arg(G(jw)) Ritardo Anticipo

2 35476,8-9:6<;;=6 >4@?BADC!EF4HG IKJ >476,8-9:6<;L;M6 N.O-P06D9RQ >QSP%P76 TUEVXWX4HOYVXQ >-4Z9[4HG\NFO.G I]6

6D9^;OYV<4`_,6badcfehgjikJ

Re(G(jw)) Im(G(jw))

|G(jw)|

arg(G(jw)) Ritardo Anticipo

Re(G(jw)) Im(G(jw))

|G(jw)|

arg(G(jw)) Ritardo Anticipo

2 lm>46,8Y9:6<;;n4o>4<?BAXC!E<4`GpIGk4qNFO.GrGsOYVXOn9^4`_,6utS6q9vQw>x6F4m>476,8-9:6<;L;L4k>4<yzO{>Q5OYNNE9vQ

Gk4N<E{|On6,>OqI}I]6D9vQ~E<VnNq9vO{_mQm>4;QSVI O€NFQS9zP768Y9:6‚-_,6,WD4`OYVXQƒCES6<P%4„I]6uI…4„tS6ZQ†>49vQoI}I]6{J

‡.ˆŠ‰

E<VIpO‹>-41NS6D9ŒIpQSVXW6>QSPx>-46,8Y9:6<;;M6

ˆ

ŽYˆ#

VI…4`_q4N.O‘O’9^4„I]6D9v>O“9^4`G\NFQoI}IpO6<P%P76T”6,GsQ€4VF4HWD476<P•QL–—

ˆ

˜Yˆ

3QoIpQS9^;n4VS6,WX4HOYVXQ=>QSP%P™6,Gk4VuIpOSI OštXQS9›Iœ4H_,6<P•Q€NFQS94xG\4`G IpQS;L4h>4hI…4NFO

‡Fˆ



ˆŠ‰

E<VIpO‹>-4(6D9^9^4„tXO

ˆ

ž ˆŸ

9 6‚Y_,6,WD4`O-V,QMC!ES6<P¡4•I]6uIœ4•tS6

ˆ

¢YˆŠ‰

E<VI…4->-4#4VIpQS9vGsQmWD4HOYVXQM_mOYV£P™%6,GsGrQ€9vQ,6<P•Q

ˆ

¤

ˆƒ¥r¦ §

4EXG\E9:6¨£>QSP{>46,8Y9:6<;;=6

ˆ

2 ?©†ª



J.«qQ_mO.G I]6<VI…4…>4…IpQS;N.Oj>-4XN.O-P¡4oOjWKQS9[4\GsQS;N<P%4`_q4œO_mOY;NP•QmGsG\4…Q_mOYV<4E,8h6uI…4

GsOYVXO‹>QK‚¬V<4„IpQbVXQSPxGrQm8YEXQSVIpQb;@O{>O(J

c ­)® ¯±°qi

¦

OFG I]6<VI QM>4{I QS;NFO ¯

²

­³® ´Sµ

°

g ¶

®

°D·

g

·¶¸

¦

OFG I]6<VI QM>4{I QS;NFO ¯º¹ ´Sµ

g¶

2 ¼xGsQS;NF4HO!J

adc[°qi¹

­o½c[°j® ¾Fi

°xc[°ƒ® ½-¿

´

i\c[°

· ® ­mÀ.°†® ­K½S½Fi

¹ ¾´ Á

­w®

°

¾(Â

°xc ­³® À.°qi

²

­³®

¾<°

´ ½ ®

°D·

­o½S½

¸

‡.ˆÃ‰

EVuIpOZ>4XNS6D9›I QSVXW6ZĔg Å ½SÆÇ

ˆ

3 QoI}I]6jÈ P765_mO.GpI]6<VuIpQ†;OYP„Iœ4NP¡4`_,6uI…4•tS6³>4aÉc[°qi

V,QSPP06ZTÊO<9Ë;=6Ì6Í_mO.GpIr6<VI…4X>-4XIpQS;N.O!Î-N.QS9EVÌG\4`G IpQS;M6ƒ>4I…4N.OϺ4PNE<VIpO€4V<4HWX46<P•Q

><QSP >476,8Y9 6<;L;M6Ð|QÑ>x6uIpO >x6 Ä^QmGrQS;LN<4`O È ¹ ¾hÒ

´

ÎƒÏ ¹ ­qÎnÓ¡aÉc[°qiÓ¹ Ô Î

– — ¹ ÕMÖ Ò

´

ÇkJ

Ó¡adc[°qiÓØ×<Ù

— Ú

¹ Û

ÓÈ Ó NFQS9Ϻ¹ ½

Ô NFQS9ÏÝÜ ­

ÞXß à†aÉc[°qi

×<Ù

— Ú

¹ á

â¡ã

– — ¹ ÕLÏ

Ö´ È ä ½

– —†¹ Õ=ÖåÕ Ï Ö´ È æ ½

ŽYˆ1

VuI…4H_q4NFOšO“9^4„I]6D9v>O“9^4`G\NFQoI}IpO6<P%P76T”6,GsQ€4VF4HWD476<P•QL–—

ˆ |

¼“G\E,çb_q4`QSVIpQ=_,6<P•_mO-P06D9vQ€4P

GsQm8YVXO‹>QSP%P06LGrQm8YEXQSVIpQM_mO.G I]6<VIpQ<J

è€é

¹ ¯!ê

ë Õ ¯œìZÅ Û è é ä ½ 

VI…4`_q4N.O’Ä^GsQSVXGrO£6<VI…4`O9:6D9[4HOhÇ

è é æ ½ íî4„I]6D9v>OºÄ^GsQSVXGrOšO9:6D9[4HOhÇ

><OStXQb¯

ê

ë

Q€¯ ì 9:6<NNq9vQmGsQSVI]6<VXOÎÃ9[4`GoN.QoI}I…4„t.6<;@QSVIpQFÎîP`Q_mOFG I]6<VI…4(>4!IpQS;LNFO£>Qm8YP%4

WoQS9^4<Q~>Qq4NFOYP¡4h>QSPP06MTUEV,WD4HOYVXQïadc[°qi

ˆ

? QSP%P™7QmGsQS;N<4`O

è é ¹ ­

¾ Õ ÀÕ

¾

´ ½ æ ½ ˆ

˜Yˆ

3 QoIpQS9^;L4VS6,WD4`OYVXQï>QSP%P™%6,Gk4VI OSIpOÉtDQS9ŒI…4`_,6<P`QNFQS9†4¬Gk4HG IpQS;L4!>-4I…4NFO

‡Fˆ

«x™6,Gs_q4HGsGð6

ñ é

><QSPP™6,Gk4VIpOqIpOštXQS9[4•I…4`_,6<P•QL|Q<J

ñ é ¹ È Á

¯!ê

ë Õ ¯œì

 ¹ È

è€é

¹ ¾´ ² ­

¾ Õ ÀÕ

¾

´ ½ ¸ ¹ Սòx¿

´ ¾

é ‡ Ž-ˆ

EVuIpO‘>-4!6D9^9[4•tXOÉĔg Å Ô Ç 3 QoI}I]6Ȁô€P06n_mO.GpI]6<VuIpQ€;OYPóI…4N<P%4`_,6uI…4„t.6=>4(aÉc[°qi

V,QSPP06bTÊO9^;M6‹6’NFOYP%4QïWKQS9[4Î NFQS9†EV‘G\4`GpI QS;M6ï>4#8Y9:6,>Oõ9vQSP06uI…4„tDOdö÷4PøNEVuIpO’>4

6D9^9[4•tXO>QSPY>46,8Y9:6<;;=6š|QL>{6uIpO>x6£ÄËQmGsQS;NF4HO“È ô ¹ ­o½YÎ#ö‘¹ ¾YÎÓ¡adc[°qi,Óx¹ ½-Î

–ù ¹ ÕM¾SÖ Ò

´

ÇkJ

Ó¡aÉc[°qiÓ×<Ù

ù ¹ Û

ÓȀô-Ó NFQS9Böï¹ ½

½ NFQS9Bö£Ü ­

ÞXß à†adc^°qi

×<Ù

ù ¹ á

â 㠖 ù ¹ Õ~ö

Ö´

Ȁôä ½

– ù ¹ Õ=ÖõÕ ö Ö´ È ô æ ½

ž

ˆîŸ

9:6‚Y_,6,WD4`O-VXQÉC!ES6<P¡4„I]6uI…4„t.6

ˆ ú

4î_mO-P%P•Qm8h6õ4P NEVIpO 4V<4`WD46<P•Qd>QSPî>476,8-9:6<;L;M6É>4

?BAXC!E<4`G I£Ä g Å ½ Æ Çn_mOYV 4PNEVI O ‚¬VS6<P•QõÄ g Å Ô ÇnT[6,_mQSV,>O 6uI}IpQSVXWD4`OYVXQ

6Ñ;E,OStXQS9vG\4BV,QSPîN<476<VXOû_mO-;LNP`QmGsGsOõ4V÷;O{>O’_mO-VX8Y9^EXQSVIpQd6F4BNFOYP%4±Q£6,8-P¡41WKQS9[4

G I]6<ü<4P¡4¡ý<4V,GpI]6<üF4P¡4±>4Badc^°qi_

§

Q‹G\4Š4VX_mO-VuIk9:6<VXO Nq9vO.8-9vQmGsG\4„tS6<;QSVIpQd6<P1_S9RQmGs_mQS9vQ

>-4hg

ˆ

¢YˆÃ‰

EVuI…4X>4F4VuIpQS9vGrQmWD4`OYVXQ†_mO-VP™6,GsGrQÌ9vQ,6<P•Q

ˆ ú

4X_,6<P•_mOYP76<VXOL4tS6<P`O<9[4X>4mg NFQS9ø4,CES6<P%4

þ”ÿ

c^adc+egjipiw¹ ½

ˆ

E,QmGpIpO’Nq9vOx_mQm>-4;@QSVIpO“NE{|O‹QmGsGsQS9RQï;OYP„IpOÉP%EVX8.OC!E<4VX>4(|Q

¦ ˆ

4EXGoE<9 6¨“>QSP!>476,8-9:6<;L;M6 4!>QK‚¬V<4HGs_mQï>476,8Y9 6<;L;M6£NFOYP76D9vQï_mOY;NP•QoIpOûP06

_SE<9›tS6

¥ _ §

4EXGð6¨Ì_

§

Qj4P,NEVI O=aÉcfegjiø>QmGs_S9[4•tXQ³G\EP,N<46<V,OÍ_mO-;LNP`QmGsGsOÌ6<P…tS6D9[46D9vQ

>-4Yg >{6ÑÕÔ 6‘®MÔ

ˆ l P>-46,8Y9:6<;;M6>4î?BAXC!E<4`GpI>QmGs_S9[4•I}I O“6F4øNEVI…4zNq9vQm_mQ

><QSVI…4T”6d9[4•TÊQS9^4;QSVuIpOÉ6<P-_,6,GsOšg ä ½ ˆ

«F6£NS6D9›I Q>QSP->-46,8Y9:6<;;M6>4z?BADC!EF4HG I

9vQSP06uI…4„t.6š6,>dg æ ½‹Gk4(OSI}Iœ4HQSVXQ>x6<PP06“Nq9vQm_mQm>QSVI Q€GrQS;LNP%4`_mQS;QSVuIpQš9^4üS6<PóI]6<VX>O

4PD>476,8-9:6<;L;M6M9^4`G\NFQoI}IpOL6<P%P™6,GsGrQ~9vQ,6<P`Q

ˆ

? QSPq_,6,GsO€4V~_SEF4YP06ÍTUEV,WD4HOYVXQ=adc[°qi6<ü

üF46‘>Qq4NFOYP¡4VXQSP%P™O<9^4`8x4VXQFÎ 4P!>46,8Y9:6<;;=6b_mO.G

|

4OSI IpQSVEIpOû|Q‘6<VX_mO<9 6

¥

6<NFQS9ŒIpOS¨

ˆ

‰

QS95_

§

4EX>QS9^P•OÐ_mO<9^9RQoI I]6<;QSVI Q‹O{_m_mO9^9vQGsQm8-E<49vQÑP06dGsQm8-EXQSVuIpQÑ9vQm8FOYP06{Jš4P±>476 

8Y9:6<;;=6>4#?BAXC!E<4`GpIwt.6=_

§

4EXGsO‘6<PP™ 4V,‚¬V<4„IpOÉNS6D9›I QSVX>O€>x6ïaÉcfeY½1ikÎ!6D9^9[4•tS6<VX>O

6adc+eY½ Æ ijQ4VXGsQS9vQSVX>O£I]6<VIpQLGrQS;n4U_q49v_mO-V,TÊQS9vQSVXWKQ‹NFQS9v_mO9vGsQ£4VšGrQSV,GrOdO9:6D9[4HO

CES6<VI…4xGrOYVXO’ÄpϱÇÍ4#NFOYP¡4¬VXQSP%P™O<9^4`8x4VXQn>QSP%P76nTUEV,WD4HOYVXQbadc^°qi

ˆ

2 ? QSP%P™QmGsQS;N<4`Od4VïQmGð6<;QG\4

§

6{J

Re(G(jw)) Im(G(jw))

s a

w = 0 ^-

w = 0 ⁺

Re(G(jw)) Im(G(jw))

s a

w = 0 ^-

w = 0 ⁺

2 ú

476 V,Qq4w>-46,8Y9:6<;;L4 >4ZyzOx><QFÎZGk476 4V C!EXQSP%P%4)>4Z?BAXC!E<4`GpIº4P_mOY;N.O9ŒI]6<;QSV 

I O >45EVS6å8.QSVXQS9[4H_,6 adc[°SiN.QS9=° Å ½ Æ Q N.QS9M° Å Ô G\4³NE{|O G IkEX>-46D9vQ

_mOYVXGk4H><QS9 6<V,>O’9[4`GoN.QoI}I…4„t.6<;@QSVIpQnP•Q~TUEVXWD4`O-VF4!6<NNq9vO.GrGk4;M6<VI…4YaL—c[°Si)Qa ù c[°qi

ˆ

2÷an—uc[°SiÑ|Q P06 TUEV,WD4HOYVXQ 6<N<Nq9RO.GsG\4;M6<VI Q >4ƒaÉc[°qi÷N.QS9š° Å ½ Æ ˆ ú

4OqI}I…4`Q

V,Q÷Ik9:6,Gs_SE9:6<VX>O IkEuI}I…44 IpQS9^;n4V<4³4V ° 6,> QmGs_SPEXGk4`O-VXQÐ>Qq4†NFOYP¡4†VXQSPP™7O9[4H8x4VXQFÎ

 

«³? w¼’G\476‘P06nT:O<9^;M6n>4(adc[°SikJ

an—,c[°qiw¹

­o½c•°ƒ® ¾Fi

°xcH°j® ½-¿

´

ioc`°

· ® ­mÀH°ƒ® ­o½S½Fi

¹

¾S½

´

½<°

¹ ¾

´ °

a — c[°qiw¹

¾´ ²

­w®

H°

¾ ¸

°xcp­m® `ÀF°qi

²

­w®

„¾°

´ ½ ®

H°X·

­o½.½

¸ ¹ ¾

´ °

2÷a ù c^°qib|Q P06ÑTUEV,WD4HOYVXQå6<NNq9vO.GrGk4;=6<VIpQ“>4aÉc[°qi‘N.QS9° Å Ô ˆ ú

4ŠOqI}I…4`QSVXQ

_mOYVXGk4H><QS9 6<V,>O’GsO-P•OõP•QdNFOqIpQSVXWoQ€>4ø°‘>OY;L4VS6<VIœ4±6<P%P™4VIpQS9^VXO’>-4#O.8-VF4#T”6uI}IpO<9RQFÎ

 

«³? w¼’G\476‘P06nT:O<9^;M6n>4(adc[°SikJ

a ù

c^°qi ¹

­o½c[°S® „¾Fi

°xc[°q® „½-¿

´

i\c^°

· ® ­mÀ.°q® ­o½S½.i

¹

­o½<°

°b°š°

· ¹

­o½

°

aùšc^°qi ¹ ¾´ Á

­w®

°¾ Â

°xc%­³® À.°qi

²

%­³®

„¾<°

´ ½ ® ° ·

­o½S½

¸ ¹ ¾´ Á °

¾ Â

°xc”ÀF°qi

² ° ·

­o½S½

¸ ¹

­o½

° 

2 «DQjTUEV,WD4HOYV<4<6<NNq9vO.GrGk4;=6<VI…4<a

—

c^°qiBQaLùšc[°qiŠGk4{NFO.GrGsOYVXOšEXGœ6D9vQZ6<PNFO.GpI On><QSPP•Q

TÊO<9Ë;LEP•QM4VI…9RO{>OqI}IpQ4VïNq9vQm_mQm>QSVXW6ïN.QS9z>QoI QS9Ë;n4Vq6q9vQƒtXQSP•Ox_mQS;@QSVIpQ=4YNEVuI…4<>4

Nq6q9ŒIpQSV,W6£Q‘>46D9Ë9[4„tDOÑGk476£>Qq4ø>476,8Y9 6<;L;L4#>4 ?BADCE<4HG I~G\476d>4±CEXQSPP¡4ø>4 yzO{>Q

N.QS9v_

§

|QMGsO-VXOb_,6D9:6uI}IpQS9[4`WKW6uIpQÌGsO-P•Ob>x6n_mO.GpI]6<VuI…4(;OYP„Iœ4NP¡4`_,6uI…4•tXQ@Q~>x6nQotXQSVIkEq6<P%4

N.O-P¡4#VXQSPP™7O9[4H8x4VXQ

ˆ

¼xGrQS;LN<4`O(J

a — c[°qi ¹ ¾

´

°

Û

Ó¡adcfehgjiÓ×<Ù

— Ú

¹ Ô

– — ¹ Õ

·

aLùšc[°qi ¹

­o½

°   Û

Ó¡adcfehgjiÓ×<Ù

ù ¹ ½

– ù ¹ Õ=¾