1 NORTHEASTERN UNIVERSITY Graduate School of Engineering ...

!#"$&%')(+*,#-.-0/1-325476$809:6$'&';9:6$8 ?9:>@ k Id

;::

))

! (

+CW

'B3W

'B(" % %

+>$%E$#'.B %

'B(" &'()' .Q # '5

'B3W

'?(+''.'B'*'.>

'5 W'. (4^5

!'. 385

'B(" # () $%G Q#,(5(S

Q#'$%I5 "

#( ".-

A 6

0/21

"

1

/87 " +

+'?(3>;X3?38,?G(;:.:

1 "

&*I#(

5-5-D5 ' P['B(+Q#'$%

(

-

J "

+

3546/ -

6 + -

6*

".-

0/=1

-

3546/

6*

3546/

,()'QY

# -

0/

354

-

@/ 1

J

#

3A4

L

* - 3A4)/

+

,+ :(7,()

,0

!'.*'5' Y() : A,(7"5Y(7'.* .

K

+ 412 "

5C(7, *Y6, ]:

812 # ",?I #, D 0'Y'' #

K

'. #

.*H!U(N 1

F)34+I38 $# '?34@'0 X"(7' Q

=

: J

Q, *0: ['.(75*V5

+

)+ Y() ( $%

3I

,P(

5

1@D 0'Y''.QI#38 Z((Y

%()''.$%@ % #@ 1N" ; #0 Y'B:

,

U/0'QY

'/%H' % 0S(75'D5'

: M :+ 412

- 5 038!, 512 5 \(734' #

(

"!2$#%&

712 # D38!'.",

#F)38]5

,'

)12 Y'5 W'.$%

;

L

"36 T 5'

:.:

(75'D9 1

15 UY U( ,P(7' Q

38 #* 5-Q# '.

,' #(('

'I5@12 . 'Q"

)+*(,-/.1032

3 -$ / 1

354

J547698

1 4

3 - $ / 476:8

$

1 " - /

< =- $ /

= $ ? 143 = - $ + = /

/ J " - K 1

>?*(,-/.@02

*

J M !K 1=B

A

+ -

$/ 1

$

* - / 1

'Q#,

:M

()

(

(75 ( DC#338, U

12

1N

,

+6 1

F)38

L

:

M

=

KJ

$

J + - 3A4)/ K 354 K 354

/

A

: +

1

L

:@( 3D;

()'. $,

1 5

1

12 # =
K

R

#+ @Q # '.38 0$% 5Q( '.

UYH W(8:OS 9

5 G(70W' #I 1

:

L

J M !K 1

1 *Y38 #!$% 5Q-5

,()'QYG(7- P W*H U(

J

354(;

*/CED < = - $ / JGF = ,

5Q J L

/

5@ )12 DP38@ 1 -Q# '.

P # W '.N M

$

L

* - 3546/

5,

: !:

(75'D *X 1

L

12 +

: +

'?( L

:# M

(75'D

03'.

R

? Q#

38(5(

5 C38 0V

712 # D(S$% [& $% (7'.Q' V 3!5Y,!5' 1

B

Y'Q#

:

5

3()%:

D; #,(4:

+" $ '?38

1 ?(

! %(

J () .'B;KU:

; #,6 #6

@(

(7'", B5' #(* 1

;>()

'.

5

Q#'$%E

6 #!5 . ()'",?5' 'I "38'.

:'/%'?(7X!,Y 5*? 5Q" 5

3

!

Q# '.

3W'H$%- "$ '?38G(

' # W!'.5I!," " 1

*'?!" WQY 1 R

, QZY

: Q 9(7'.",B' #>(7 #,BI (),

$%"Y , (8:

5I$# '?34[G(7'.I 1;*

- .

* 0!H WY5 W(4: + #,Q

,(7'.Q65

5*G(7'.Y 1+

*()'.

,

/% 5] 1N

G(7'.

+C38'. W38.(" 5(7H! 6 0

>B#(7>(734' #]:

$# 5'BP38"'C U! @5 634 !V 5 J

'.

J ! 5K+'?(1 ' 5Q# % 06 ()!U5' I 1 5

G(7'.

, (

()'",?5' P(-+ , B

PG$%

D # 5I(75'D5'

R '.E )12 DP38" 9 /!'.Q>!

L@: + 'B( M

(+Q# UG

'.I- , 5 ' Q

G38S 13WQ#'QD"., 5'QY/% 5&36Y(7HE(9(7' 12' Q #(

N

'P38 #(7(4:

+ - 5/ ! E'I()'D5' #6$# 5'BP38

(

3

2

Amplitude

1

0

−1

−2

−3 0

20

40

60

80

100

120

140

index

: ' +"G(7'." 1

'.Q, 5

034(('5

R

1

5 0!,38E'5E"G(7'.I* 00 WY5 W( "

B

;G38 Y(+ U(7X! %( @5 W(7?

'. C 1

#( "

3CI(7H612

5Y (),U(

(7H(7'.'$0' 5 Y 0!&*'?(7DW3WE038 G(7G(8: '.Q

T3#(7(4 R

'Q#,

:>

()

'.Q, 5

H$%B(- P

1

5

:

R

5

1

:

WY5 :+()+$# 5'B38( QH W@12 & 12

12 #

:

-

N

!' : %: - 5

H386) 'B(

G(7'.'.

(7'.Q' V 30"()'34*'.-. 0,(* E F)38D'

15* , 5 ' Q

'.*'.B &38, $%G(!$%H

$# '?34(S#(

(

(7H['.

, 5 ' Q-/% 5%5@$# 5'BP38 '5

/% H 1

N

1

B

(@1 '. C#338, U5(75'D5'

6 WQC 1X

, '.Q-/%H 38 Y(+'?! +5

5 '$0'BS , 5 ' Q

712 # D38

!HQ W#!(4:

Standard deviation of alpha with respect to SNR 0.6

0.5

Std. Dev.

0.4

0.3 sigma=1.5 0.2

sigma=0.5 0.1

0 0

'.Q, 5

5

10

15

: ' +Y$# 5'BP38" 1

$# 'B38@12 # L

()'." 1

5'Y("[ 1"5

$% U(7,( +

35

R

40

: + C38'. W38.( 5(7H!

(75'D'. ]:

, !., 5

'.!Y 5

OS +$%H C0Q U' #

3H(7Z:

#((7$% 5%: + @ (),U( 1 3W

"(7 +G*

'.

(+5

38 #*G(S'B!H 5" 34 () ,P38'. 634 Y(S",3W6.((@()()''.$%-5

Y 0!&*'?(7DW3W]: + 'B(Y(P

'65

3()- 1"'B0 # W

Y 0 (+!Y P(7 U5*'.(75'.; )12 5O+.(7'.38 .Q # '5

30

M 56 )12 DP386#(!Q# W#!

()'D5' # 1 9 F)38'B( ., 5'Q # W

25

A 6 0 . ()'",?5' P(+ 1

Y, '.QC W # W( 1 N E$ '?38C'B(

20 SNR

'. $%"'.5"

389

5

38 #(75 ,34' #

@Y 0!Y'B()W3W-12

5* 538 #(75 ,385' #]:

0$% W()% 'CD3()*

" 38 #(75 ,34' #E'B(@()()''.$%-5 * 00 Y'B(7DU3 @ 1

*

/% H

()'D5' #[ )12 5(+$% * :

'Q#,

: D(7

(- *

34@ 1

5*0," @ 19(* .(@,

WY5 W(4:@( 0 385!5@$# 5'B38 12

1 ()

:+!,(Y X(* .('

L

"38 #(7U0

R

A

+'?(+ #+'B(

1 M

5Y(75'DG(

15

!G38 #(7((9!," 1N(* .( '.38 5()(8: ML

I

N

1

, 'B3W/!#3 '.$%

B

: +

() 1&5

"'Q# 9!Q#

!34 #(7@'?(

1#338, U3 '.

(>

Standard deviations in estimation of alpha

Std. Dev.

0.3 0.25 0.2 0.15 0.1 0.05 0 0

0.2

0.4

0.6

0.8

1 sigma

1.2

1.4

1.6

1.8

2

1.6

1.8

2

Standard deviations in estimation of kappa

Std. Dev.

4.5

4

3.5

3 0

'.Q, 5

N :

:>

'

0.2

0.4

0.6

+ +$# 5'BP38

15

0.8

(

D

()'D5" 1 #Q'?3&

38 'B( +

1

0," @ 1

+"

(3HG( 'P38 #(7( 12 5 '5

5Y,(7Y 1

Y 5*

$%(7

*G(7'.I'5

R

*@$%H W(7,P( 5

(7

> :

$%.@H$%B(,

*$# 5'B38 1

15 W>

1

L

M

;Y 55 >

'B(

'.38"5

(@ "!," 9 1 3W'.$%

S, *5 6 *.Q5

15

(3(+ #,B #- U385'B3:

Q# 5' 6* 00! P W*H U( 3#(7(4:

*? 5Q"., 5'Q # W

#338, U3 C 'CD* 0!H+ WY5 W(

:

#3 C(53.%]'@'?(

#338 U."#338, U3 > 'C* Z(7 5 ,Q#

:

'P38 #(7( ()'.' #I3H38, W#3 Y 3I?(7 "

G$%H9(3(4 ' 1 'B(@'B(@ G(7 # %:

+

38 Y 5'B() E'P38 #(7(4 -$# 5'BP38

"$# 5'B38Y!34 #(7(@() 5

(@

+!,P(

, 5 '.Q UYH

-, '.Q+12,34' #]::]#(75% 'Q#,

, Q" ,P(7 1P

D /E! ] '5 '.Q

(3HG(S$#'.B 12 #

F)G38$%385 +'.I'?(+ #>

1.4

C(75'D5" 15D(Y ."$ '?38G(

(S5"!, ";H S 1

'. 038 G(7Z:

1.2

(75'DG( 1=+IP

+ WY5 ](75'D5' @12 # S34 ()W0 (7

1 sigma

3

5"Y()'D5' #E;HQ'P(

#

*

R

[12 #

.$0'BEE5 5B'$%"'.(7H(7'.'$0' > 1

@ F)34 G(7'.'. 5 - @*'?(7DU3 Y'5

0:+

* 0!HB(+#(+#((7 '.I3 P 5

Standard deviations in estimation of alpha 0.5

Std. Dev.

0.4 0.3 0.2 0.1 0 0

50

100

150

200

250 N

300

350

400

450

500

400

450

500

Standard deviations in estimation of kappa 8

Std. Dev.

6 4 2 0 0

'.Q, 5

50

100

'+$ '?38 1 :

150

200

250 N

300

()'D5( 1 +IP

350

*-$% U(7,(5+0," & 1 (5Y G(

:

5

Q # '.\Q'$%G(

,(

E(75'D # @'?3 E )12 D(S& $% S5Y38?((

'.Q )12 538

'B(+H!Y Z:

1

3H(7G(

Standard deviations in estimation of alpha 0.5

Std. Dev.

0.4 0.3 0.2 0.1 0 2

2.5

3

3.5

4 4.5 Wavelet Levels

5

5.5

6

5.5

6

Standard deviations in estimation of kappa 8

Std. Dev.

6 4 2 0 2

'.Q, 5

H$%B("H

:

'

2.5

+$# '?34+ 1

3

5

3.5

4 4.5 Wavelet Levels

G(7'.(] 1 +>

12 # @-V 0 !, ";H + 1 (Y .(8:

*

5

$% W(),(]0," & 1 $%.

+'?(

5()'B(S Y' 6",P(7Y 1

() 03W()'B3- #F)38 #( (7 Y

+'?(

'

6:

'()(7'.'.$%+

R

! "12 W#38W '.

Y 0!B(12

Y 0!Y'B()W3W-,P! @ WQ

(7'.38"*'?(7C 6,P(7YY* 00B(@'

5'B38,? >38 #!'5' #(+ 5E'B!0' V

@K] 5@(5Y@34 !'.'. (

'B(Y* Z(7>334, W%:

E 0'Y'G'.

CB()

Y()'D5' #E 1

+(7

5'

*'.

J 5

((7 Y 5

R

(8:

'.&'()#6(75'D

H CC* 00

38 0''. (

Y 0!?(

(7'.,'. (@ 5

! %(I$%

'.QH

., 5'Q>/% H+

'Q#

(75'D'. " 1] SY 0!?(

C 5'B34,B *12 5",B' #

0 ;G38W' #

1X

0 . '5'Q Y 0!# UY U( .

Q# '.

L

1 U # W(

/0 A"5 ,X(7W'?(7'?3(S 1 -,/0 C F)389P

(7H(7'.'$0' > EY 0!+Y'B()W3W]:

'0$% W()@ #H6:+" 712 # D38" 1

.'G

'.(7H(7'.'$0' I 'B(@'.* 5W!

+Y0

L

(]+Y 5 I34'0

'Y .*H!U'. ]:

M

'0 5 0!,385

0," 1 '?(738 # ,

5

(7 #,5' E 5

,' 5(

(5Y (4:

(S0'

"'Y'5

#H( 15'B( 0 ; 125-'. 38 #!'5' #

5"'0 5 0!,385' #E 1

#(SE() E )12 5

15-Y 0! .

# 1 38 $% 5'QX"!Q# W06()'QP12 #

() Y" '.

34 () W'0W(4:

"!

+

]'.65'B( #"#(@" Q#,B 'G'. > 56:+

'.Q.$%B( 1

(7'.* 'B34' 1 #) " UY U(8:

(7Y % 5(5(@ -'.* Z(76'. 12,

(7'.* .' V 3H'. D3I

L

* 0!H

0''.'

HW'.' Q*5

'Y %(7G

, ; #65

A

>

Y 0!0@H'Y'P'.Q + WY5 * : +'?( 'B(D! %(()'.9(75'D'.Q 'C * 5 038(5( G!,38(+5 : '.*'.5("D 0'Y''. E()

1

* #0 Y'B:

I0 . '5'QY -Y 0!

#'B(7Z 5D(Y"D 0'Y'' #C(75

5

E 0'Y'' #"Q # '.

$% #'B(()/0'QD*34 %()*12 5

'/%H' % 0X12,P38'. Y'H W5'$%

$#()Y'P38 #(7( 5

338, W5Z:

Y 5

., 5'QI6 'B()%]*Y 5"

L

R

H( 1&Y 0!Y'B(7DU3 "'.*Y'P

() $%G

5- #- ! '?(7W(4:

UQ#E 1

DU3 E5" 5,Y38

+ E(7H(7'.'$0' E'.38 G(7G("(

*'?(7DU3 ]:

D'. " 1] +Y 0! W*5 W(4:+ ! 34W5' #

+ \Q# 5'

* 00 3

5 E #,(7H:938 Z((-6 UQ# 1

' E '.38 G(7G(-(-5/% 5 34 Y( 5 : ()'D5' #[",P(7 712 #

L

P

5 B#38(S'.S'.

'.6 "* # "34 Y

(7 #$0'Q*12 #

" 5 %

3()" 1, '.QD

12 5 \D(7'.* .Y3()3HC;Y'Y .*H!5:+'?(

(7 G* 1&'.* .Y!U5' #!' Q-

'5I",3 DB 5Q $%G38 # W(+'I.((+5'Y%:

9 ''. " "() .$%S 5 .D(

A

>

$% W '?(-()'B(-#(*()

5Y

* 0!HB(Y >E,(7412, % #

L

+

(7 34' V 334B(5(- 19'0$% W()* D(8:

I(75'D5 1 5

12 # Y(7 .$!'.Q

I 5 ,()" EY 0!Y'B()W3W] )12

(7'.*'.B S12,385' #E >38B#(()'B3 Q#,B ' W(4]P 5 W(4:

L

, !' Q

'.

(75'D5' I 1 5

" )12 YE#338, UH

(75' +$%H D I #(7 38U(

5

0 # %:

L

:+ '.

Y'B()W3W

,P! -5I38 #!'.' #( 1

UQ#- 1N'B!5( U

( #@>38 Y .34 $%H : + '?(++ 5/I

* 00]*'?(7DU3 I'B(5(7,

R

'. U # W(

9,(5(7'B

., 5'QI12,385' #

12, 5 + ! . U'. I34 ,?

D Y 38 YY # ;H W5 U(S()Y'I()'QP]'DQ#@ 034(()'Q : 6 5'B(- /

!'?

5 ' ,'. C(

Y0 # 5I ;H 712 538

5

5 6Y DQH W () ,?[

9,(5(7'?]:

!Q U'. 5

1 3 P 5

12 @5(7" D(

.

@Y

(7'Q#' V;30

5I F)38Y0'B(

() 5'B385' C'B(@ 5B!

D5 '

,(7'.QS5'B(] 9(7 #$% 12 &

M(> $ '?3 ". (N5 '.6 -$%.

:.:

0,38'. C'

1 5

,'. ( (7 .$!'.Q@12 S'.!12 5' #

1 #F)38:

# /@P(

1 () 5 !'.' #* 1&'.!12 5'. Y '"

! #']:9() ] Y() ;H

'38 5(): + S ! 38U5' Y() Y

12, 5

@,(()'B

38 Y ,U5'

! #+'.

U'.Q

'.6 "! 34W5' #E(75 6 ,?6#[5 .

12 #

B 5Q X(7'.QB(8:9!'5' #.

* 0!H]*'.Q0?(7 Y# Y !,P38'. 1 '?((75 ]:

'5

,!H W(75 % 0:

3()'.

0

!'B() 5',5' #(8& )12 538'. * Z(7X38 U'.C!G3C

M :+ #,QY + 5/ Q # '.

38 5 %(5("

(8: + -5 # 5'B3+ # /I'B(+Q# U] ,Q#6 Y'P38 5 ; 5 412

A

!:+'?(S (7'?( 0 . G[ ",(7

1 L

>M

Y 0!B(+12 9 Y!'.*H(7'. ()'QPB(4:

, U&0()' # 1 5'B(+'?(+)+ Y!'.*P(7' #]'.Q(4:

5$0' ,P(S 34 Y*P5' ](7'.38"DF)

38 () U'0

:

'DQG(

'?3

;

, C'?(S+ # /E'?(SY()'

Y' * G(7 # %:

* 0!H W*5 W(9

,(7G6Q #.>34 %(5(S - #"()'Q# : 'DQ#(8]Y(7 P'?.> '.$%

'.* .Y!U5' "D*

, ' V5' Q"@Y 0! "5

5812 WZ: +'?(++ , B* 5

Z((7'." '. U5'Q12 #

(53.(8:+'?(++ #,BI# :

+ # /I(>! #

'.Q(4;() 38'BB Q

. 03()W'B()'?3(

Y

+ #,B34 U' - 8V 12 5 O5

#'?( 5 .>: , 5 + # /D38 P!,385

1 5

'..%'?(*+ # /

!'?

5 "",3W5 712 # D38

#6 # ()W' # 6'.Q(4:

I'Y .*H!"5(7EY 0!?(*'

#!$0' #,(@!5()' C >'?(@+ 5/E'B( 5] 5 .>:

Y 1 5$%.] 5 @5+VH

0'Q>Y G(7,.W(

S

#38,P@ 5 .D(8: CD.Q 5'5

./.!#"$%&('*)+,-(+,-.0/12435)6"$-2,.&(+'*).0378. 937(.:';/"3;) '*l/.:/1 @ a}| /(,"G k 'T)-. @ (?8. @ /1.& @ P-.:/~BIHKJ*JL+(M#NO%*PNQ, F*1RJS*!T%'!)(#F*&%'+LUV%8D 1+F*&(90RHW&%'+YX 8s :':'\ B

^] B"_)"G-2QB' G" -2Q"$ k QB B*n"$