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$2,"%!,4+$725!+,' A6%$%4+$%836%,56%/!"!5!>%/0%25)!",2. +,)!)5)+4

n

s

)27*.%)8 +,.1

n

s

/2

$2,"%$%)+.#5!+, %..)2$%2E2!.20.%'

D +$/!,"5+56%H1C#!)5 $!5%$!+,856%72I!7#70%254$%C#%, 15625 2,0%#,270!"#+#).1

7%2)#$%/!)62.456%)27*.%4$%C#%, 1' A6%72I!7#7$2,"%!)56%$%4+$%/%5%$7!,%/0156%

)27*.%4$%C#%, 1'J!5656%2!/+4?&'K@2,/?&'&@856%72I!7#7$2,"%4+..+3)2)(

R

max

=

cPRI

2∆f

f

s

2

=

c

2∆f

n

s

2

[m],

?&':@ !,36! 6

f

s

!)56%)27*.%4$%C#%, 12,/

n

s

!)56%,#70%$+4)27*.%)!,56%/!"!5!>%/0%25)!"F ,2.'L1$% 2..!,"5625

n

s

/2

)27*.%)2$%2E2!.20.%!,56%$2,"%)*% 5$#7856%$2,"%$%)+.#5!+, !)"!E%,2)(

δr =

c

2∆f

[m].

?&'M@ !"#"$ "&'()&*+$,-(!,". J6%,56%52$"%5!)7+E!,"$%.25!E%5+56%$2/2$82,2//!5!+,2.N+**.%$4$%C#%, 1)6!45

f

d

!) )#*%$!7*+)%/+,56%0%254$%C#%, 18.%2/!,"5+2,!,E2.!/$2,"%7%2)#$%7%,5' A6%N+**.%$ 4$%C#%, 1)6!45!)"!E%,2)89MO℄(

f

d

=

2

λ

dR

dt

=

2v

d

λ

[Hz],

?&'P@ 36%$%

λ

!)56%32E%.%,"56+456%5$2,)7!55%/)!",2.2,/

v

d

!)56%$2/!2.E%.+ !51' A6%N+**.%$4$%C#%, 1)6!457210%%I5$2 5%/01#)!,"25$!2,"#.2$4$%C#%, 17+/#.25!+,8)%%

!"#!!$"%!"&'$()*""!+'$+"%!! %-(*.$'/+0&*$."%!01(/-1!#*// !"%!+*22!&!$ ! !"#!!$

"%! !'"2&!30!$ 4+0!"-"%!&'$.!'$+"%!5-11/!&2&!30!$ 4(%*2"6 7*)*/'&/48+0&*$."%!

+-#$(/-1!"%!+*22!&!$ !2&!30!$ 4*("%!(0)-2"%! !'"2&!30!$ 4+0!"-"%!&'$.!'$+"%!

5-11/!&2&!30!$ 4(%*2"9

upslope : f

d

−

b

= f

b

− f

d

[Hz],

downslope:

f

d

+

b

= f

b

+ f

d

[Hz].

:;6<=

>%! !'"2&!30!$ 4+0!"-"%!&'$.!)'4 !!?"&' "!+ 4"'@*$."%!'A!&'.!-2"%!2&!30!$ 4

+*22!&!$ !#%!$

f

b

> f

d

8BCD℄6

F-A*$."'&.!"()'4'/(- !+!"! "!+ 4'11/4*$.(#!!1G"-G(#!!11&- !((*$.8BCH ℄GBCI℄6>%!

(*)1/!("2-&)-2(#!!1G"-G(#!!11&- !((*$.*(' '$ !//!&"%'"(0 "&' "((0 !((*A!(#!!1(6

>%!$8("'"*-$'&4"'&.!"('&! '$ !//!+-0"'$+-$/4)-A*$."'&.!"(&!)'*$6>%!1%'(!+*22!&G

!$ ! !"#!!$(0 !((*A!(#!!1( '$ !0(!+"-!("*)'"!"%!A!/- *"4-2)-A*$."'&.!"(6>%*(

*(%-#!A!&-$/42!'(* /!2-&(/-#)-A*$."'&.!"(6

! "#$%&'()(*+*( -. (/%012.)3*(-.012

! #$$%&'()*%!+,'#!+%-./#(+ &0'12$#-3

J2&!!G&0$$*$.*+!'/-( *//'"-&.!$!&'"!('1!&2! "/4(*$0(-*+'/(*.$'/6 K$"%'" '(!8"%!(1! G

"&0)-2 "%!-( *//'"-&L(-0"10" (*.$'/!?%* *"(' (*$./!1!'@ '" "%! '&&*!& 2&!30!$ 46 >%!

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>%!&!2-&!8"%!(1! "&0)-2'1&' "* '/-( *//'"-&L(-0"10"*( -)1-(!+-2'1!'@'""%! '&&*!&

2&!30!$ 4#*"% &-'+(*+! '$+(6K$1&' "* '/-( *//'"-&(8"%!!22! "-2')1/*"0+!M*""!&*(0(0G

'//4$!./*.* /! -)1'&!+"-"%!!22! "-21%'(!M*""!&8BCC ℄6 >%!&!)'*$+!&-2"%*((0 (! "*-$

#*//"%!&!2-&!2- 0(-$"%!1%'(!M*""!&-& ! #$$%& '()%!*+ #!*6 N( *//'"-&1%'(!$-*(!'$+

*"(!22! "(%'A! !!$("0+*!+!?"!$(*A!/4-A!&"%!4!'&(8BCH℄GBOP℄6

N( *//'"-&1%'(!$-*(!1&-A!(*)1-&"'$""-QFGRS&'+'&(8(*$ !"%!1%'(!$-*(!(*+! '$+(

'((- *'"!+#*"%'/'&.!:0$#'$"!+=(*.$'/!22! "*A!/4&'*(!"%!$-*(!T--&6 >%*()'4 !"%!

'(!!A!$*2"%!)'*$(1! "&'/ -)1-$!$"-2"%'"(*.$'/*(-0"(*+!"%!2&!30!$ 4 '$+-2*$"!&G

!("6S*"%*$"%*( -$"!?"8"%!+*&! " -01/*$. !"#!!$"%!"&'$()*""*$.'$+&! !*A*$.'$"!$$'(

*('#!//G@$-#$1&- /!)*$QFGRS&'+'&(6>%!"-"'/1&-1'.'"*-$1'"%-2"%!+*&! "G -01/!+

(*.$'/*(A!&4(%-&"6 >%!&!2-&!8*"()'*$(1! "&'/ -)1-$!$"*('"A!&4/-#2&!30!$ *!('2"!&

+!)-+0/'"*-$U"%'"*(2'&-0"(*+!"%!2&!30!$ 4 '$+-2*$"!&!("2-&)-("'11/* '"*-$(6V-#G

!A!&8"%!1%'(!$-*(!(*+! '$+()'4!?"!$+#!//*$"-"%!2&!30!$ 4 '$+ -2*$"!&!("6 >%*(

*('$*)1-&"'$" 1&- /!)8(*$ !"%!+*&! " -01/*$.*(0(0'//4)0 % ("&-$.!&"%'$ "%!

! %-(*.$'/(6

>%!!22! "*((*.$*W '$"/4&!+0 !+#%!$'2&' "*-$-2"%!"&'$()*""!+(*.$'/*(0(!+'(/- '/

-( *//'"-&:XN=(*.$'/*$"%!&! !*A!&8(*$ !*$"%'" '(!"%!1%'(!$-*(!-2"%!! %-(*.$'/*(

-&&!/'"!+#*"%"%!1%'(!$-*(!-2"%!XN(*.$'/8B<D℄GB<Y℄6>%*('%+,* ''*$%&# +*--* & '$

!)'?*)*Z!+ 4"0$*$."%!1'"%/!$."%-2"%!XN(*.$'/"-"%!1&-1'.'"*-$1'"%-2"%!+*&! "

-01/*$.8BCH ℄GBC;℄6

>%!1%'(!$-*(!1-#!& '$ !&!+0 !+*$-"%!&#'4('(#!//6 N A*-0(/48"%!0(!-2'$-(G

!" $%%&'()$ *'&+,$%-./0 ℄-.23 ℄4.56℄7

!"#$"% '()""*+,%-.%"/!.0'

8'")*$!&9 "!):')%;%)$9 :!:9$)$!&%)*$<!$+,$' ;%=$$ '"'>&'$:!&);-.23 ℄4.?6℄-=*& *&%

,%,:>>;$@ !$%%$A:%: $! $'):($"<)*$)"):>%=$$ 7 B*$')*$%=$$ &%'"'>&'$:!-)*$C$:)

<!$+,$' ;&%'") "'%):'))*!",(*",))*$%=$$ &')$!D:>:'A)*$!:'($!$% "'%$&%C!":A$'$A7

E*$$<<$ )"<%=$$ '"'>&'$:!&)&$%&%!$A, $A=*$': "!)&"'"<)*$)!:'%9&))$A%&(':>&%,%$A

:%FG%&(':>-%&' $&')*:) :%$)*$%=$$ '"'>&'$:!&);"<)*$$ *"%&(':>&% "!!$>:)$A=&)*

)*$%=$$ '"'>&'$:!&); "<)*$FG %&(':>-.53 ℄7 E*&%&% :!)& ,>:!>;)!,$<"!$ *"$% "9&'(

<!"9):!($)%:):%*"!)!:'($78':':>;)& :>A$D$>" 9$')"<)*$$<<$ )"<%=$$ '"'>&'$:!&)&$%

=&>>C$(&D$'&'%$ )&"'07H7

E*$$<<$ )"<%=$$ '"'>&'$:!&)&$%9:;C$!$A, $AC;: >;&'(:>&'$:!&I$! &! ,&)7 E*$>&'4

$:!&I$! &! ,&)%*",>A*"=$D$!C$<:%)$'",(*)"<">>"=)*$<!$+,$' ;)!:'%&)&"'%:))*$$'A

"<$: *%=$$ -.?6 ℄7

!"#$"% '()""*1!/%2.0.,%2

8))*$C$(&''&'("<:'$=%=$$ -)*$C$:)<!$+,$' ;$+,:>%)*$>:!($A&<<$!$' $C$)=$$')*$

&'%):'):'$",%!$ $&D$A<!$+,$' ;:'A)*$&'%):'):'$",%)!:'%9&))$A<!$+,$' ;-%$$J&(7H7KL:M7

E*&%<!$+,$' ;&%,%,:>>;",)%&A$)*$!$ $&D$!N%C:'A=&A)*7 O"!$"D$!-)*$<!$+,$' ;)!:'%&4

)&"'%C$)=$$')*$%=$$ %:!$); & :>>;'"'>&'$:!:'A)*$)!:'%&))&9$%:!$P'&)$- :,%&'(A&%4

)"!)&"'%&')*$C$:)%&(':>7Q' !: )& $-)*$ :!)%"<)*$C$:)%&(':>:!",'A)*$%=$$ )!:'%&)&"'%

:!$)*$!$<"!$A&% :!A$A-.50℄-.?6 ℄4.?K℄7

!" #$%&'()$%)* ,-%.)/.%0121.3.*( *-4%

Q' "'D$')&"':>!:A:!%;%)$9%)*$:I&9,)*!$%">,)&"'A$)$!&"!:)$%:%!:'($&' !$:%$%-%&' $

)*$:')$'':C$:9=&A$'%7E*$:I&9,)*!$%">,)&"'&%(&D$':%R

δAz ≈ θ

Az

R

[m],

LH75M

&'=*& *

θ

Az

&%)*$:I&9,)*04AS:')$'':C$:9=&A)*7 E*$:')$'':C$:9=&A)*A$ $'A%"' )*$:')$'':>$'()*

l

-./6℄R

θ

Az

≈

λ

l

,

l ≫ λ

[rad].

LH7?M

8% :'C$%$$'<!"9LH75M:'ALH7?M-)*$:I&9,)*!$%">,)&"'&9 !"D$%:%)*$:')$'':>$'()*

&' !$:%$%7

Q'%;')*$)& : $!),!$!:A:!:>:!($:')$'':>$'()*&%%;')*$%&I$AC;9:T&'(,%$"<)*$9")&"'

"<)*$!:A:! >:)<"!97 Q'J&(7H70)*$:&!C"!'$%)!& 9: 49"A$U8V($"9$)!;&%%*"='7 E*$

:')$'':C$:9&%"!&$')$A'"!9:>)")*$W&(*))!: TX*$' $:%)!& "<>:'A :!:>>$>)")*$W&(*)

)!: T&%&>>,9&':)$A78%)*$!:A:! >:)<"!9W&$%C;-:):!($)"')*$(!",'A&%&>>,9&':)$A<"!

: $!):&' $!&"A"<)&9$A$ $'A&'(, "')*$!$:>:')$'':C$:9=&A)*7 Y,!&'()*&% $!&"A:

',9C$!"<%=$$ %:!$)!:'%9&))$A:'A)*$ "!!$% "'A&'($ *"$%:!$!$ $&D$A7

E*$ "*$!$')&')$(!:)&"'"<

n

e

$ *"$%;&$>A%:%;')*$)& : $!),!$"<>$'()*R

L

sar

=

n

e

v

!"#"

v

$%&!"#'('#)*'&+,#-."*, $&01

PRF

$%&!"% "")#")"&$&$,2+#"34"2 01'2(

T

sar

$% &!"567,8%"#.'&$,2&$-"9 :0 ,-8$2$2;<=9>?'2(<=9@?1&!"%02&!"&$ '2&"22'8"'- $(&!

+,**, %'%A

θ

sar

=

λ

2L

sar

[rad].

<=9BC?

D!"+' &,#,+=$2&!"("2,-$2'&,#$%$2&#,(4 "(&,' ,42&+,#&!"+' &&!'&&!"'2&"22'

8"'-$%+,#-"('+&"#&!" '."%!'."&#'."*"(&,&!"&'#;"&'2(8' E1FGC℄9

D!")!'%"#"*'&$,2%!$)8"& ""2&!"%4 "%%$."" !,"%1,# !"#$%&'& ()&"(%*+,1$%'+42 &$,2

,+&!"#'2;"&,&!"&'#;"&A

ϕ

Az

(t) =

4πR(t)

λ

[rad].

<=9BB?

D!"#'2;"&,&!"&'#;"&&!#,4;!,4&&!"567,8%"#.'&$,2&$-" '28" #$&&"2'%A

R(t) =

q

R

2

0

+ v

2

t

2

[m],

<=9B=?

$2 !$ !

R

0

$%&!"%!,#&"%&($%&'2 "&,&!"&'#;"&'2(

t

$%&$-"9 D!"&$-"

t

$%("I2"(,2&!" $2&"#.'*

[−

1

2

T

sar

,

1

2

T

sar

]

9 J%4'**01<=9B=?$%'))#,K$-'&"(80&!"I#%&&"#-%,+ $&%D'0*,# %"#$"%"K)'2%$,21F>= ℄A

R(t) ≈ R

0

+

v

2

t

2

2R

0

[m].

<=9BL?

6% '28"%""2+#,-<=9BL?1&!"#'2;"&,&!"&'#;"&$%2,& ,2%&'2&(4#$2;&!"567,8%"#.'&$,2

&$-"9D!"#"+,#"1&!"'M$-4&!)!'%"!$%&,#0$%2,& ,2%&'2&'2(&!"24-8"#,+" !,"%&!'& '2

8" ,!"#"2&*0$2&";#'&"($%*$-$&"(9

N2-* $()/ 0121&!"#"*'&$." )!'%"8"& ""2&!"%4 "%%$."" !,"%$% ,-)"2%'&"( $&!&!"

'$(,+&!"E2, 2)!'%"!$%&,#0<=9BB?9N2&!" '%",++, 4%"(5671&!"-'K$-4-24-8"#,+

" !,"%A

n

e,max

=

θ

Az

R

0

vPRI

[ ],

<=9BG?

'2&!"#"+,#" 8" ,!"#"2&*0 $2&";#'&"(9 D!"-'K$-4- 24-8"# ,+ " !,"%&!'& '28" $2O

&";#'&"( (")"2(% ,2 &!" &$-" &!'& &!" &'#;"&$% $**4-$2'&"( '2( &!4% ,2 &!" #"'* '2&"22'

8"'- $(&!9

P!"2$2(""(&!"-'K$-4-24-8"#,+" !,"%$%$2&";#'&"(1&!"%02&!"&$ '2&"22'8"'- $(&!

+,**, %'%<804%$2;<=9@?1<=9BC?1'2(<=9BG??A

θ

sar

=

λ

2θ

Az

R

0

[rad].

<=9BQ?

62(I2'**01&!"567'M$-4&!#"%,*4&$,2 '28" #$&&"2'%A

δAz

sar

=

λ

2θ

Az

=

l

2

[m].

<=9BR?

R

0

!"#$%&'( *

θ

Az

−

1

2

L

sar

1

2

L

sar

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

v

d,max

= v sin

¡ θ

Az

2

¢ ≈

vθ

Az

2

[ms

−1

_],

D&'EFG .4/5:9#8!4"D&'HG5+-% ,$$%80,4/!4"*,001%$2$%=#%4 98-!2+2,11,B8.8)

f

d,max

≈

vθ

Az

λ

[Hz].

D&'EIG >-%8.301%$.+%!4 .J!3#+-/!$% +!,48-,#1/:%-!"-%4,#"-+,:%.:1%+,#4.3:!"#,#819 3%.8#$%+-%*,001%$2$%=#%4 98-!2+' K22% +!6%195+-%

PRF

$%0$%8%4+8+-%.J!3#+-8.301% $.+%'>-%

PRF

8-,#1/+-%$%2,$%:%.+1%.8+)

PRF ≥ 2f

d,max

≈

2vθ

Az

λ

[Hz].

D&'ELG !" #$%&'( *+ (,-./0+12'(*+./0 ?@A0$, %88!4"3.M%8#8%,2+-%M4,B4.J!3#+-0-.8%-!8+,$9D&'EEG'>-%0-.8%-!8+,$9!8 -,B%6%$/!8+,$+%/:9 !"#$$%%&%#5/%"$./!4"+-%?@A!3."%=#.1!+9'@4!4N/%0+-$%./!4",2 0-.8%%$$,$8B!11:%"!6%4!48% +!,4O'O'

!!"!#$%& ' ()$ #*'+ )"-.%(/#)*01 #2345℄7389℄: ;()$1## )1"(2)$ *<< !=1.1)#)" 01-- ! () =%## #"-*( ".< (#%) 0.")1"( !!"!#>1==' ! &1 > 0: ?$ 0 !1&%)1"(#"-)$ *<< !=1.1)#>1==' ! < %) 01(%<< (01@A: ?$ !"##7)!% B& =" 1)/ ".<"( ()1#01! ) 0 ("!.%=)" )$ %="(C7)!% B 01! )1"(1( )$ #=%()7!%(C <=%( :?$ %="(C7)!% B& =" 1)/1#0 D( 01()$ %="(C7)!% B01! )1"(: !"#$%&'( *+,!" -./0''"' ?$ %="(C7)!% B& =" 1)/"-)$ !%0%!<=%)-"!..%/' %##*. 0)"&%!/#=">=/ ".<%! 0)" )$ EAF"'# !&%)1"()1. : ?$ !!"!.%/)$ ! -"! ' "(#10 ! 0 "(#)%())$!"*C$"*))$ EAF"'# !&%)1"()1. :?$ !!"!#$"*=0' '"*(0 0'/G

dv

at

≤

v

λR

0

δAz

2

sar

[ms

−1

],

H9:9IJ 1("!0 !)"=1.1))$ K*%0!%)1 <$%# !!"!)"

π/4

2389 ℄:A="(C7) !.%="(C7)!% B& =" 1)/ !!"! %*# #%C ". )!1 # %=1(C !!"!: 1'"22%&'( *+,!" -./0''"' A !"##7)!% B& =" 1)/ ".<"( ().%/' %##*. 0)"' "-#$"!)) !.0*!%)1"(2#1( %="(C7

) !. ".<"( () %("(=/ @1#)1-)$ <=%)-"!.(%&1C%)1"(-%1=#: E* $%& =" 1)/ ".<"( ()

= %0#)"%(%L1.*)$01#<=% . (): ;("!0 !)"=1.1))$ 01#<=% . ())"= ##)$%(%(%L1.*)$ ! #"=*)1"( ==2)$ ".<"( ()#$"*=0' ! #)!1 ) 0)"2389 ℄G

v

ct

≤

v

R

0

δAz

sar

[ms

−1

].

H9:9MJ 1'"22%&'( * ,!,'(.-"#0''"' ?$ !"##7)!% B% = !%)1"(#$"*=0' '"*(0 0'/G

a

ct

≤

2v

2

λR

2

0

δAz

2

sar

[ms

−2

],

H9:99J 1("!0 !)"=1.1))$ K*%0!%)1 <$%# !!"!)"

π/4

2389℄: A #$"!)7) !.% = !%)1"(= %0#)" 0 -" *#1(C2>$ ! %#%="(C7) !.% = !%)1"(! #*=)#1(%L1.*)$# %=1(C !!"!#%(0D(%==/1( %'#"=*) <"#1)1"(1(C !!"!#: #$3!('4".-"#

E)!1 )=/#< %B1(C2 %))1)*0 &%!1%)1"(#"-)$ <=%)-"!.0"(")C1& !1# )"<$%# !!"!#: ?$1#

1#)!* >$ ()$ %() ((% <$%# () ! HANOJ1# =" %) 0%) )$ .")1"( () ! HPOJ "-)$

<=%)-"!.:Q"> & !20* )"%(C*=%!.")1"(2)$ %() ((%C%1(.%/&%!/0*!1(C)$ EAF"'# !7

&%)1"()1. :A(C*=%!.")1"(.%/)$ ! -"! 1()!"0* %.<=1)*0 &%!1%)1"(#:

;(<!% )1 2%= & !%!.1#*#*%==/<! # ()' )> ()$ ANO%(0)$ <=%)-"!.PO:;()$%) %# 2

%(C*=%!.")1"(>1==1()!"0* %001)1"(%=%="(C7)!% B%(0 !"##7)!% B& =" 1)/ ".<"( ()#:

5-#32"-6(!4".-"#0''"'2

R*!1(C)$ EAF"'# !&%)1"()1. 2)$ !%0%!<=%)-"!.1#=1B =/)"0 &1%) -!".)$ 10 %=)!% B:

?$ <$%# !!"!# %*# 0'/)$ 0 &1%)1"(#0 < (0"()$ %'#"=*) 01& !C ( -!".)$ 10 %=

!"#$ &'$()*(+,)-$./$! 0'1!/'(12&*3("1(!4

f

e

< 2/T

sar

56"#$3("1(!3&07$&88-(91, 3&"$2&'$1"#$-*1!$&-(-./&2-&"1 6:;<℄> )"#$3("1(!1'&''/3$2"(7$*1!$&-6& -('',"-& ?

@$*( 1"0 (38(!$!"1'8-$'$!"> A#$3&1!$))$ "1'&!&B13/"#21'8*& $3$!"&!2"#$

/88$-7(/!2"("#$ -('',"-& ?@$*( 1"01'&C&1!C1@$!704<><D56:EF ℄>

G#$!"#$'1!/'(12&*3("1(!1'6(!"#$("#$-#&!26&''/3$2"(7$./&2-&"1 6"#$@$*( 1"01!

"#$'*&!",-&!C$21-$ "1(!'#(/*27$*131"$2"(6:;<℄H

v

ct

≤

λ

4πf

e

T

sar

2

[ms

−1

_],

4<><I5 1!(-2$-"(-$'"-1 ""#$./&2-&"1 8#&'$$--(-"(

π/4

>

J1C#,)-$./$! 0'1!/'(12&*3("1(!4

f

e

> 2/T

sar

5C1@$'-1'$"('8/-1(/''12$*(7$'>K(-&8$&? '12$*(7$*$@$*"(8$&?3&1!*(7$*$@$*-&"1(()

p

6"#$@$*( 1"01!"#$'*&!",-&!C$21-$ "1(!'#(/*2 7$7(/!2$2706:EF℄H

v

ct

≤ λf

e

√

p

[ms

−1

].

4<><L5

%2 (5+*6,(*+./7 !"#$%& "()$*&+,%-".$*"/*+*!"01234-$/$-$,/5678-&, &8."%9"-":&;",<=,

%" *&+,><?@*!"%""()$*&+,%9&..#")%"/*+/"*"-A&,"*!"/"A+,%*-$*+-%B%*"A8$-$A"*"-%<1+-"+;"-@

*!"A$C+-%B%*"A &A8"-D" *&+,%+D01234 -$/$-%@ #"&,:*!"/&-" * +)8.&,:$,/D-"()", B%9""8

,+,.&,"$-&*&"%@9"-"-";&"9"/< !""DD" *+D%9""8,+,.&,"$-&*&"%9&..#"&,;"%*&:$*"/&,A+-"/"*$&.&,

%" *&+,E<?< !"A$&,8-$ *& $./&DF ).*B&,567%B%*"A%$-"*!"A+*&+,"--+-%< !")88"-.&A&*%*+*!"

/&DD"-",* $*":+-&"%+DA+*&+,"--+-%9"-":&;",< !"%")88"-.&A&*%9&..#")*&.&G"/&,%" *&+,><E*+

()#*+,% -%,#./,% .0 "/ 123 4 -"5"& !"#!$"%& !"#$% #'(")*+"#)*)%(,!%),-'!./012*'3'*%4%")5",'%$!67)(,$!""'*6)"8$779) 3)*$:)3+%"'*"$!68$"#"#)$3)'7 '%); <=9%)>=)!"74+%):)*'7%4%")53$%",*"$,!%8$779)$!"*,3= )3'!3 "#)$*)--) "8$779)$!:)%"$6'")3; .$!'774+"#)"#),*)"$ '7?!3$!6%8$779)):'7='")38$"#"#)'$3,-' ,5(=")*%$5=7'"$,!; !" #$%&'(&)%

!"#"$%&'$"(&) %&*'(()#+"(,*--."/"#*0"/.1)$$23*'+(!)((!"45678 #)/)#$1$("3

*$*/")-9 8!"'$),(&&(!:#";2"' 13&/2-)(*&'*$)%%-*"/=(!"(#)'$3*(("/$*+')- )'."">6 %#"$$"/)$?#":"#(&4*+9@9A?)BBC

s

t

(t) = V

t

cos¡2πf

c

t +

π∆f

PRI

t

2

+ ϕ

0

¢,

?D9AB *',!* !

V

t

*$(!"(#)'$3*(("/$*+')-E$)3%-*(2/"=

f

c

*$(!" )##*"#:#";2"' 1=)'/

ϕ

0

*$(!" *'*(*)-%!)$"94&#(!"$)F"&: -)#*(1=(!"*'*(*)-%!)$"*$)$$23"/(&."G"#&9

!"#"$%&'$",*--."/"#*0"/:&#)$*'+-"$,""%9 !"(*3"

t

*$(!"#":&#"/"H'"/&'(!"

*'("#0)-[−

1

2

PRI,

1

2

PRI]

942#(!"#3&#"=(!"'&'-*'")#"::" ($)#&2'/(!"$,""%(#)'$*(*&'$=/*$ 2$$"/ *'$" (*&'@9@=)#"*+'&#"/9

!"" !&$*+')-:#&3)$()(*&')#1%&*'(()#+"( )'.",#*(("')$)(*3"6/"-)1"/)'/)(("'2)("/

0"#$*&'&:(!"(#)'$3*(("/$*+')-C

s

r

(t) = V

r

cos¡2πf

c

(t − ∆t) +

π∆f

PRI

(t − ∆t)

2

¢,

?D9@B ,!"#"

V

r

*$(!")3%-*(2/"&:(!"" !&$*+')-9

I'(!"#" "*0"#(!"" !&$*+')-*$/"3&/2-)("/.13*>*'+*(,*(!(!"JK $*+')-=-")/*'+(&

(!".")( $*+')-9 I' 45678#)/)#$= (!"JK $*+')-*$ 2$2)--1) '&'/"-)1"/#"%-* )&: (!" (#)'$3*(("/$*+')-9L:("#/"3&/2-)(*&'=(!".")($*+')-:&--&,$)$C

s

b

(t) = s

r

(t) · s

t

(t) =

V

r

V

LO

2

¡cos(ϕ

LO

− ϕ

r

) + cos(ϕ

LO

+ ϕ

r

)¢,

?D9DB ,!"#"

V

LO

*$(!")3%-*(2/"&:(!"JK$*+')-9 !"0)#*).-"$

ϕ

LO

)'/

ϕ

r

#"%#"$"'((!"%!)$" &:(!"JK$*+')-)'/(!"" !&$*+')-#"$%" (*0"-19M&("(!)(

ϕ

LO

)'/

ϕ

r

)#"(*3"/"%"'/"'(9

!"#"$%&'()$* ,-./'&"&$0,1)2 ,)3"/&',) ,-.,)")%$%#$&"#$)0$)0$)4.2 ,)3"/&',)

,-.,)")%$/,4)0

2f

c

5 6)./$ %' "7%!"4.2 ,)3"/&',) ,-.,)")%'&,4%&'0"%!"/" "'3"/8& #$)01'0%!$)0'%'&4&4$**9:*%"/"0,4%1'%!$*,12.$&&:*%"/5 6)%!$% $&"7%!"#"$%&'()$*

/"04 "&%,;

s

b

(t) = V

b

cos¡2πf

c

∆t +

π∆f

PRI

(2∆t · t − ∆t

2

)¢,

<=5>? ')1!' !

V

b

=

1

2

V

r

V

LO

!"#$%&"%'()*+(,%#%-( $./'-).$ 1'2%3(%4(1 (,%53%&"%' * 416-.'#*-77)*.'/-81"3.%3 (3-'$5136(19: ;<=

S

b

(f

R

) =

γ

Z

−γ

s

b

(t) exp[−j2πf

R

t]dt,

9: >< ?,%3%

f

R

4%'1(%$3-'/%@53%&"%' *+?,. , -'#% 1'2%3(%4(13-'/%?.(,(,%-.4159A B<-'4 9A A<+-'4=

γ =

PRI

2

.

9: C< 8.'-))*+(,%%2-)"-(.1'159: ><3%$")($.'(,%3%$71'$%(1-$.'/)%71.'((-3/%(=

S

b

(f

R

) = γV

b

exp[ j(ϕ

1

+ ϕ

2

)]sinc¡2πγ(f

b

− f

R

)

¢

+ γV

b

exp[−j(ϕ

1

+ ϕ

2

)]sinc¡2πγ(f

b

+ f

R

)¢,

9: D< .'?,. ,=

ϕ

1

= 2πf

c

∆t,

9: E< -'4=

ϕ

2

= −

π∆f

PRI

∆t

2

.

9: F< G,%3-'/%(1(,%(-3/%( -''1?#%51"'4#*4%(%36.'.'/(,%6-H.6"615(,%3%$71'$% G,% 6-H.6"6159: D<1'(,%.'(%32-)

[0,

1

2

f

s

]

.$)1 -(%4-(=

f

R

= f

b

,

9: BI< ?,. ,.$ 1'$.$(%'(?.(,9A A< !" #$%&'%( *+,%%-./(01(%2$13* G,%3%$71'$%.' (,%73%$%' %15- $?%%7 '1').'%-3.(*?.))#%4%2%)17%4 8.3$(#*-$$"6@ .'/(,-((,%'1').'%-3.(*.$$.'"$1.4-)-'4 1'$%&"%'()*#*-$$"6.'/(,-((,%'1').'%-3.(*.$

!"#$%!&'( )**+,%"(!"*'-!./

!"#$!"%&"'("# *+,""-#.#/0#"1&0$*0+1++(2"3$.4"+0#(+.031/5$!"0#+$1#$1#".(+%&"6

'("# *.%$!"$&1#+20$$"3+07#1/ 1#4",&0$$"#1+8

f

t,i

(t) = f

c

+

∆f

PRI

t + ∆f

e

cos¡2πf

m

t + ϕ

e

¢,

9:;<<= ,!"&"

∆f

e

0+$!"21>02(214+./($" 3"?01$0.#%&.2 $!"/0#"1&+,""-5

f

m

0+$!"%&"'("# * .%$!"#.#/0#"1&0$*51#3

ϕ

e

0+$!"0#0$01/-!1+".%$!"#.#/0#"1&0$*; @!"#.#/0#"1&0$*A+0#0$01/ -!1+"0+1++(2"3$.4"B"&.;C#$!0+ 1+"5$!"$&1#+20$$"3+07#1/%.//.,+1+8

s

t

(t) = V

t

cos¡2πf

c

t +

π∆f

PRI

t

2

+ D

m

sin(2πf

m

t)¢,

9:;<D= 0#,!0 !8

D

m

=

∆f

e

f

m

,

9:;<:=

0+$!"-"1E1#7(/1&3"?01$0.#;@!"" !.+07#1/ 1#1710#4"">-&"++"31+1$02"63"/1*"31#3

1$$"#(1$"3?"&+0.#.%$!"$&1#+20$$"3+07#1/8

s

r

(t) = V

r

cos¡2πf

c

(t − ∆t) +

π∆f

PRI

(t − ∆t)

2

+ D

m

sin(2πf

m

(t − ∆t))

¢.

9:;<F=

C#$!"&" "0?"&$!"" !.+07#1/0+3"2.3(/1$"3,0$!1#.#3"/1*"3%&1 $0.#.%$!"$&1#+20$$"3

+07#1/9$!(+$!"GH +07#1/">!040$+$!"+12"+,""- #.#/0#"1&0$*1+ $!"" !. +07#1/+=; I* 30+ 1&30#7$!"(-6 .#?"&+0.# .2-.#"#$5$!"4"1$+07#1/%.//.,+1+8

s

b

(t) = V

b

cos¡2πf

c

∆t +

π∆f

PRI

(2∆t · t − ∆t

2

)

+D

m

sin(2πf

m

t) − D

m

sin(2πf

m

(t − ∆t))

¢,

9:;<J= ,!0 ! 1#4"&",&0$$"#1+8

s

b

(t) = V

b

cos¡2πf

c

∆t +

π∆f

PRI

(2∆t · t − ∆t

2

) + D

′

m

cos(2πf

m

(t −

∆t

2

))¢,

9:;<K= ,!"&"8

D

′

m

= 2D

m

sin(πf

m

∆t).

9:;<L=

I*1++(20#7 !""#$%! &! '()*#&+(!,-# 5$!"4"1$+07#1/ 1#4"1--&.>021$"34*5MN: ℄8

s

b

(t) ≈ V

b

cos¡2πf

c

∆t +

π∆f

PRI

(2∆t · t − ∆t

2

)¢ − V

b

D

m

′

cos¡2πf

m

(t −

∆t

2

)

¢

sin¡2πf

c

∆t +

π∆f

PRI

(2∆t · t − ∆t

2

)¢.

9:;<P=

@!0+1--&.>021$0.#0+?1/03%.&+21// ?1/("+.%

D

m

; Q0#1//*5 $!"1--/0 1$0.#.% 1Q.(&0"& $&1#+%.&2&"+(/$+0#$!"&"+-.#+"8

S

b

(f

R

) = γV

b

exp[ j(ϕ

1

+ ϕ

2

)]sinc¡2πγ(f

b

− f

R

)

¢

+ γV

b

exp[−j(ϕ

1

+ ϕ

2

)]sinc¡2πγ(f

b

+ f

R

)

−

γV

b

D

′

m

2j

exp[−jϕ

3

]sinc¡2πγ(f

m

−

b

− f

R

)

¢

+

γV

b

D

′

m

2j

exp[ jϕ

3

]sinc¡2πγ(f

m

−

b

+ f

R

)

¢

−

γV

b

D

′

m

2j

exp[ jϕ

4

]sinc¡2πγ(f

m

+

b

− f

R

)

¢

+

γV

b

D

′

m

2j

exp[−jϕ

4

]sinc¡2πγ(f

m

+

b

+ f

R

)¢,

!"#$% &'()& )+

f

m

−

b

= f

b

− f

m

,

!",-%

f

m

+

b

= f

b

+ f

m

,

!",#%

ϕ

3

= −ϕ

1

− ϕ

2

− πf

m

∆t,

!",,% .'/+

ϕ

4

= ϕ

1

+ ϕ

2

− πf

m

∆t.

!",!%

0123 !"#$%&4 .'56 2' 78/6/4).4.9&'892&/.79(66:'2'7&'6.1&4;:12/8 699:81&2899&/6<

7256921 !"#$%$ '($).128'/4)621&=&'.7169:2'96" >2(6?61@2'69)287/56.1&'3&'/4).4

&'16/8 &'= !"#A%42 !"#B%@'.112(5.'/.'=7632/87.4&2'(.9.99836/"C':1. 4& 6@.9&'8<

92&/.79(66:'2'7&'6.1&4;(&77:12/8 6.'&'D'&46'835612E).132'& 9"

F2162?61@4)6.3:7&48/62E4)6:.&16/6 )269/6:6'/98:2'4)64&36/67.;" G)616E216@E21

9)214/67.; 4&369@4)6.3:7&48/6&916/8 6/9&='&D .'47;" G)&96EE6 4&9/86424)6E. 44).4

.:214&2'2E4)641.'93&446/9&='.7).9566'896/.9HI9&='.7@.9(.9.716./;/&9 8996/&'

96 4&2',","

C':1. 4& 6@4)632/87.4&'=E16J86' ;

f

m

(&7756?61;72( 23:.16/424)6

PRF

"G)69(66: '2'7&'6.1&4;(&774)616E216512./6'4)6169:2'961.4)614).':12/8 6/&94&' 4:.&16/6 )269"

!"#$"%& ()**+,-./&.*"$&%0

C'4)6 .962E.J8./1.4& 9(66:'2'7&'6.1&4;@4)6&'94.'4.'6289E16J86' ;2E4)641.'93&446/

9&='.7 .'566K:16996/.9+

f

t,i

(t) = f

c

− ∆f

e

+

∆f

PRI

t +

4∆f

e

PRI

2

t

2

.

!",L%

G)6'2'7&'6.1&4;).9566'/6D'6/&'98 ).(.;4).44)63.K&383/6?&.4&2'E1234)67&'6.1

9(66:2 819&'4)63&//762E4)69(66:"

G)6:).962E4)641.'93&446/9&='.7E2772(9.94)6:1&3&4&?6E8' 4&2'2E !",L%3874&:7&6/5;

2π

+

ϕ

t

(t) = 2π(f

c

− ∆f

e

)t +

π∆f

PRI

t

2

+

8π∆f

e

3PRI

2

t

3

.

!",M%

G)6:).962E4)66 )29&='.7 .'56(1&446'.9.4&36</67.;6/?619&2'2E !",M%+

ϕ

r

(t) = 2π(f

c

− ∆f

e

)(t − ∆t) +

π∆f

PRI

(t − ∆t)

2

+

8π∆f

e

3PRI

2

(t − ∆t)

3

.

!",A%

!"" !$%&'()*%)+")')&(,"-$,.*)/",0&/!)($(,"*)1",2+) /&$($2/!"/+)(%-&//",%&'()*3

!"(/!"4!)%"$2/!",$0(5 $(6"+%&$( $-4$("(/&%'&6"()%7

ϕ

b

(t) = 2πf

c

∆t −

π∆f

PRI

∆t

2

+

2π∆f

PRI

∆t · t

− 2π∆f

e

∆t −

8π∆f

e

3PRI

2

¡−3∆t · t

2

+ 3∆t

2

· t − ∆t

3

¢.

893:;<

=$(%">."(/*1?/!"&(%/)(/)("$.%@")/2+">."( 12$**$0%)%/!","+&6)/&6"$2893:;<,&6&,",@1

2π

7

f

b,i

(t) = f

b

−

4∆f

e

∆t

2

PRI

2

+

8∆f

e

∆t

PRI

2

t.

893:A<

B&/!/!")&,$2893:A<?/!"6)+&)/&$($2/!"@")/2+">."( 1/!+$.'!$./)%&('*"%0""4 )(@"

)* .*)/",3C(/!"&(/"+6)*

[−

1

2

PRI,

1

2

PRI]

?/!"2.**@")/2+">."( 16)+&)/&$(&%7

∆f

b

= f

b,i

(t = PRI/2) − f

b,i

(t = −PRI/2) =

8∆f

e

PRI

∆t.

893:D<

!"%4" /+)*0&,/!$2/!"E()*+"%4$(%" )(@""%/&-)/",@1/!"%>.)+"+$$/$2/!"%.-$2/!"

%>.)+"%$2/!"%4" /+)*0&,/!$2/!"&,")*+"%4$(%"8/!)/&%

1/PRI

<)(,/!"@")/2+">."( 1F% %4" /+)*0&,/!

∆f

b

?G;9℄?GDI ℄7

r

¡

1

PRI

¢

2

+ ∆f

2

b

.

8939J<

K.@%">."(/*1?)*&-&//$/!"-)L&-.-)@%$*./","6&)/&$(2+$-/!"*&(")+%0""4 )(@"%4" &5

E",@1-)M&('.%"$28939J<3N"/F%)%%.-"/!)/)-)L&-.-+"%$*./&$(*$%%$2OJP&%)**$0",?

/!"(7

q

¡

1

PRI

¢

2

+ ∆f

2

b

q

¡

1

PRI

¢

2

≤ 1.1.

8939O<

Q&()**1?@1.%&('893:D<?8939O< )(@"+"0+&//"()%7

∆f

e

≤

√

0.21c

16R

max

,

8939:<

4+$6&,&(')( .44"+ *&-&/ /$ /!"($(*&(")+&/1 )%) 2.( /&$( $2+)('"3 R% )( @" %""(? /!"

%4" &E )/&$(2$+/!"($(*&(")+&/1&%*"%%%/+&('"(/2$+%!$+/+)('"%3 S*")%"($/"/!)/8939:<

4+$6&,"%$(*1 ) +$.'! .44"+ *&-&/? %&( " 8939J< &%T.%/ )( "%/&-)/" $2 /!"%4" /+)* 0&,/!3

Q.+/!"+-$+"?4+) /& )*($(*&(")+&/&"%)+"($/*&M"*1/$@"84"+2" /*1<>.),+)/& 3

U1 $-4)+&(' 893OJ<)(, 893:A< &/ )( @"%""( /!)//!" @")/2+">."( 1 &%)22" /", @1/!"

%0""4($(*&(")+&/13 !.%?)4)+/2+$-)*$%%$2+"%$*./&$(?/!"4+"%"( "$22+">."( 1%0""4

($(*&(")+&/&"%)*%$+"%.*/%&()(&(6)*&,+)('"-")%.+"-"(/3

! "#$%&'()*+,-&,'&./0

V(/!"4+"6&$.% %" /&$(%&/0)%)%%.-",/!)//!")-4*&/.," $2/!"" !$ %&'()*&% $(%/)(/3