWLRQ 7KH35' LVGHILQHGDV 1
35'
¦ [>Q@ [>Q@ Q
1
¦ [ >Q@
Q
ZKHUH [LVWKHRULJLQDOVLJQDO [ LVWKHUHFRQVWUXFWHGVLJQDODQG 1LVWKHQXPEHURIVDPSOHV LQWKHVLJQDO
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
4GEGPV#FXCPEGUKP$KQOGFKECN'PIKPGGTKPI
)LJ &RPSUHVVLRQ SHUIRUPDQFH FRPSDULVRQ &) YV 35' EHWZHHQ WKH -3(* DQG +$9&LQWUDLPDJHHQFRGHUVXVLQJWKHFRUUHODWLRQVRUWLQJSUHSURFHVVLQJVWHS
)LJ 5HSUHVHQWDWLYH UHVXOWV IRU D PV VHJPHQW RI D 6(0* VLJQDO &) D XQFRPSUHVVHGE FV-3(*F FV+$9&LQWUDG -3(*UHFRQVWUXFWLRQ HUURUH +$9&LQWUDUHFRQVWUXFWLRQHUURU5HFRQVWUXFWLRQHUURUVDUHPDJQLILHGE\ IROG
%QORTGUUKQPQH5WTHCEG'NGEVTQO[QITCRJKE5KIPCNU7UKPI6YQ&KOGPUKQPCN6GEJPKSWGU
&RPSUHVVLRQ)DFWRU 1RUULVHWDO %HUJHUHWDO -3(* FV-3(* +$9&LQWUD FV+$9&LQWUD
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
%QPENWUKQPU
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
4GHGTGPEGU
$FKDU\D 7 7VDL 3 6 -3(* 6WDQGDUG IRU ,PDJH &RPSUHVVLRQ &RQFHSWV $OJRULWKPV DQG 9/6, $UFKLWHFWXUHV -RKQ :LOH\ 6RQV ,6%1 +RERNHQ1-86$ %DVPDMLDQ - 9 'H /XFD & - 0XVFOHV $OLYH 7KHLU )XQFWLRQV 5HYHDOHG E\ (OHFWURP\RJUDSK\:LOOLDPV :LONLQV,6%1%DOWLPRUH86$
4GEGPV#FXCPEGUKP$KQOGFKECN'PIKPGGTKPI
%HUJHU3$1DVFLPHQWR)$2GR&DUPR-& GD5RFKD$) &RPSUHVVLRQRI (0*6LJQDOVZLWK:DYHOHW7UDQVIRUPDQG$UWLILFLDO1HXUDO1HWZRUNV3K\VLRORJLFDO 0HDVXUHPHQW9RO1RSS²,661 %LOJLQ $ 0DUFHOOLQ 0 : $OWEDFK 0 , &RPSUHVVLRQ RI (OHFWURFDUGLRJUDP 6LJQDOV XVLQJ -3(* ,((( 7UDQVDFWLRQV RQ &RQVXPHU (OHFWURQLFV 9RO 1R SS²,661 %UHFKHW//XFDV0)'RQFDUOL& )DULQD' &RPSUHVVLRQRIELRPHGLFDOVLJQDOV ZLWK PRWKHU ZDYHOHW RSWLPL]DWLRQ DQG EHVWEDVLV ZDYHOHW SDFNHW VHOHFWLRQ ,((( 7UDQVDFWLRQV RQ %LRPHGLFDO (QJLQHHULQJ 9RO 1R SS ² ,661 &DURWWL ( 6 * 'H 0DUWLQ - & 0HUOHWWL5 )DULQD ' &RPSUHVVLRQ RI VXUIDFH (0* VLJQDOV ZLWK DOJHEUDLF FRGH H[FLWHG OLQHDU SUHGLFWLRQ 3URFHHGLQJV RI ,((( ,QWHUQDWLRQDO &RQIHUHQFH RQ $FRXVWLFV 6SHHFK DQG 6LJQDO 3URFHVVLQJ SS ² ,6%1;7RORXVH)UDQFH0D\ &KRX ++ &KHQ