Program List for Fourier Analysis [81, Chapter 2]

Program List for Fourier Analysis [81, Chapter 2]

2 APPENDIX Program List for Fourier Analysis [81, Chapter 2] This appendix contains the program list to compute the Fourier coefficient of a periodi...

257KB Sizes 0 Downloads 56 Views

2 APPENDIX

Program List for Fourier Analysis [81, Chapter 2]

This appendix contains the program list to compute the Fourier coefficient of a periodic nonsinusoidal function. An output example is given for a rectangular wave.

C

5

R E A D (3,132 ) (Y (J, I), I=l, NPTS+4)

132

F O R M A T (Eli. 4,2X, Eli. 4,2X, Eli. 4,2X, Eli. 4,2X, Eli. 4) Input Do

A2.1 FOURIER ANALYSIS PROGRAM LIST

Y(I,J)=I.0

1321

Y(I,J)=-I.0

test,

ECHO

ANAFOR

square

COMMON

i0

J=21,41

THE

i0

DATA

i000

FORMAT(//'

SCREEN.

SET

NO. ',I4, ' S C A L E

FACTOR : '

COMMON

*, F 1 6 . 1 0 /

NPTS, NPS, INT, INC, NH, GA,

BEFORE

PI, WW, OM, NC, RF, ER, EL

'Y - C O O R D I N A T E S S C A L I N G : ' (/5EII.4))

SUBTRACT

ERR, I T M A X

D.C.

MULTIPLY

Y(30,365),SCALE(30),

DO

Y M A X (30) ,X(365)

30

COMPONENT

THE

SCALE

AND

FACTORS

J=I,NSETS

Y M A X (J) :0.

DIMENSION

DC=0.0

C U R V T (100 ),

DO

C U R V C (10 0 ) ,CLTRVS (10 0 ) ,C U R V P (10 0 )

37

37

K=I,NPTS-I

D C = D C + Y (J, K)

DIMENSION AMP(30,100), A N G (30, i00)

WRITE(0,*)

READ

DO

DATA

THE

J, S C A L E (J) , ( Y ( J , I ) , I = I , N P T S )

NW, mEG (361 ) ,R A D (361 ) ,

DIMENSION

ON

J=I,NSETS

W R I T E (0, i000)

wave

X V ( 3 6 1 ) ,Y V A L U E ( 3 6 1 )

COMMON

1321

Y(1,42)=I.0 DO

PROGRAM

data J=1,20

1320

Do

Following is the program list (in FORTRAN) to compute the Fourier terms (DC offset, even and odd harmonics) of a periodic nonsinusoidal function:

of

1320

FROM

DATA

DC=DC/(NPTS-I)

FILE.

20

'DC:',

DC

I=I,NPTS

Y (J, I ) = S C A L E (J)* (Y (J, I) -DC) OPEN(5,FILE='INDUCTOR.

20

IF

DAT',STATUS='OLD', ACCESS='SEQUENTIAL')

30

C REWIND 5 CWWWwwwwwwwwwwwwww**

C

NSETS=I

WRITE

THE

DO

J:I,NSETS

C

C L O S E (UNIT=5)

C

OPEN(3,FILE='FODA.DAT',

SCALED

W R I T E (0, i010)

i010

FORMAT(//

DATA

NO. ',I4, ' P E A K

V A L U E : ',

*FI6. i0 / ' Y - C O O R D I N A T E S

AFTER

S C A L I N G : ' (/SEll. 4) )

STATUS:'OLD',

DO 50

3

50

I=I,NPTS

X (I ) = F L O A T (I- 1 ) NSPACE=NPTS- 1

5 J=I,NSETS

Power Quality in Power Systems and Electrical Machines ISBN 978-0-12-369536-9

,SET

ABSOLUTE

ACCESS:'SEQuENTIAL') DO

40

40

S C A L E (i) =i. 0

C

YMAX(J))

J,YMAX(J), (Y(J,I),I=I,NPTS)

CWWWWWWWWWWWWWWW

REWIND

.GT.

CONTINUE

NPTS=42

C

(ABS(Y(J,I))

Y M A X (O) =ABS (Y (J, I) )

DEGMULT

473

=

360.0/NSPACE 9 Elsevier Inc. All rights reserved.

474

APPENDIX 2

DO

19

19

IF(YVALUE(I)

J=I,NPTS

X(O) IF

(J.EQ.NPTS)

137

X(J)=

W R I T E (0,1013)

STATUS:'OLD' ) (0, *)

KNOWN

CONTINUE W R I T E ( 0 , *) ' Y M A X (J) =', Y M A X (J)

O P E N (i0, F I L E = ' F O D A 0 1 . WRITE

'THE

POINT

NUMBER

(NPTS)

J , Y M A X ( J ) , (YVALUE (I), I=I,NPTS)

OF 1013

IS

FORMAT(//

(0, *)

DATA

'THE

SETS

NUMBER

(NSETS)

OF THIS

AND

PART

'THE

KNOWN

F(X) IS

ALGORITHMS

ARE

BASED IN

OF

VANDERGRAFT

OM

=

314.1592654

GA

=

0.017453292

PAGE

THE

DO

I=I,NH

144

A N G (J, I ) = C U R V P (I )

DO

144

DO

14

I=I,NH

K=I,NH

CURVP(K) 14

= CURVP(K)/GA

CONTINUE W R I T E (0, *) , *************************,

INT=42 INC=5

WRITE(0,*)

NW=I

W R I T E ( 0 , i00) ( C U R V T (K) ,K:I,NH)

NH=29

W R I T E ( 0 , *)

RADIN

=

PI/20.5

PHASOR

DEGIN

=

180./20.5

=

T2

=-DEGIN

DO

22

T1

= TI+RADIN

T2

W R I T E (0, *) 'T H E THE

I=I,INT

IF

(CURVT(1)

(DEG(I),

WRITE(0,100)

I=I,NPTS) I=I,NPTS)

END

1 J=I,NH+I 12

CONTINUE

CURVS(J)

=0.0

i00

FORMAT

CURVT(J)

=0.0

E N D F I L E (10 )

CURVP(J)

=0.0

REWIND

THEN

K:I, NH)

DO

THDI=0.0

I=i,361

Do

X V (I) = F L O A T (I) -i. 0 iiii

CONTINUE

(100.*CURVT(K)/

10

C L O S E (10 ) iiii

K=2,NH

T H D I = T H D I + (C U R V T (K ) ) * (C U R V T (K ) )

J:I,NSETS

T H D I F I N A L = (S Q R T (THDI) ) /

I=i,361

W R I T E (0, *)

C U R V T (1 )

NC=J YVALUE(I)

Do

CONTINUE I=i,361

THDIFINAL

RMSIWITHOUT: 0

= Y(J,I)

Y M A X (a) : 0 . 0 137

.EQ.0.00000) (0.0,

(6(IX, I P E I I . 4 ) )

CONTINUE

DO

THE

IF

=0.0

13

OF

A',

C U R V T (1 ), K= I, NH)

C U R V C (J)

DO

AS

ELSE (RAD(I),

Write(0,*)

12

OF

W R I T E (0, i00)

= T2

CONTINUE

DO

BASED

FUNDAMENTAL : '

= T2+DEGIN

17

COSINE ARE : '

MAGNITUDE

HARMONICS

*'PERCENTAGE

: T1

Write(0,*) DO

'THE

ANGLES

W R I T E (0, I00) ( - C U R V T (K) -90.,

-RADIN

DEG(I)

' C U R V T ( ' , N H , J , ')=:'

K=I,NH)

T1

RAD(I)

13

133

A M P (J, I ) = C U R V T (I )

INTF=42

17

HARM

133

119

.

PI=3.141593

22

AFTER

(YVALUE, CURVC, CURVS, CURVT, CURVP)

POINTS

9 ' ON

PEAK

S C A L I N G : ' (/5Eli. 4) ) CALL

(0, *) X

NO.',I4,'

V A L U E : ',

*FI6. i0 / ' Y - C O O R D I N A T E S

OF

IS'

,N S E T S WRITE

'SET

ABSOLUTE

', N P T S WRITE

YMAX(J))

W R I T E ( 0 , *) 'J=' ,J

X(J)+0.001 DAT'

.GE.

Y M A X (J) : Y V A L U E (I )

= X(J) * D E G M U L T

1112

1112

K=I,NH

R M S IWI T H O U T : R M S IWI T H O U T + (C U R V T (K)) * (C U R V T (K))

475

Program List for Fourier Analysis [81, Chapter 2] R M S I W I T H O U T F = (S Q R T

D 4 = C 4 * S I N (Xl)

( R M S I W I T H O U T ) )/i0. W R I T E (0, *)

D S = C 2 * S I N (X2)

RMSIWITHOUTF

D6 =C 6" S I N (X3)

R M S I W I T H = (DC) * (DC) Do 1113

1113

D L I = D L I + A I * (DI+D3) + A 2 * D 2

K=I,NH

D L 2 = D L 2 + A I * (D4+D6) + A 2 * D 5

RMSIWITH=RMSIWITH+

(CURVT (K) ) *

33

(C U R V T (K) )

CONTINUE C O M P C (J) = D L I * 2 . / 4 1 .

R M S I W I T H F : (SQRT (RMSIWITH)) /i0.

C O M P S (J) = D L 2 * 2 . / 4 1 .

W R I T E (0, *)

C O M P T (J) = S Q R T (COMPC (J) * * 2

RMSIWITHF

STOP

+ C O M P S (J) * * 2 )

END

If

SUBROUTINE

HARM

(VALUE, COMPC,

NW, mEG (361 ) ,R A D (361 ) ,

X V ( 3 6 1 ) ,Y V A L U E ( 3 6 1 ) COMMON

COMPP (J) =-ATAN (COMPC (J) /COMPS (J))

NPTS, NPS, INT, INC, NH, GA,

END

PI,WW, OM,NC, RF, ER, EL COMMON

IF

ERR, I T M A X

DIMENSION

V A L U E (361) ,

44

C O M P P (i00 ) ,

W R I T E (0, *) (VALUE(I),

PHASOR

I = i, N P T S ) AFTER

THE

i00

FORMAT

AS

OF

F K 3 = 0 . 5 * P * (P-I.)

IF

J:I,NH

THE

((CHECK.EQ.I)

.EQ.

NWW))

DLI =0.0

EMDIF

=

DL2 =0.0

DO

I=I,INT

H = F L O A T (O)

51

.AND.

0

DO

52

J=I,NH, I

T I = H * (RAm(I))

H = F L O A T (J)

T 2 = H * (RAD (I+l))

V A L U E C (I ) = V A L U E C (I )

T 3 = H * (RAD(I+2))

+ C O M P C (J) *COS (H*RAD (I)) +

Xl = F K I * T I +FK2 *T2 +FK3 *T3

* C O M P S ( J ) *SIN (H'RAm (I)) 52

X3 =FK3 *TI +FK2 *T2 +FKI *T3

CONTINUE D I F = A B S (VALUE (I ) - V A L U E C (I) )

C 1 = V A L U E (I )

IF

C2 = V A L U E (I + 1 )

EMDIF=DIF

C3 = V A L U E (I + 2 )

mI FN= F L O A T (I )

C4 =FKI *CI +FK2 *C2 +FK3 *C3 D I = C 4 *COS (Xl)

(NC

THEN

V A L U E C (I) =0.

I=I,INT-2,2

C 6 =FK3 *Cl +FK2 *C2 +FKI *C3

OF

A',

(6(IX, I P E I I . 4 ) )

NWW=I*NW

X2:T2

BASED

FUNDAMENTAL :'

F K 2 = (i. +m) * (l.-m)

33

MAGNITUDE

HARMONICS

* 'PERCENTAGE

A2=8./9.

DO

COSINE ARE : '

(-COMPT(K)-90.,

W R I T E (0, *) 'THE

AI=5./9.

44

')=:'

K=I ,NH)

S C A L I N G : ' (/5EII.4))

F K I = 0 . 5 * P * (I.+P)

'THE

ANGLES

WRITE(0,100)

' Y-COORDINATES

P : S Q R T (0.6)

DO

'COMPT(',NH,J,

W R I T E ( 0 , i00) (COMPT (K) ,K=I,NH)

C H E C K : 1.0

FORMAT(//

CONTINUE

WRITE(0,*)

V A L U E C (361 ) WRITE(0,1013)

0.0)

.LT.

COMPP(J)+PI

W R I T E (0, *) ,**************************,

C O M P T (100 ) DIMENSION

IF (COMPS(J)

COMPP(J)=

COMPC(100),COMPS(100),

1013

THEN

ELSE

COMPS, COMPT, COMPP) COMMON

(COMPS(J) . E Q . 0 . 0 0 0 0 0 )

C O M B P (J) =0.0

(DIF.GT.EMDIF)

THEN

ENDIF 51

CONTINUE W R I T E (0, *)

D 2 = C 2 * C O S (X2)

'***CHECKING

D 3 = C 6 * C O S (X3)

ANALYSIS* '

FOURIER

476

APPENDIX 2

W R I T E (0, *) WRITE(0,*)

0.I024E+01 'VALUE(361)

AT

0.I024E+01

0.I024E+01

0.I024E+01

0.I024E+01

NC=', NC 0.I024E+01 W R I T E (0, i001)

0.I024E+01

0.I024E+01

(VALUE(I), 0.I024E+01

0.I024E+01

I=i,42) WRITE(0,1001)

(VALUEC(I),

I=i,42) i001

FORMAT

0.I024E+01

0.I024E+01

0.I024E+01

0.I024E+01

0.I024E+01

(10(IX, IPEII.4)) -0. 9 7 5 6 E + 0 0 - 0 . 9 7 5 6 E + 0 0 - 0 . 9 7 5 6 E

W R I T E ( 0 , *)

'THE M A X I M U M +00-0. 9 7 5 6 E + 0 0 - 0 . 9 7 5 6 E + 0 0

DIFFERENCE I=',

IS

: ' ,EMDIF, 'AT

DIFN

-0. 9 7 5 6 E + 0 0 - 0 . 9 7 5 6 E + 0 0 - 0 . 9 7 5 6 E

ENDIF

+00-0. 9 7 5 6 E + 0 0 - 0 . 9 7 5 6 E + 0 0

RETURN -0. 9 7 5 6 E + 0 0 - 0 . 9 7 5 6 E + 0 0 - 0 . 9 7 5 6 E END +00-0. 9 7 5 6 E + 0 0 - 0 . 9 7 5 6 E + 0 0 -0. 9 7 5 6 E + 0 0 - 0 . 9 7 5 6 E + 0 0 - 0 . 9 7 5 6 E +00-0. 9 7 5 6 E + 0 0 - 0 . 9 7 5 6 E + 0 0

A2.2 OUTPUT OF THE FOURIER ANALYSIS PROGRAM

-0.9756E+00

The output of the F o u r i e r p r o g r a m for a square wave is as follows:

THE

NUMBER

IS

NO.

1 SCALE

KNOWN

OF

DATA

1.0000000000 BEFORE

0.1000E+01

0.1000E+01

SCALING:

0.1000E+01

0.1000E+01

NUMBER

KNOWi~ POINTS

0.

0.1000E+01

0.1000E+01

0.1000E+01

0.1000E+01

0.1000E+01

SETS

(NSETS)

OF X A N D

0.153248 0.612994

0.919491

1.075

1.68573

F(X)

ARE

0.306497

0.459745 1.22599

0.1000E+01

0.1000E+01

(NPTS)

1

THE

Y-COORDINATES

0.1000E+01

POINT

FACTOR: IS

0.1000E+01

OF

42

THE SET

0.I024E+01

0.766242

1.37924 1.83898

1.53248 1.99223

2.14548 2.29873

0.1000E+01

2.75847

0.1000E+01

2.45198 2.91172

2.60522 3.06497

3.21822 0.1000E+01

0.1000E+01

0.1000E+01

0.1000E+01

0.1000E+01

3.37147 3.83121

-0. 1000E+01-0. 1000E+01-0. 1000E

3.52472 3.98446

4.13771

4.29096 4.44421

+01-0. 1 0 0 0 E + 0 1 - 0 . 1 0 0 0 E + 0 1

4.90395

-0. 1000E+01-0. 1000E+01-0. 1000E

3.67796

4.59745 5.05720

4.75070 5.21045

5.36370

+01-0. 1000E+01-0. 1000E+01 5.51694 -0. 1 0 0 0 E + 0 1 - 0 . 1 0 0 0 E + 0 1 - 0 . 1 0 0 0 E

5.97669 0.

+01-0. 1000E+01-0. 1000E+01

5.67019 6.12994

8.78049

5.82344 6.28319

17.5610

26.3415

35.1220

52.6829

61.45

43.9024

-0. 1 0 0 0 E + 0 1 - 0 . 1 0 0 0 E + 0 1 - 0 . 1 0 0 0 E +01-0. 1 0 0 0 E + 0 1 - 0 . 1 0 0 0 E + 0 1 70.2439 DC=

96.5854

0.1000E+01

-0.1000E+01

NO.

1 PEAK

ABSOLUTE

VALUE:

1.0243902206 Y-COORDINATES 0.I024E+01 0.I024E+01

87.8049 114.146

122.927

-2. 4 3 9 0 2 E - 0 2

131.707 SET

79.0244 105.366

158.049

140.488 166.829

149.268 175.610

184.390 AFTER

SCALING:

0.I024E+01 0.I024E+01

0.I024E+01

193.171 219.512 245.854

201.951 228.293

210.732 237.073

:

477

Program List for Fourier Analysis [81, Chapter 2] 254.634

263.415

280.976

289.756

272.195 298.537

-0. 9 7 5 6 E + 0 0 - 0 . 9 7 5 6 E + 0 0 - 0 . 9 7 5 6 E +00-0. 9 7 5 6 E + 0 0 - 0 . 9 7 5 6 E + 0 0

307.317 316.098

324.878

342.439 J=

351.220

333.659 360.000

-0.9756E+00

COMPT(

1

YMAX(J):

0.I024E+01

* * * ** * * * * * * * *SUBROUTINE* * * ** * * * * * * 29

30)=:

1.2717E+00

1.02439

3.4488E-02

3.6450E-02 SET

NO.

1

PEAK

ABSOLUTE

VALUE:

2.4608E-01

1.6870E-01

4.0489E-02

4.1067E-02

1.0243902206 Y-COORDINATES

AFTER

SCALING:

9.1722E-02

6.8664E-02

3.7860E-02

3.4436E-02 0.I024E+01 0.I024E+01 0.I024E+01 0.I024E+01

0.I024E+01

0.I024E+01

0.I024E+01 0.I024E+01

3.1712E-02

0.I024E+01

0.I024E+01

2.4685E-02

2.5122E-02

2.0924E-02

2.2261E-02

0.I024E+01 0.I024E+01

3.8456E-02

2.5107E-02

THE 0.I024E+01

3.8801E-02

0.I024E+01

0.I024E+01

BASED

-9.1272E+01

0.I024E+01

PHASOR

-9.0034E+01

-9.0036E+01

-9.0246E+01 -9.0040E+01

5.1330E-02 3.0685E-02 3.7949E-02 2.1601E-02 2.7380E-02 ANGLES

ARE:

-9.0420E+01 -9.0039E+01 -9.0123E+01

0.I024E+01 -9.0041E+01

0.I024E+01

1.2299E-01 4.0183E-02

3.0684E-02

COSINE

-9.0169E+01 0.I024E+01

4.1969E-01 3.8742E-02

-9.0092E+01

-9.0040E+01

0.I024E+01 -9.0069E+01

-0. 9 7 5 6 E + 0 0 - 0 . 9 7 5 6 E + 0 0 - 0 . 9 7 5 6 E +00-0. 9 7 5 6 E + 0 0 - 0 . 9 7 5 6 E + 0 0

-9.0038E+01

-9.0034E+01 -9.0032E+01

-9.0039E+01 -9.0038E+01

-9.0025E+01 -0. 9 7 5 6 E + 0 0 - 0 . 9 7 5 6 E + 0 0 - 0 . 9 7 5 6 E +00-0. 9 7 5 6 E + 0 0 - 0 . 9 7 5 6 E + 0 0 -0. 9 7 5 6 E + 0 0 - 0 . 9 7 5 6 E + 0 0 - 0 . 9 7 5 6 E +00-0. 9 7 5 6 E + 0 0 - 0 . 9 7 5 6 E + 0 0

-9.0025E+01

-9.0025E+01 -9.0021E+01

-9.0022E+01 THE

***

CHECKING

-9.0031E+01 -9.0038E+01 -9.0022E+01 -9.0027E+01

-9.0031E+01

MAGNITUDE

APERCENTAGE

-9.0051E+01

OF OF

THE

THE

HARMONICS

AS

FUNDAMENTAL:

FOURIER

ANALYSIS*

-0. 9 7 5 6 E + 0 0 - 0 . 9 7 5 6 E + 0 0 - 0 . 9 7 5 6 E VALUE(361)

AT

NC=

1

+00-0. 9 7 5 6 E + 0 0 - 0 . 9 7 5 6 E + 0 0 1.0244E+00 -0.9756E+00

1.0244E+00

0.I024E+01

1.0244E+00 1.0244E+00

1.0244E+00 1.0244E+00

1.0245 Y-COORDINATES 0.I024E+01 0.I024E+01

AFTER

SCALING:

0.I024E+01

0.I024E+01

1.0244E+00 1.0244E+00

0.I024E+01

0.I024E+01

0.I024E+01

0.I024E+01

-9.7561E-01

0.1024E+01

0.I024E+01

-9.7561E-01

-9.7561E-01

-9.7561E-01

-9.7561E-01

-9.7565 -9.7561E-01

0.I024E+01

1.0244E+00 1.0244E+00

1.0245

0.I024E+01

-9.7561E-01 0.I024E+01

1.0244E+00 1.0244E+00

0.I024E+01

-9.7561E-01

-9.7561E-01 -9.7561E-01

-9.7561E-01 -9.7561E-01

0.I024E+01 -9.7565

0.I024E+01 0.I024E+01

0.I024E+01

0.I024E+01

0.I024E+01

-9.7561E-01 5.0335E-01 1.0407E+00

-0. 9 7 5 6 E + 0 0 - 0 . 9 7 5 6 E + 0 0 - 0 . 9 7 5 6 E +00-0. 9 7 5 6 E + 0 0 - 0 . 9 7 5 6 E + 0 0 -0. 9 7 5 6 E + 0 0 - 0 . 9 7 5 6 E + 0 0 - 0 . 9 7 5 6 E +00-0. 9 7 5 6 E + 0 0 - 0 . 9 7 5 6 E + 0 0

+00-0. 9 7 5 6 E + 0 0 - 0 . 9 7 5 6 E + 0 0

I.I156E+00 9.6388E-01

9.8548E-01 1.0831E+00

9.7205 9.5716E-01 1.0748E+00

i. 0 4 5 1 E + 0 0

9. 9 4 2 7 E - 0 1

9.3542E-01

I. 0 6 3 7 E + 0 0

-9.6836E-01

-9.0364E-01

1.0225 -8.8539E-01

-0. 9 7 5 6 E + 0 0 - 0 . 9 7 5 6 E + 0 0 - 0 . 9 7 5 6 E

1.0244E+00

-I.0717E+00 -9.4575

-9.4528E-01

-9.9542E-01

478

APPENDIX 2

-9.5329E-01 -I.0258E+00

-I.0331E+00

-9.2584E-01

-9.5068E-01

-I.0254E+00

-9.3105 MAXIMUM

5.0335E-01 DIFFERENCE

0.521040AT

I=

-9.0032E+01

IS

:

1.00000

-9.0025E+01 THE

29

i)=:

1.2717E+00 3.6450E-02 1.6870E-01 4.1067E-02 3.4436E-02

3.7860E-02 3.8801E-02

3.1712E-02 2.5107E-02

3.8456E-02 2.4685E-02

2.5122E-02 2.2261E-02 COSINE

4.0489E-02 9.1722E-02

6.8664E-02

THE

3.4488E-02

2.0924E-02

4.1969E-01 3.8742E-02 1.2299E-01 4.0183E-02 5.1330E-02 3.0685E-02 3.7949E-02 2.1601E-02 2.7380E-02

3.0684E-02 BASED

-9.1272E+01 -9.0036E+01 -9.0169E+01

PHASOR

-9.0034E+01 -9.0246E+01 -9.0040E+01

1.0000E+02 2.8661E+00 1.3265E+01 3.2292E+00 5.3992E+00 2.7078E+00 2.4936E+00 1.9742E+00 1.9754E+00 1.7504E+00

ANGLES

ARE:

-9.0420E+01 -9.0039E+01 -9.0123E+01

0.444086 0.139151 0.139172

-9.0031E+01 -9.0038E+01

-9.0025E+01 -9.0021E+01

-9.0022E+01 -9.0027E+01

-9.0031E+01

MAGNITUDE

APERCENTAGE

2.4608E-01

-9.0039E+01

-9.0022E+01

-9.0040E+01 -9.0051E+01

-9.0038E+01

-9.0025E+01

***********MA******************** CURVT(

-9.0092E+01 -9.0038E+01

-9.0034E+01

-5.0985E-01 THE

-9.0041E+01 -9.0069E+01

OF

OF

THE

THE

HARMONICS

AS

FUNDAMENTAL:

2.7118E+00 1.9350E+01 3.1837E+00 7.2123E+00 2.9770E+00 3.0510E+00 3.0239E+00 1.9410E+00 1.6453E+00 2.4127E+00

3.3001E+01 3.0463E+00 9.6712E+00

3.1597E+00 4.0362E+00 2.4128E+00 2.9840E+00 1.6985E+00 2.1530E+00