!" ! " #$% &'( )*+ ,-./ 01234567(897 :';< =>6? =>6? (* @AB?C D ,E1.F' *+ ;GH(5I 0BGJ K "L " M1NO.P 01234 #$% &'(567(89Q ,/+ 1Q # @71R1FS8J (* @AB? C D =J TI ;U( 1' V56WF7 TI (* =O.P 1' +8%# X1-P 1Q V56WH D 56WH YH*+ "KZ " [;O6P 1Q @H ='1NO-./ @Q \ ] @OF7 ^NJ *16.Q _ # ] `'(* a1b1cOS( _ d9eJ f+;HVX( 56WH ,/+ *16.Q C g($'$E h( M*16.Q @F'+8%# 1Q =OI *+ ^b h1Q V5Wb1Ui a1F7 &'( h( V*8FWH @.>% """ K " ,# *+? @#%> =A) +'B C7D1 5E 2# @!> 5E $; F( =># *+? GH:1 < *+? 8+'" FIDJ 0K LM1 8!MNOP5> F" Q ?5*@8?(@ A)(B *+ 56$78 ( ) ( )tE t , t x t dtt= 2121 2( )NE N , N x[n]n N==2121 2 ?(@ A)(B *+ '8"9( )( ) E t , tP t , tt t=-1 21 22 1( )( ) E N , NP N , NN N=-1 21 22 1+1 ? A*5)* >4.B6 C#)D 3EF G3H! ='#D 8;/. ( ) ( ) x t T x t + =x[n N] x[n] + =? =I#J K> +,#$6 L3/ #M$6 CT C>50 =NO! P T ='48 ? =I#J K> DT P N 1>.Q .;#0 PC>50 =NO! 30 R,SQC/DE ./#0 TD8F . ; T WTTa=03U4 x[n] #0N0430 P./#0 +,#$-!1 x[an] D45V& =/4> T WNNa=0 ? =I#J K> DT )D P & AXNa0! R>#' YZ)! .J #6 4K( $[& T 7 , \K5] #6.*5/",4>4.Q4,>3DPG3H! 8@8 4K> ; R./R>#'3E[^\K5]P\K5_$Na0P +,#$6 RK,> C#)D x[an] ='48J"KL# !"#$%ba bq qxq dxln aa-= b a bq qnqqn a+-=-=11 +$%< M/. P%$Q#PR(K7 5(HI(=>/.( )atx t ce =nx[n] c = aS T PU/UVW T P."=/.( ) ( ) ( )j tx t e cos t jsin tw= = w + w00 0( ) ( )j nx[n] e cos n jsin nw= = w + w00 0? PXE8 ;5/ 8 ? e;4fc4 #0 w0\43&&g6 =Q3' P x[n] ()* >#;9 #!,fI>5/ 8 ? !(=>/. '8"9 j te w0 P PT= =1 ? "#$%&' C456j ne w0 P PT= =1 ? P."=/. 5(HZ/7"#*([Y( ) ( )jk tt e,kkwf = 0Z? P."=/. 5(HZ/7"#*([Y 7 n 3DN0>.Q (I45-! @jk n[n] ekwf =0 ? '8"9( ) sin t w0< ( ) cos t w0 P PT= =12? '8"9sin[ n] w0 = = 50 .D45V8^R$Q9 Yt t trect *rect L = t t t t 1 iXj# `B(9? j0#6 K>t L t P t 2 ='4 kI#l 1#$Ml7 8 t ='4 rsO! Y&;#l , q#0 .J8 @

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v

5(HK-1/. LTIK-1/. '(#) *+ ,-."/0 5(H K-1/. '(#) *+ ,-112 5(H 5(HK-1/. N/K[8 LTI Y * @ 1#M)-E&' %&sv6 LTI R>#'='4 36 8 < @ 19#EI.! =&s0#` )-E&' #0 (:;f&c 1#M )-E&' 1#M LTI,7"K7 J"KL# l*"wB `B(9 xR([ Y ( ) ( )( ) x t x t d+= t d - t t-x[n] x[n] [n k]k+= d -=- yd"I"7(4 !8$>-78 Y yd"I"7(4 `Kz Y( ) ( )( ) ( )( ) y t x h t d x t h d++= t - t t = - t t t-- y[n] x[k]h[n k] x[n k]h[k]k k+ += - = -=- =- ? >,.J Y&&B6 K>t A0< (! Aw56 A-:*T&$F W * } (*#/5&)D =&Bi, ('K307 1#$Ml A0 Aw56 #0 %&' $ #MI# @< } C>50 Ao0#i TD 3U4 ( ) x t ,( ) h t P.$/#0 R+;, j0456 .`#c( ) y t >50 .D45V A-'5&l8d "I8"7(4 3Kp *+ Pj=@ "{p | Y ( ) ( ) ( ) x t * t t x t t d - = -0 0x[n]* [n n ] x[n n ] d - = -0 0 K> C>3F 5I45*#F ( ) u t 94 13&%I43%-*4 ">#B! P - #6t (!./#0 8 ,&`> \K#NQ A0 36 W K> C>3F 5I45*#F u[n] 94 13&U#)%&' ">#B! P - #6n (!./#0 8 \K#NQ A0 ,&`>36 W( ) ( ) ( )t tx t *u t t x d-- = t t-00 n nx[n]*u[n n ] x[k]k-- ==-00 } "I8"7(4 ?8"@* } Y/5I5*#F -3Q< } (;#"0#w 7 1>,K, , A03i .'#l 1#w ^(;#"0#w @/ } 13;tl =F3/ 7 13' 1#M)-E&' @0 } j)w 1,K 13;tl j;956 7 1945! 1#M)-E&' @1 } ,-X! W( ) ( )( ) ( )( ) dy t dx t dh t*h t x t *dt dt dt= = )* 5 W( )( )y[n] y[n ] x[n] x[n ] *h[n]x[n]* h[n] h[n ]- - = - -= - -1 11 ^R$Q9 AxY( ) A x t dtx+= - A x[k]xk+= =- !5X* |5!43c ,so! K.` 8LTI $Rq0 ' nI>#B! DT (sF =I#J K>W( ) ( )M Na y n k b x n ik ik i- = -= = 0 0 ,/{( Y (*#!9 #M$6 P=0#z h;43i #0 (oV %&E*43;> AI>#B! a'56 R./ C#&0 T-E&' ); LTI ./#0 A&I,4 C5:' K> T-E&' AF ='4 (sQ ,7 W t01>,K, "#)Q4 nuvI@( ) ( )( )( )ny t y' t ... y t-= = = =100 0 0 ,/{( Y (*#!9 #M$6 P=0#z h;43i #0 (oV k*3;> AI>#B! a'56 R./ C#&0 T-E&' ); LTI ./#0 A&I,4 C5:' K> T-E&' AF ='4 (sQ ,7 W t01>,K, "#)Q4 nuvI@( ) y[n ] y[n ] ... y[n M ] = - = = - - = 1 1 00 0 0 M T;K4> A&I,4 L3/8P4"XB xR(K7 )R(0 $E(=p~ @ > R.$$F +3i3I#:'4 K 8 @ R.$$F j)w 9 @ 3&%b-X! ~ @3I#:'4 K> R.$$F +3i 8 @ R.$$F j)w 9 @ R.$D> 3&V#6

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LTILTI LTI LTI LTILTI n-1/.b l&+(Q# ,R!L9 /.,R!L9 )I+(Q# e/4$9 )I+(Q# ,R!L9 )I+(Q# e/4$9 )I+(Q# 3c ~ }( ) x t cos k tdtkTTa = w0200,( ) x t sin k tdtkTTb = w0200 x(t) =DCK4.b! < ( cos k t sin k t)k kka w +b w =0 01 3c < }( ) B x t cos k tdtkTT= w0100, ( ) C x t sin k tdtkTT-= w0100 x(t) =DCK4.b!< (B cos k t C sin k t)k kkw w =20 01-P9(jXj# )R*"% 5$.7 =I#J K> abc CT @? 5c 13' (6#OsO! %:/ 1430 abc PA;K ( ) x t (! C#&0 (b&bJ 1#D >5/ 8? 3c ~ 3c , K4.! , \#&i#;K =,K> K> q5)B! P 8 (! K#:0 "#$%&' =K> K> q5)B! P >,K 7 8 3c 94 q5)B! Y! ~ (! R>#-'4T$F 8@8? no04K \K5_0 A;K5c 13' h;43i jk ka B jCk k ka- b= = +2(!./#0 8? K> =K> K4.b! P('.$M! (i#;KDC 30430 4K "#$%&' a02(! y;3B6K4.b! PT-E&' , "#$%&' =K> K> (I, .$$F DC 30430 4K "#$%&'a0(! y;3B6.$$F >>>? (! ('5$&EF , ('5$&' h;43i C./ 3] rQ#0 h&636 A0 P>3c , G,9 CK#b6 .*5/ 8? CK#b6 M"# n/7 3] rQ#0 P C./ h;43iM5/ 7 8 >>3U h&F36 (sN` n-:* #0 @8? nN'#v! 1430 ( ) H jkw0PT-E&' (E*#F3c .'#l 1,K 94( ) H jw n;K5c %;.N6 C#)D #;( ) h t =E&c#F P ( ) H jw KK> 4 C/DE ;*({# w0T&0#&0 8,R*"% 5$.( )jk ta x t e dtkTT- w=0010 J .$-ED #)%&' \K5_0 RK45)D #M;3' 7 8 (:; f"0 @( )jk tx t a ekkw==-0 C ='4 +,#$6 ); 1,K P#M;3' #)6 >,.J 7 8 (:; f"0 @jk na x[n]ekNk N- w==< >0010 6 RK,> #0 +,#$-! +,#$ N0 jk nx[n] a ekk Nw==< >00 ,R*"% 3Ro~9 ( ) ( )j tX j x t e dt+- ww =-( ) ( )j tx t X j e d+w= w wp-12 ( )j j nX e x[n]en+w - w==- J \K5_0 RK45)D #Ms;.N6 "43%-*4 .$-ED7 8 (:; f"0 @ +,#$6 RK,> #0 +,#$-! p 2( )j j nx[n] X e e dw w= wpp122 C ='4 C43:&0 P#Ms;.N6 #)6 >,.J 7 8 (:; f"0 @ ak#D , X .$os-H! #D 8 a0#D ,( ) X 0 #D b! P ;># 3 DC "#$%&'.$-ED 8h

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( ) ( ) X z Y z, min ofR R 1 2 Z

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( ) x tt WA"&-* **a ak k= - WA"&-* < ( ) ( ) ( ) ( ) Re a Re a,Im a Im ak k k k= = -- - WA"&-* / a a, a ak k k k= = -- - F.S. WA"&-* * ( ) ( )*X j X j w = - wWA"&-* < ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Re X j Re X j, Im X j Im X j w = - w w = - - wWA"&-* / ( ) ( ) ( ) ( ) X j X j ,X j X j w = - w w = - - w F.T. x x* = ($B; x ./#0 (b&bJ87 CT #;DT ()* (`3c P .$F @8? D>#)* P(b&bJ 1#MI#$%&' 1430 1# * ,@ (! T&D45H0 #"F 3D 4KT;K4t%0 T&*456 8Fb? RK45)D P(b&bJ 1#MI#$%&' K> 1#M-)E` ?

1#M-)E` ?=0J0= ,4-K CK#b6 P#Ms;.N6C!K .*K4> ? K> AF (-I#J x 43`30 q#0 a04,K C#)D P./#0 A-EEU (I#$%&'1#w A0 abc .*K ( ) X jw 94 P( )jX e w(! R>#-'4T&$F 8ak='4 G,9 , (b&bJ8*a a ak k k= = -

F.S.( ) ( ) ( ) x t x * t x t = = - ( ) X jw ='4 G,9 , (b&bJ8( ) ( ) ( )*X j X j X j w = w = - wF.T. Or ( ) X s >5/ (! >3c (B0#6> L

[ ] [ ] [ ] x n x* n x n = = ? K> AF (-I#J x 1#w A0 abc .*K43`30 q#0 a04,K C#)D P./#0 A-EEU (I#$%&'( ) X jw 94 P( )jX e w(! R>#-'4T&$F 8ak='4 >3c , (!5D5!8*a a ak k k= - = - - F.S. ( ) ( ) ( ) x t x * t x t = = - - ( ) X jw ='4 >3c , (!5D5!8( ) ( ) ( )*X j X j X j w = - w = - - w F.T. Or ( ) X s (B0#6G,9 >5/ (!> L

[ ] [ ] [ ] x n x* n x n = = ? K> AF (-I#J x 1#w A0 abc .*K43`30 q#0 a04,K C#)D P./#0 A-EEU (I#$%&'( ) X jw 94 P( )jX e w(! R>#-'4T&$F 8( ) ( ) ( ) ( ) Re a jIm a ev a odd ak k k k+ = +F.S.x x xe o= +( ) ( ) ( ) ( ) ( ) ( ) Re X j j Im X j X j X je ow+ w = w + wF.T.

-3c #0 x (b&bJ Fh? Re , ev A0 L503! A;K5cxe, .$-EDIm ,odd A0 L503! A;K5cxo.*30430 PR./ A-/5* h&636 C#)D A0 , .$-ED>!8".*(0 )uB8*[ ] P x n ax kNn N k N= = =< > =1 2 200 0 F.S. &' 1430 "#$% D>-EF= [ ] x n ( ) P x t dt ax kTT+= = -1 2 200F.S."#$%&' 1430 D>-EF= ( ) x t[ ]( )jE x n X e dxn+w= = wp=-p21 222 F.T.

"#$%&' 1430 -5D>-EF= [ ] x n( ) ( ) E x t dt X j dx+ += = w w p- -1 2 22 F.T. "#$%&' 1430 D>-EF=-5 ( ) x tPR+, )-Z7 Y %;.N6 1#D DT 7A;K5c %;.N6 TD , 13' TD @ R4K5)D P o=B