! &&& &&& 2 " # $ % &&&&'&&&& &&&&'&&&&( &&&& &&&&)* + ! , - '. / . 0 1 3445 6 7 " 89 : !( !; $ < : 7 * : =>? @ 6 7 D% 16 7 E 1 2F F G 3F H ! D% 4H I G D% 5E; (F 6H 'J 7D Plotting3 M N O )P $ K7 L 8D PlottingQ F O N O )P $ K7 L 9AB C : =>? 7/04/2006 ) U (1/04/2006 R E F ST @ AB C 6 7 E D% 16 7 E 1 2F H ! D% 3F F G 4H I G D% 5E; (F 6- 6 7 D% WV * [! Y @ H 7 E \ N \ !. H ! $ % Z, * HV Y A X T6 7 T 6 7 \ < differentiation \` ' \ ( 6 7 E 0 B% ] N _A ^ H 7 E ( ] E H 7 E !` ' HV [ S; Algebraic Equations % EY HV \. $ % [ S; Integration 0 B% \ [ > c d _\J J \J b ! a H >Differential Equations $e! B B% B Partial fraction MeY B< H !( \ $ % _ MeY \` ' \ ( 6 7 E \ 6 7 E 0 B E ) * _ % ;F ) ST _ % ! / ! ] E; ] b Mechanical Field, < 7 < @ Y Control System, L<. K7* \N HV Y 0 1 = @ Y [ S; Automotive Industry, H B ( ^ Electronics H 7 < P ; . [ S; . H E N< Aerospace and Defense, f Y R ( ji4 U % hb G ' Nissan = B 7 b H B ; 8 h b _[ > 0 Y! ;g* ) 6 7 F U Paper Model Based Design / F !( L J @ E ? h b k . $ K7 U T ( Y ;e;; ;%Y8 (B % @ % Model Based Design, T ) . ; 8X = B 7 ; # Without MathWorks tools for Model-Based Design, Nissan would not have become the first company to meet the CARB PZEV standard CARB= California Air Resources Board PZEV= Partial Zero Emission Vehicle c @ % ST L< < % http://www.mathworks.com/company/use...ml?by=industry d /E lEJ7 ) 6 7 E ST \N L! !( .! 1 . h.E^* 1 < 0% B $ 0 . ( J 6 7 d C D% \ k1 7N D !; T @ F _= J 8 6 7 E d m $ b D !; 1 Y# 1 ] ( % #( N;F Computer Science a . $ !( H ` % > U T . < B< 7 1 '7 Intel Hypercube organization T Hardware && J OU ( H d n * T A7* ; _ 6 7 E $F ; # MathWorks ; 8 U @ 7P $ % =* \EbArdent Computer . ! 6 7 @ FDC D !; \ k1 . 6 7 c 0` ( B A7* ; Mathworks ; # d C T opqr $ ( MIT 1 a . $ !( < + % !< !( \^ ) k 1 opr4 $ ( '7 1 M.S.E.E 8 !( \^ ) A7* ; \ k1 ...L!< B% L !B J \n * A !( . 7 _ ! S L ! = <% =* _0 Y! * = <% =* : @m .$ P % 0 \1* _D . b( a ! ]E 6 7 E !( $ B J _ : . fS _ L ! ] * E7 7 % ST \1* 6 7 E U/ L _s E R )9 n(F H Et ] E a * ] E _$ Bb* U 6 7 L! LB L ST D! % 1Simulink ; . 2Control System Using the Matlab $ ? L<. K7*3Signal Application Using Matlab $ ? 8F H E 4Digital Signal Processing Using Matlab $ ? b 8P H ! (5Numerical Application Using Matlab $ ? E% ` % H % K 6Image Processing Applications Using Matlab $ ? J Y H E 7Radio Frequency Applications Using Matlab $ ? % H 1 H E 8Mechanical Applications Using Matlab $ ? < 7 < H E 9Radar Applications Using Matlab $ ? H E 10Robots Applications Using Matlab $ ? H H E 11Electronics Applications Using Matlab $ ? 7 < P H E 12Semiconductors Applications Using Matlab $ ? H ^ u E8* H E 13Automotive Applications Using $ ? H B ( ^ B H E 14Matlab Aerospace and Defense $ ? f Y R 9 n' $ !( B H E 15Applications Using Matlab Communication Applications Using Matlab $ ? HV J P H E 16w U # ST @ < U !( % =* : @m * _\% v # =? $ < 7 U ; T sE R # \Eb uS * V0` O O[ T= < 1;. 2$ ? L<. K7*3% < F uS x ] 1 % = : @m * $ hb = ) " # 3445y4QyQo s $ *E R ` ST z E G !( / ' P V _$ < 7 * R E F u%. L% 9e1 " 8 L %1[ S; R E F @ R B B' P 9 n({ B % ) R E * \; @ * " # L% L %2L B' U !( .6 7 E! s E L ' ( 1 U \J7 ) _ a @ A) 8 L aY%3E< R ` @ simulink $ ? ;. ; [ S; L! ;\ . `4!d<7 < !d<7 < T6 R ` @ 6 7 E \ . 9 n({ < % _ 6 7 \ . 5." #! a $ e P 0 _6 7 E " 8 ; # 9 n({ < %6_ B' P @ ) | # \ % =* VU A !( _A) 8 sE b R ` @ ) B' U n ! = ; =* ) 7.] EB " # 9eY [ > H B' U 0 u B' U 0` | # $ % ) L B' U } L < % _ ^ \M 9 E ; # 3i ( L ; # \ %S Y 9 n({ EB 8. ~ J # D! 7 <P f % h ` _ 7 <P f % !( .[ > F , bU >U J A) 8 L % l ` `9, ! R ` H B' U R ` 6 7 @ )L B' U 9 n(F L %10U u B' U \ | # $ % R ` u B' U 0` n $ b =* ) .! R ` H B' U R ` 9 n(F \ % V ) [ > , R ` H B' U R ` H E! H B' P $ 11\ LB | # $ %, ] R ` u 0` n $ b ) _ N; aEB . R ` H B' U R ` Uu aEB 9 n(F \ % V ) [ > , R ` H R ` <# H $ 12u \ LB | # $ % _] R ` u 0` n $ b ) _ N; . R ` H R ` U %e " 8 R ` H * < _ vP !( S (* s : @m * =* 0 ]) 8 B _ % ; _6 7 E ^ 6 7 : =>? ! 0b sE ;> U \J V _9 E \Eb ] n%* _$ < 6 7 E J ; # 0b http://www.mathworks.com H N% . [ S; _ 6 7 E H ^P . 6 7 E Z %e !Y7P I! ( w 0b ST University of Utah http://www.math.utah.edu/lab/ms/matlab/matlab.html 6 7 E BE % Y 0b %}) Indiana University http://www.indiana.edu/~statmath/math/matlab/ 6 7 @ ) % . Y 0b ] n%* $ % .6 7 E < ' U !(* U \J7 s ) _ ( E U \<# c : @mB7 uST % Y L %: K) Y 7 * }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`a b &\ #< , O c >(> c 1+ ' P52 _ d " cd #h )A # $9 # c ;Q 7=3 + & gZ # <.=>1 j 1 i D." 1 Zc 4, 9 < (5A" Y Q 7=Y - >* >&C D." 1 ;_o e 8 f Y >M _Y 1+ ' IB" @ " 1d !2 2 < @Y -. I &2 /BC < @3 IB" 1 " ) * 1 '( 7 :Y #< M 1 [ = 1+ ' P52 , =a !Z .k1 b 9" , =m ( * I 7 " #45 , G l*. \ A & B # U" _ @ 45 & P52 n " / ( :*. Y p 3 45 , G0 &&d1( .k1 #D." 1 4, 9 1+ Z [O H A1 !dA ! ( 1+ ' P52 : Y #h U K b &* q 2 & F=Y %f + F=0 c V ; d c I( A B B Z s 45 & _ d" ) * t(Y \ ' (> " I( A B B Z 45 & _ d" ) * ! 12 _ 1+ Z &(> /' ( 1+ Z k 5 & I 56 # FB O1 D." 1 < FB c '& I&d1( ) * ; kd 2 s 3 45 =u # &91 6 K ? 9"m + \ >*Y 2 B 5 & _ d" r r # 1+ Z (, t < >C 1 # 1+ ' IB" N '" ) * (S BM m UB D." 1 !B " I 56 #< k(>A D t v 7 ; j1M f \ \3 < B1 ^ _`a N ? & D." 1 3 ] /BC b &\ 16 #@> w3 jV k 4, 9 45 :Y# 1d #N d =Y < B1 ] h 1 ' xyx 2 j1MB b 1 S D." 1 j1M .C 5=W" 2 N Z,Y 4, [ m jV D." 1 N ' \ y j1M &1Z `0 .k1 A {B* 45 , G l*. \ # @S 4 ' w 1 '& !Z 4, 9 : Y # F\3 45 / 0 z2`0 3 45 {A [Y 3 4, 9 16 # + & (> " 45 }.sa !Z # / 0 "& U &1Z & Y | F& 1' " & , G l*. \ # 3 45 d !Z # \ \3 V 3 45 4@ C l*. \ 4, 9 : Y # 2 4>(>M 4, 9 4, 9 >6W B 4, 9 : Y # ~ r .k1 #D." 1 :Y# e ~ :Y# H " • /BC hrfS ,v 7 B1C 5=W" .k1 #h • f S , D t B1C 5=W" .k1 #h € f S , 1 ' B1C 5=W" #i " F1 * " # $ /BC TUt ?.= c S 52 /BC ? 9A cd1( #h • f w3 S , 5=W( 4, 9 : Y # ~ • .k1 W J K7* _sqrt F ; s% v ( Lb fF SY S * SY S * L % E N ' 1 c( &C jV ! # 2> P>( #M ; z d ! #h ƒ f ( ‚ ! " #$% & # c kd 2 s ## %& @ " 16 c QS E N ' & j 1 k _ d" ) * .C jV Y> _Y c > R # _ &C jV D." 1 F 4, 9 l*R 6 _3 I ` #T' 1 Z =u {BM\ Y ) * # 4, 9 : Y # S , X 45 BdK I & _ :*." 16 cd jM ! & ) * S , 5=W" ,3 + & 4, 9 e : Y #E N>O 1 B=>( 1 ' b A 5=W( ) A #b A + & „( " ! ( ;c b * 1 Z 6 5=W" ) * # 1" { 0 >Z BdK1 _ " 16 , Ga N '( D." 1 _Y 2 # BdK I &2 _ d" M /BC &B9* Y # 1 Z &B=@Y 1B6 & Y 2 # BdK1 …J †@‡( E Y c * D d1 6 / 0 †@‡( 1 # 3 45 M & I 56 B=>1 1 ' 4, 9 : Y #T % dK ! " .k j1M M & ? =@0 B1C cd f , : c M & I 56 B=>1 1 ' Q F=Y ! ( M zB% > Y B=> 1 Z 6 > h ' f .C jV $( % cC hN>O 1 P W( 5 F& D." 1 N '( p <.=>1 b * jV $( % cC # I ` N>O 1 zB% `0 B=>1 ! ' Y M & , G0 ! ( h .k j1M f 4, 9 : h ' f , 651 S S N >O \0 _ @ B71 M & Y ' () 4, 9 :Y * + , -' . ! ' / 0 1, 67 :( 4, 9 : Y #S 5 1 Z jV N '&\ ) * #E 1 Z 3 45 2 h U" †Y # 1 ' P52 } 34' , 5 f & 6 `0 E Y &1B " d &&d1( 16 #E d {1Z i _ @ #h + & M " 45 M " Y 5 F&" > cd * # 8 9 "0: f + & B=>1 ! ' i D." 1B cd1( 4, 9 : Y # Y N >O \a I ` b ( R D." 1 _ l*. \ #D." 1B ' F( {1Z b A c b * †Y jV !Z >6W B 4, 9 : Y #_o BC 6 $( % cC #T' >* 4, 9 U1 i 1C cd11 c # 16 ( ) * (&) c .d ! Z &(> $ / 0 ;< = d B6 i B1 N ' _Y % J L ? k1 F # U 1 !\0 ! Y " 4, 9 N !d 5 &2 F 6Y >s ^ _`a 1d Q C> !d W\Y : Y #T' ( ) 1 Z i 1 N '&\ ! ^ _`a ? & &\ #D." 1 [O 3 ] + , + & , & 1d #N d kBk1 d kBk1 (>+ S d (>+ S ? ? ? ? =0 > > > > kBk1 ? > R Y + - + + . † +> (>' ( S w ' D." 1 N '( :*. 4, 9 l*R X / ˆ O QSM k6Y 9F QSM 52 v J ! \ 5 ) 4@ , " <A B ) C D () 5 e , E >> ? E FG4H 5 JK#, I+% >> ? < ? < ? p ! # , @ / ( 1, () L M NO, # & PQ FG4H I+% () L M NO, # & PQ FG4H I+% 5 5 < ? < ? @ &+4 1, < ? D ?4HQ Q 4 /R2 -' !" 0 ,14 ?(8 & () S L4 5 ^ _`a ? & &\ #D." 1 0 k ‰ \3 < F91 1d #N d =Y 6jV 1 ? & < F91 2 D." 1 < F91 6 F6 < F91 A < B1 [ = < F9 F91 c @>A 9&C Š O \0 F91 9&C U" dK 5=W" #4>1CY b F[ 4, [ ! \ 16 #<R@ 1 c C 1M * # ; 5d2 V !( < F91 2 c C 1M 2 @ >A < k6 * < F91 N>O " ;^ _`a ‰ \m 52 '*R E* J D." 1 k ! #? 3 „9 [ &C < F91 6 F6 d F91 ? =@0 ! ( k F9 6 .k1 N Z,Y c 9F ! ( #? 3 „9 [ &C 6 ! ( E W !B ( _Y j 1M /BC # ! ' ? =@0 Z cd ? 3 „9 ! Z ? =@0 > #N Z,3 c 1 Y (1) B[ F 0 ? 3 „9 v F /BC TUt 0 hE1 Z ? =@0 ! \ †5 f k „9 [ &C cC ? 3 „9 [ &C 9 ! ( 4, 9 : Y # ( ' ) % '&1 B[ F N >O \a Y ;} 7 j 1 >* dK ;;;; 1d ( < F91 ! Z ? =@m 4@> z \Y H 1d b Gz _6z #v K cC D U 4 ? % /BC 3 ‹@ ,5 CY #Q SC3 =Y E BC ,@ ' I ` E 0 } F / 0 1 ^ & CY #< A m < F91 /BC A < B1 ˆ O QSM v J N !d 1d Œ< F91 /BC ! " \ \3 < B1 j1M v 7 D t ! ' \3 F91 2 1 r r r r r j1M ;c LF I 56 # F9 j1 • J 65 _Y R Y zM( D." 1 N >O \0 Q> ‰ K k F91 P G &( Z c F9 j1 • J F9 &(> _Y | F& ; 4>1C3 @>C 3 1 1 cd1( _ _ F91 .k1 b F9 @>C LF E 12.6 _ d( _Y 1 1 • K #2 * - c 4>1C3 b F9 @>C LF _.1A( # Q> P G &( / 3 c F9 j1 B1C ! " „ 6 .k ? 3 „9B ? 3 9& j1M j1M B1C ! " ;? 3 „9B ? 3 9& & 1 >Z _ d & 1 >Z _ d 3#456 F91 ? 3 „9B k 9& j1M k 9& ? 3 „9 j1 & 1 >Z _ d # k F91 /#6537 4, 9 B1 g OB" cd1( # F91 6 N 1"0 / * 5d2 1 / 3 F91 D." 1 j1M ' \ &1B " 16 #-Ž2 c F91 6 R Y zM( 4, 9 : Y #j1M B1C ! B hyf j1M S , N >O \0 ! X ;;;;; 1d ( e H 'J €H 'J d'7 ) v * " v• 8 T 1L% H 'J = < =* • #% } ) _0 Y • 8 d'7 T | 'J ( T m } ) (F ( n}) J K7* 6 7 p " v !( @ N d'7 \ J K7* =• L ) H 'J 7N 'J | 'J €H 'J ] % B n1 F !( @ N ` `• 8 T 'J (* ( = <% =* T m2 J K7* d'7 @ ? =• $ 'J f* `• 8 J K7* H 'J AE 7 V < Bb N< B 1 7* . < _H 'J : =>? ] )V ) 8 L HV \. $ . N; HV \) ' ; " 8 V_ B •;= % =* x 6 \<# = < ; = !) < % = X=-2 Y=3 €[ > L % D < 'J ^ = ! B !; 1 GE 7 B uS E _ T 1 \ ( ' ; L< " 8* =* \Eb ' !; 0` \. = % v [ T =* ;S7 T |S. % v1H 'J Bb2J K7* _|S. % v ] % ;>m H 'J , * Bb T 7 N J % U * < % I B% b IJ J ; B, !( A € (F hB • 8 H 'J H 'J ) (F ( f B% | 'J ( f* X =* E (P S F 0 _ J 'J n7 =* < % A7* Y7 Bb aY% X !( @ J. \1* )7 Bb > < B% ST 'J = < =* inv Y%U ( • #% < 0` s% v ( X & Y b Y%U < % n ! ( B J ; < b >? T : =>? $ H 'J + !( H ! "# $ Column Vector #% &' + Row Vector , $ "# 56 7 ( $ % / ! ) ( * &' # -.! $ # 5/ 010 $ 2 3 34 89 ! 2 :13 ; 23 2 < 4 3J ( |S) ! ( ƒ‚ J ( 9 7 ƒi ^ ( ( 9 7 ƒ5 E;F J Y%U ƒq I^F J Y%U ƒr ^ ` \^ ) Y%U ƒp \; @ M# H ! % : =>? \ J' T uST H Y J !( H ! ; T , F ! 'J '^ AY D% $ 7 =• @ v T f X ( AY !( ! d'7 \ ( < % ! U =• \ 7 $ J( J F S 7 J e length K7* _ 8 F \ 7 ! ;_ `U f ( AY 0` Lb ;m ! _o4 T AY ST J K7* _ ! 7 f* _ #( % . 1 7 $ ^ o34 Lb ( =* _l` T ; `U % 7 7* \ 7 p < % 1 Lb J `? K7* _ b >U > _oo 7 J ( f* `U L % L U o34 Lb o3 7 `U h s B @ N b = < > _oQ Lb W K) J( `? s! 9eY ) 8 b = <7 S J( Lb \; @ U V] < % oQ 12 oo H 7 J €\ N;* ^ ;_, ) !( `U ( Y _Lb 1000 * Lb o44 @ U L >U _hb ! ]S' B $b F ( Y D n =* H * >U $ B a <7 o4 U 1 $b F ( Y ;S7 =* % 1:10 a <7 o344 U 10 $b F ( Y ; % 10:1200 a <7 N ; oQ U oo $b F ( Y ; 11:13 J ; < = < `U % 7 7* x ' [ > E% b < % v[ T 7 (]N 7 ( 7 * >U ^ ( Y `U ' ; ) 8 b = <7 [ S J(@ E U oi Lb • 8 ( a! J(@ E U ! ( \' ] 1 J = <% =*1J ST = < . =*2U Q Lb V] } N J @ E B =* 7 * @N ; T A! !( \; A(3)=15 u I % fS J , .% fS AY TA}) AY AY ) J ( f* I =* 0 B @ J(@ E U ! (" 8 ST !( 7U b = <7 S ' ^ ( ( Y @ E U J ; ^ ( ( Y @ E ? $ _ ^ ( ( Y @ E U ! (" 8 ^ ( ( Y 7U b = <7 S `U ' ; ) 8 ; AY J ( |S) = =v # % =* aY% AY J ( |S. $ A S) % fS J % . 1Lb f* Square Brackets ~ b* 0` 2J K7* _ 8 7 J |S) % 7 7* l` % @N AY ) J ( |S. s! 9eY " 8 * b = <7 S ^ ( ( Y |S) J K7* _ ^ ( ( Y |S. s! ^ ( ( Y |S. 9eY " 8 h * b = ;* S J(9 7 AY = < f* J b !( @ J. T A ;@ [> < % J(9 7" 8 X * b = <7 S J J(9 7 J( Command Window F S 7 !( J( e N;* 9 N;* 9 7 • \ ~ Lb _AY 9eY . ^ ( ( Y L b !( @ J.! ) 8 b = <7 S AY \<# A AY p E;F J %U < % } ) max, E;F Lb F $ Y%U ' ; " 8 Y%U U L % _AY % 7U b = <7 S E;F J Y%P AY !< J U T I^F J , • \ : =>? ] E% b Y% Y%U J U T min F $ U aY% _AY \bF f*minimum Lb AY \ I^F Y%P \<# \ ^ ' *E _ 1 \<# ';L I^F J Y%P 7* =• (* 7* AY =* aY uS ' ^ (R Y % v S m% =* V F ST =* } ) sum F $ J S' % =• AY product J U T prod A ; @N \ ^ F $ Y%U ? _AY ^ (0 10 1 < % $ ` \^ ) Y%U ? [ > _AY ^ ( ` ^ J F ST S m% =* aY% ] E V] N S m =• % H 'J H 'J !( H ! =( 7[ K _H 'J R 7* D% aY% V] * t 'J 1* K 'J 2H 'J !( L | H ! * AY @ v1J ( `U2J ( @ E U3A! ;m ( * D^ |S) ! (4J ( 9 75^ ( ( 9 76E;F J Y%U7I^F J Y%U8'J ^ ( R Y Y%U9^ ` \^ ) Y%U10Diagonal 'J b Y%U11U 0M # H ! T uST : =>? \ J' ) 8L 'J LY) Y%U V } ) size, F $ U aY% _ 'J (F | 'J ( Y%P @ 7 7 ( * 'J LY) Y%P 7 ( F l` _H 'J d H Y $ B% length m length, F $ U l!J% ( f B% V | 'J ( =* f* X K t 'J \ $ V] * _ F ST " # cBE @ N \ $ 7 \<# ; Z (F 'J LY) c | 'J size F < $ ( | 7 =* 7 * >U * • \ $ 7 • c 'J $ N< L ' !) \J (F ( | 7 =* 7 * >U * < $ 7 U J( ? $ 7] M _ \ ]1 H ! ) @ N 9 (? $ 7 =* aY% F [ > l ` 'J D% < $ 7, d ` !( 0 ? $b[S _ 7 N DJ L b 0` L % L _d .] '^ @N $ ? [ > " n%U < % € 'J } N 7N @ F 0 DJ 11 `U _ T ^ ( ( * J( ln ; `U ! ( 6 E V] * $ ‚3 Lb 0` ! } N DJ $ 7 =* % 7 7* x ' @ F DJ =? „) ^ ( ( `U 7 * >U > oQ i‚ Qo (F `U % 7 7* $ ; \<# @ [> < %_ J(@ E U \ ^ ( ( * J(@ E U 7< U } ) _] 1 T < _ UL% ] 7 ! ] EB 7 ;> ; 'J D% $ _ ^ uST l ` _ 'J '^ Lb % 7N U@ F } N DJ @ F DJ @ E B7 =* % 7 7* \ _c B @ N \ '^ } N U@ F J uST = < b @ E ? $ [ > < % _ ^ ( ( @ E U 7 * >U J( \ \ [> < N;* |S) J ( |S) @ t A7* } ) _ 'J c ) J \ ; ( * \ ; D^ |S. $ =* H * >U < _L b L !( \ ! 'J \ V] * $ 7 A!; } N DJ |S) % 7 7 \ \ Lb _A!; 0 |S. |S) ! DJ _ $ %V 'J J(9 7 _ 'J !( % ) J ( !( @ J. 7 A7* f* _ \ ]1 TH ! _c B @ N \ $ 7, F ST l ` _ J ST A fS s B @N T ;> L 'J d'7 } N 0 ]N F J @ F DJ U 7N 7 N DJ 9 !( \J.7 =* % 7 _ [ [( J !N F ]N $ 7_ J( % J(9 7 ! ( DJ Lb ;S [ > % 7 7 \ Y) | 7 <7 L >U > 7 N DJ %e N;* Lb < _ % ] N;* 9 'J " # LY) | 7 7* ! ( $ ) ST E;F J \ E;F J ( }.E% D < _D! \<# 'J !( \ $ %, [ > \ $ % _ 'J ( \; E;F l` ! @N K7* _ ( \; !( M #7U L 'J ] EB 7 ;> ; max F d'7 X Y%U ; aY% L E;F Lb \<; 'J P _ E;F Lb F s% v ( E;F J J ( }.E E;F Lb A AY =• % Y%? $ %_ $ % 'J < L ( \; E;F J !( \J.7 _… ? 6 ! $ b ! „) ; I^F J E;F J Y%U T ;> s B H d'7 T _ '! H E min F $ UL% < @ N L< U ^ !( e ( \; 0 1 Y%? Y%U $ %0 Y R Y ! ( < sum $ P N; ]n%* ! uST Y%U F $ ? $ 7 ! ;R Y Y%P @N ^ 6 _ p 1 ; _AY ^ 0` ,) ` \^ ) Y%U 0` L % , ) !( ( \< = < n ! ( < _ 'J n \^ ) 6 _ 1 AY ^ ( `L%, * @N K7* 'J ^ ( ` < % F $ U L >U _AY 'J X 'J 'J ^ $ ^ [! =* ] ^ J [ S @ N ST diag, F $ 0 Y ! ( !( @ J. ^ X [! b Y%U _] 1 T < _ % ;* $ UH>= < b ! U L % _Z (F ( f B% | 'J ( % 7]N _ 'J ` \^ ) !( @ J. b !( H ! % 7 7* * % \ ( =• uST < % X M-File @ U %Y ! uST D! % b > < _ F S 7@ d < F @ P ! T € F .%1 F @ U (U aY% = ; N;* * J ( \% 7 * >U _ B7 ; F @ U ! ( 1%1 F ; aY _m 1 >U2.a d' %1 F 0 1 @ U aY% , * ! (U 7 * _ E; 6 7 E ; >U3., U % E F @ P (? $ E< 6 7 E S F a m † ) >U4Debugging9 { l .J ! ( \ ( a J%5$ B ! † .% fS \! U `P ST ] E; ] b / I B% 0E ST _\ I# = V] * ] ; 6 7 E ; !( M-File B% \ ( L _ !<# uS ] ) ] Ev (U * _, * ; U 1 . = L‡ \% !( ^ uST _A! I# L % A 9 7P . F ST !( F @ U J 0E U € ^ [! \ I# L % D < \<# S m _ % 1 uS 7 T X K $ X + : =>? \ \ J' M-File S 7 !( | M-File S 7 J K7* M-File, S 7 !( | =• $ T 6 7 E „') ( X • • #% < _6 7 E „'. [E _\ I# ˆ !( cIn $ b m * E%V =*1] ] * = <% V =*2!^ H B !( L P f .% V =*3‹ _ Š _ ƒ _ ‰ \N ^ ˆ !( f . V =* ƒ‚ 6 7 E S' $ % VU • # [! ( aY% B S =• < @N S' L J l` T ; \ I# ˆ !( cIn L %1- ( < training1A B X _V] * 6 7 E „'. E 2- Command Window and Workspace \<# X ;_ 'J ! L G ]; L I $ 7 M-File K 3- U 4- S 7 T 8 LO _ XX B (P 1 . = ] M ! „'. =• Command Window $ F _6 7 E \ I# =• $ 5- F 0` L % _ !<# uS ] . , 1 L% 6 7 E L b \K 6 7 E! }% . ! ( \; A7? „) ; . F S * E =* V ! $ 7 6 E 0 1 * E = <% ST _6 7 \; @ * CLC [ > l` % @ N $ 7 7 ( Xe M-File&&& K Xp Command Window L ' _\ % CLC * =* ;m 7 ) _@ N < =• $ \% =• $ %Y L A,B,CL b !( , . e 9 '< \ % CLC F =* ;m 7 S Workspace S 7 T #7 7 ( < S T# D,E,F U A,B,C c ˆ I s% v ( 6 7 E c B \% L Workspace w 6 7 f* b f* lB $ % } . clc F Clear * 0` aY% _ !<# uST .: =>? ] )V ! ( L 6 E 0 1 ] n%* F ST h EN aY% Workspace , =• 0 # / ' „) clear, F 0` < 6 7 E d'7 S ' =• $ e F G : =>? B \<# ( _ E;F Lb L I^F Lb F G S * linspace % . s% v ( _AY … 7U ! ( b %ST t c J S m% oi b i _ • 7 o4 $ V plotting L $ B% fS U ' ; l` % Randomization System in Matlab ! M # $K Œ %e M #( $ K7 AY =* T $ K ST e e _$ U @ 7P \Eb P @N B% ST N; F ST B; • T !( d randint l .^ ( $ K7 $ K7 d < _Lb { M #( $ K7 m# ] M #( \ ] Jb * ] % % e d A $ b F $ K7 =* ; _s B J S m% !( e F ST $ ? c B @ N ST F F \N ` F ST _ 'J * AY \<# e ( A mB% A'% 6 7 E Input \ Y% A U@ $ B $ %})_ $ B $ % ] E [> 9 * | ) ) * \ $ _[ @ ? [E % 7 * >U ] N ; L % _Lb d L U TA UL =m ] 1$T ! | 7 =* 7 * >U F ST Str2num & num2str Lb e € String and Character / ' V] * !; * | ) Tstring $b • ( Y * Lb ( E( Tcharacter [ S; d< string to Character \% . $ % * [ T T num2str str2num F uST '% < input F $ ? $ _ F uST J L ' )cB @N $ U ) \ _=• I B * E _$ b * @ ? $ string J T 8 _[ > t Ž8 f* $* $ b * 7m; !( | ` e J a!v @N U AY eX T 8 _Lb * character U string \% . str2num $ _A!<8 I% V A < _ , D% =* ] EB 7 ;> ; ( 7 =* aY% < _AY ? =• $ num2str 7 N F ~ J > ; string U $ b F \% . F ST $ B% B L P 0n LO _ B L P @ U T ; d c string * $ b * !( f .% F ee O N M N L s! 9eY 9 E! U L U !( .7 =• B% T )* c b ( \ B 2D Plotting F M O L = < L ! ( L<. b = < = T F M OL dependent B% • independent <. V A b =* f* \ B I f* independent Variable &&& J I L b !( A b %}) • I f* dependent Variable J S m% } ) plot F " # $ _ % J %ST " 8 =• % I sine WaveL - „) ep Sine Wave L J ' < c B @ N ST \ !b ( ST Sine Wave , L \<# c • 7 o4 7 U b 7* „) \<# p ; _AY \ • ( %ˆ V _ !<# uS ] ) ] N; h B. b p =* „) = ( Y-Axis H J . X-Axis H B . @ ) H B 0` ' ; $ + S m '; _ n / N;* 0` [ S; _ = I '; _ !( <E8 0` _ ! Œ: =>? ) S 7 !J' H ( 9 #7U ' ; _ !J' S 7 \; \ ( p \ _= F I \N @ L !( \J.7 •M J J S m } ) plot F •M J p H U •M J `U H , ~ G I ]1f n = <% = )F G ( Y T uST _ T t k 7 $ Y7 U !J • I n •M J G \% $ )F U c uST = < _ uS * s B @ N = I ]N $ \ •M J !( ] (U [! 0` L % D < J $ Y7 ( p E( 7U \J ] d c !( \J.7 = <% =m %1 ^ `? =• L \<# p !( \J.7 (] ^ 6 f* X 9 \<# \ p H ) $ Y7 !( \J.7 =* 7 * >U !( \J.7 •M J ) 8 b = <7 T L L !( !( <E8 0` L %. \ B = <% } . _L !( <E8 0` plot F grid F S m } ) ;L pX ! ( \<8 = < $ % \<# S m } . _= pe % = <% } . ;S U `P * \ $ =• $ ? [>L%_ hold F 0` L % -U L % D < _c F F % 7 _ ) S 7 J ;= pp -? $ _6 7 E \ I# ( < 0` L % < plot F \Eb Hold on F K7*off, = < !J' S 7 '! F S 7 H 0` S 7 ` $ S d'7 H 0` V] =• $ [ > 1 _] J' A ` L >U t S 7 l ' $ % fS figure F J T8 t = ! % S 7 -? $ b = „) !( U … .7 !( L % figure * \; A7* ] !( figure * fS plot L * S ' L A7 .A) 8 sE fS grid * \N uS • •M J [ > !( c B @ N ST % S 0` [! 1 }) !; %S 7 !( \J. € ST † ) D < , ) S 7 ˆ b S ( =* „) _, * 6 7 E \ I# Lb =• S 7 7N L $ % LO _ 7N L L F S !( @ *L $ % L % } . clear F close all F $ ? Lb !<# uST \. figure F 1 aEB % 1 V * O O[ T= < \; 6 7 E \ I# ( [ > \Eb ) ' h7 ; S 7 f* / tU LT 6 7 f* \ ( L % \; U clc clear close all \% \ !b S A! ( L fS @ N T ST ) S 7 !J' H 9 #7U H ( 0` $ 7 =* \ \T < _ S d'7 !( N;* \ $ 7 =* 7 < ? 7* 7S * plot * \; \Eb subplot F $ ? [> < % . _ ) S 7 !J' 0` !(subplot F $ % } ) _ T -? $ H ( %. @ subplot F \ % _ ` '; T K H ( F $ U ( aY% _AY * 'J 7m; J H 0` $ ; F %. \<# $ U \n'% \<# ; n Y ` $ _ aY% HV % =* @ _V] N S m _ F 7 S m F ] _ 3 (F ( o '^ ( AY 7m; = < 7N 7 S m 7N subplot F $ U ( \ J' u % . aY% ST ;= < subplot F J $ B7 LO l` J F ; V @ F \<# L J F ; V 7 N \<# L b = < ] ; 6 7 E 0` $ =F = \<# X ; M = < \<# S m _ [ e + bF $ UL% 7 N;* \I# !I# H 7 0 1 $ b *] @ N 9 (? $ J \<8 !( … \<# = <% =* % 7 h7 ; >U K) _ !( 5 i ‚ Q 3 o F p T N N \I# p H7 !I# H 7 $ b * Q (F ( Q | 'J $b * q 7N \I# H7 $b * \<# = <% 6 7 E ( =? ; Y = < . B X-H B . B $ 7 =* 7 * >U ] N _ . T F \Eb 9eY S ' =• $ } ) ylabel F $ ? $ 7H J . B $ 7 =* 7 * >U xlabel F $ ? $ 7Axis ; T ) ^ % F ; S m% ylabelH J . !( A E L % Ž# d'7 E @ N \ =• $ J !( \J.7 !(* title F @ l` [> \<# T ; A !( H % = ( 0` \; !(* = ( 0` F ST = <% } ) 0` s B @N < % UR 1 J !( \J.7 L \ N;* * J S m% text !; 0` ST •M J %. K Y AY 6 7 E F $ @ )9 \ ; ? [ > _L 7 !( •7 0` !( N;* * 7 !( •7 `U < % ) M 0` LO _ E;F Lb Y%U ' ; ] B V] N S m maximum point J = < Y%? $ % F ST find $ F " # $ 7 7 ( E;F J !( }.E \ $ ]N _ J ;L Y7 _6 7 E \ I# ( < \ J $ Y, &&&! K7* workspace, K (X K Y K b !( @ J. 7 * >U X b =? „) ; !( K K !; 0` ; @N K sE $ =• X legend F F 0` $ ]N _L !( = \; % > E L J S m% =* V F ST =* ] !( !( ;6 e 6 7 E Y .'^ !( \ 0` @N legend ; < % F ST $ B% = ; uS * sE fS @ N \<# A Y L p ] N _L _= OU \ Hb Hb ( =* f* ( !( K % legend F =? , Y%U LO b ( L $ ; B% ; = < d< . EB d [ S; H B A ; plot F legend F $ U L % =* ( aY% b %. %1 S 7l . , IJ K L %. % 1 S 7 l !( J S m% fS axis, F $ ? [ > _H J T E @N H '^ = < } . L ! S 7 l ' Lb o4ƒ T H B . b \b* ƒo o4 T H B . b E;* ƒ3 o4ƒ H J . b \b* ƒQ o4 H J . b E;* ƒ‚ \. H @ ? Lb F S 7 S [ K % + $ "Y L ! S 7l ';" 8 S [! !( T % •M J U@ L !( c @ U ' ; $ + : %( * b = <7 0` =• [ < % T ]1L $ L; !7 + * + @ • @ U '; @ • @ U b % < _H 'J *H Y $ ? L @ U < % A7* ! L% T UL% • =* % S L !( • ? $ 7 7F ] K7 _+ $ ? L ^ H J H B . L b 0` L % _H J . b H B . b !N .AY J F [ > ; L % _+ $ ? • @ U ! ( ginput F $ B% \<# .l ' ;, @ ) P • 7 ( ;> $ Enter " ' [> < %• !( cIn T [ !( E @N M 7V (@ \; • @ U U 7 * >U * 9 7P [ S; o4 T H B . b E;* '^ T H B . b \b* _ <E8 L ! S 7l' $ ( Ev L % • uST ginput, F $ ? L !( • E; ( @ U LO _H J . EB .9 ) M \<8 !( \<# F ;L% S [ '; K U @ $ P $ P Enter !( cI`U @ ? Y E / . !( cIn P ! ($ U L _" Y Y • _• MeY uST " 8 -U @ P S 7[ * b = <7 K F O OL = N %X&Y ] ; =* X , Y & Z , . _ . O O !( % F O OL =* ! ; L L% ) < _ . 1 • L b T L [! < _R ' P \N % Z . =* _ F , B $ % } ) meshgrid F $ ? [> ! [ > D% $ 7 =* aY% F , B 7 f* $ % ; Y-Axis, H J . @ v d' X-Axis H B . L b < L % 'J … 7? , B T 7 < 'J = < S X-Axis, H B L b @ v d' Y-Axis H J . Lb < L l` T ; F A O OL < plot Ab ( H J . DJ .H J H B ; J S m% meshgrid F \% E; $ B% fS 0` . c F =* !( mesh F $ U L % meshgrid F $ U F E @N $ X-Axis H B . L b D% @ N ST $ 7 b 0` $ 7 ] w d ] * _H B . ; Y = < X • 7 ( 7 N;* >? X & Y ]< • ( Y [ S; Y b e ;= < Y Œ X 6M =• / ' „) -P / I B hb <E8 ( E( Y =? [7* (* ˆ !; • ( H ˆ !; K) =? , ; % R E P ST .: =>? TS * L e @ 7| _} N ( E U T _ E !N { • ! ST _$ % \; H I L b Y%U HV † O@ !( ( 0` H B . 0 [! . h. ) B Y%U _L Curve Fitting ƒ‚ L< \ < B7 _$ < 7 * E @N " 8L _ E !N F U ' ; ƒo 0v c 7 Y%U ƒ3 !( = 7 U ƒQ EVAL =* \ , @ N ln 0M N;* | T A fS eval F T $ T * ;> V _@ F s E J ` L < Sine Wave % e a 1 % Workspace&& aEB F $ [! p U TS aY% string ^ 9 E \Eb 7* ;m ! G% a J% = ; < _ G% t L b D% V % e a1 1 L ? [ > e1 . [ > / 7 =* aY% T , G% ! e1 ) N T + bF [! _ b T 1 n% L % | L ( }.E% LO _+ bF ( }.E !( F \ % } )eval, ;6 7 E ;L%| , @ F sE ; Y K S' U L * !( =• .7 HV = ]N _HV O O \) \) @ ; U !( !( [ > ; 6M Y7 A ; < % =* ! ; \; HV sb @ • . a! % P 6 7 \ ( aY% $ HV ST _ ! coefficients H @ U L % =* • #% ST < B ! ] B _}.E / I B hb ˆU HV H N; >? _ O O \. 6 7 \ $ ] N _$ ; \<# J H ` aY% HV uST \. L b .% =* !( aY% _ O N HV @ ? $ B $ % (_ ; <' aY% [ S "=" ( ( }.E% \Y !<# uS ] ) _H I L b \) Y%P V] * =* x ' $ LO _ \< H I !( , .% fS 9eY D% $ LO _ \< x=1 , y=0,z=0 O N HV xH L b !( \J.7 x=0, y=1, z=0=* x ' LO O N HV yH L b !( \J.7 x=0,y=0,z=1=* x ' LO O N HV zH L b !( \J.7 [>l` L%| DH L b Y%U , E % L _ O N HV H !( !J) b = <7 . !( 6 7 E ; ( \<# ; HV ; 6M O O 0` = < =• $ [! @ P S 7 \ ( ' ; ] )V S m 9 e1F G " ` $ ( ) _ ! E; h7 ; HV HV ( f* \) < % @ V _" Y @ F s E d'7 !( * b = <7 S Zero Crossing ,H B b % L . 0 v sv !( 9 b ˆ M 0` _ L \<# S m =* aY% <'7 7 ( _] !b <' Y%? $ % LO Y=0 • ';" # $ U … .% 6 7 E < _] E% ] ( }.E% fS 6 7 E < $ 6 7 E ; _• [! $ @N 6 7 E ST =m G E } ) _=• • 8 f* ST % b <'% \<# Y = < Digital Domain T Digital Domain, && B% EE ) _ !<# uST aE • ( !( _• ( Y 7U \J c ( E( hB L% f* =* [ > sine wave a Y L 6 7 \ b >U ] N _• [! \ ^ LO _ L T UL \<# ;, \ !b • 7 \<# S 6 7 E X \ Lb [ > ;m ! _ Y \^ • % . $b =? _, ; J e = < _ Y =? 6 7 E d'7 • ( %e L ; †) ;H B . 0 0v 6 7 E \ $ 7 7 ( _0v p =• Digital Domain B% ST = < V =* < _• H t [ T @ e%V @ )9 ) M - $ ( aE T ST _A! Digital Domain ^ < @ F , ; b fS 6 7 E J K Lb =* <' < _Lb !( \J. T , • H B . / c , )U h7 ; >U ,H ` 6 7 =? H B . \' * ; = ; >U _ [! !( 9 ) M 0` L % LO _0v 7 % J < _ 7* } ) %Y d'7 D% F Lb =? 7 ` (, !<# uS ] ) ‘ 7 7 ( =• B . / = = ) ] E1 = <% b * _] E = <% 6 Lb =? H B . h. S a Lb - >U =* f* _] E1 = <% T8 LO y D% s% v ( [ > _ ! • ; y b h7 ; >U ] N _] L ` LO _ ) Lb |S) L 7 \; ; _] '^ Lb = <% =* \n'% _L [! [% . L Lb \ m A !( a !^F c ) b m = < 6% 6 7 E < $ =• ` T !( \; ( `? $ LO @ v* = < „) . .^ h.E^* b 7N sE = < % S . $ !( = ? @N 7= 7 ST $ LO _ < _ h. ) B Y%U L H D% $ })_ H E @ N ST 9eY \ !K $ 7 _ [! )B Y%? $ LO _L T %%1 % * . h. ) B Y%Ptrapz ) B [! \ !K area area F " # $ J S m% } ) [! \ !K LO a Y L ; !( c B @ N S ' K $ J S m% } ) _ . aY h. ) B . h. ) B Workspace S 7 @ Y%U Y%U )B $ B trapz cB 6 7 \ b „) $ F ~ J * H1 LO _ G% [! $ . LO inputs H @ ? $ _uS ' h. ) B 1 LO _ !( = . ) B \ !K $ ; H - _= M #( = 7 % 7 fS 6 7 E U A1 7 =• ? $ LOoutputs UL ; # X "Y L b} N sE = <% S uS ' L uST F 0 sE Curve Fitting Y%U ] 1 T ! uST =* } ) Curve Fitting T F } N E @ N S m =• $ S m outputs … =* „) inputs H ( Y @ U ( ] N _$ K7 fF m < b ( b ( = < „) curve fitting $ U ( *_ . b ( Y V # • ( Y .$ K D ^ E% b ( f* Y V$K 1 • ( Y ^ uST = S! zeros ones T % * " # $ o u ^ ( 0 1 AY * 'J = <% =* 0 B%ones '^ u ^ ( 0 1 AY * 'J = <‡ % =* 0 B%zeros % F ; ; % v J „)V \<# e 6M - „) < < %_ < % p Curve FittingR 7* ( L!< =• * % ( R 7* [ T 1- linear 2- Quadratic 3- Sinusoidal 4- exponential @ F R @ =• * _0 @ F R @ Linear Curve Fitting \b* L B c 7 \; % B = < }. L B c J T# Y%U L % $ K ST 70 H J . b (H J \<# b H B . b \; @ N l` T < . !( 7 \< =? Linear Curve Fitting % v $ B7 7 } ) J a< b uST _H B . !( . HV < $ 7 ; 7 Y J J $ 7 ;0 HV [! \) ( D! ! ; ! $ 7 =* 0 B7 7 ( >? ; < % B7 Linear Curve Fitting && ^ X I ! L b ( Y D% ;S K&T UR 1 ]; b !( !J) b = <7 S ! ]E ] Y b Y ; < % \N X&Y $K! b b b 6 7 E X I ! L N;* !( \J. N;* % = < L $ 7 < 9E ( Y $ Y =• D% b !( @ J. =• $ X b N;* % =* x ' =• 7? ] EB 7 ;> ; X&Y b J \<# ` < % =* } ) Y `U LO Column Vector f ( AY ] EB ! ; ones • ; \. \. U Row Vector DJ AY \% . F $ ? ) A b0 1f ( ^ = < =* aY% K & T L b !( \J.7 ) A7* G E $ K% b =• \ _V 0E € =• [ S; T \ _ 'J A b h7 ; >U l .^ ST < ^ =* f* inv F $ UL%V (\) ! B ( 0` L % hB 'J = < l .J h7 ; >U •; \b* • A % c B [>L \. = <% = < }. ] J 7}. • 7 ( T L = < _ < % D% Y $ =• =? \<# L !( \J.7 T A !% fS s E U\ 7 Exponential Curve Fitting Exponential Curve Fitting X& b ; < % Exponential Curve Fitting , T \<# Y J a< N;* 'J 1 ^ !( 6 7 E 0` T % S uST _ ; < % $ =• 7 F sE N;* H 1 >U =• S m ;6 X K : \n' e 7* b = <7 ST E)* 0 U K Y% =* : @m * _ uST 9 7U !( L 7* fS : <% = _+ ' 1 \ ST O \ Y% =* _A ) B ŒA !( [> A7U _L% < 1 )U . • !E L; * &&&'&& &&&'&&&( &&& &&&)* p .