Chpr 5 Fourir Alysis 5- Fourir Sris o Prioicl Fucio Vio Empl o Fourir Sris o Prioicl Rcgulr Fucio: Vio Empl o Fourir Sris o Prioicl Swooh Fucio:
Fourir sris: ( is prioicl ucio wih prio i o irvl: -. (( h ( b si whr ( ( b ( si cs ( is o v b Prsvl s iy or Fourir sris: ( [ ] b Orhogoliis: m m m m m si si m Eg. Ep ( (( io Fourir sris 5 (Sol. ( (( Ev ucio b ( ( ( ( ( ( si ( ( 8 : o 8 [ ( ] m ( m : v ( ( ( 8... 5 (... 5 7 8 8... 5
Mlb lgug w c us h ollowig isrucios o obi h ii sum o ( ( 5 8 (i - (. (i i >> :.:*pi; y; >>or i:5 yy-8*((*i-*pi*//(*i-^/pi^ >>plo (y 8 - ( 8 8 5 5 8 5 7 5 7 8 5 7 9 5 7 9 ( ( 6
(Sol. ( b ( b Eg. Ep ( (( io Fourir sris. Fi ( ( m (b m ( m. [ 文化 m ( m 電機轉學考 ] si. O ucio ( si si si ( [ ( ] ( [ ( ] ( S ( [ ( ] si (b ( [ ] b si... 5 7 9 [ ( ] 5 7 m m ( ( m... 5 7 9 6...... ( m 5 7 m 8 (... 8 (... 5 7 9 5 7 9 Mlb lgug w c us h ollowig isrucios o obi h ii sum o [ ( ] si 5 (i si. i (i >> :.:*pi; >>y; >>or i:5 yy*si((*i-*pi*//(*i-/pi 7
>>plo (y si( [ ( ] si.5.5 -.5 - -.5 6 8 6 [ ( ] si 8 [ ( ] si [ ( ] si [ ( ] si [ ( ] si [ ( ] si 8
k Eg. ( Ep ( (( io Fourir sris. (b k Fi... [8 台大電研 5 師大電研與 7 台聯大電研 5 7 9 類似題 or k] k k (Sol. ( ( ( b si. O ucio k b ( si si si ( k k k k (b S / k k k ( si... 5 7 9... 5 7 9 ( ( ( si ( 9
Eg. Fi h Fourir sris o ( < < < si us h rsuls o show h... 5 5 7 7 9. [ 台大電研 ] (Sol. [ ] [ ] ( ( ( ( [ ] > si( si( ( ( si( si( si( 6 57 ( ( ( ( si( si( ( si( ( ( ( ( ( si si ( ( b b ( ( ( (6 (8... si( 5 5 6 ( ( ( ( ( (... 5 5 6...... 5 5 6 5 5 6 b... 5 5 7 7 9
Mlb lgug w c us h ollowig isrucios o obi h ii sum o ( ( (6 (8 (... si( 5 5 6 599. >> :.:*pi; y/pisi(/; >>or : yy-*(**/pi/(*^- >>plo (y si( ( si( ( ( si( 5 ( ( (6 si( 5 5 ( si( 5 ( si( ( si( ( si(
Eg. Fi h Fourir sris o ( clcul ( [99 交大材研 成大電研 ] (Sol. ( ( ( ( ( ( ( ( ( ( [ ] ( ( ( ( si si ( ( ( ( ( ( si si ( ( ( ( Ev ucio b ( ( ( ( (b ( ( ( ( Mlb lgug w c us h ollowig isrucios o obi h ii sum o ( ( 6. >> :.:*pi; y/pi; >>or :6 yy*(-^(*(**/(*^-/pi >>plo (y
( ( ( ( ( ( ( ( ( 5 ( ( 6 ( ( ( (
Discr spcrum o (: si ( b c c 5- Fourir Trsorms vrs Fourir Trsorms Fourir Trsorm pir i i Egirig: ( ( [ ] ( ( ( [ ] ( F F F whr ν. Fourir Trsorm pir i i Mhmics: ( ( [ ] ( ( ( [ ] ( F F F whr ν. Fourir Trsorm pir i i Physics/Opics: ( ( [ ] ( ( ( [ ] ( G G g g g G
Prsvl s iis or Fourir Trsorm pirs [(]F( [g(]g(: * ( F( ( ( ( ( g * F G Coiuous Spcrum o (: ( F ( Covoluio i Fourir Trsorm: ( τ * g( τ ( τ g( τ τ τ Corrlio i Fourir Trsorm: ( τ g( τ ( τ g( τ τ τ Bsic horms o Fourir Trsorms [(]F( [g(] G(:. [(bg(]f(bg(. [(][F(/]/ - [F(][(/]/ > (Proo For > l u [(] F[( ] ( (. [( ]F(- - [F(-]( ( ( ( u ( u u (Proo [( ] ( ( ( F(-. [ (] F( [ ( (]( F( i cs o (± (± (± (Proo [ (] '( ( - ( - ( ( - (- (- By mhmicl iucio w hv [ ( (]( F( i (± (± (±. ( F( 5. [(*g(]f(g( 6. [g*( (]F(G*( whr g*( G*( r h compl cougs o g( G( rspcivly. 7. [(-] - F( - [ - F(](- (Proo -u [(-] ( ( ( - ( ( ( - u ( u u - F( 5
8. [ (]( F ( ( (Proo [(] ( F ( By mhmicl iucio w hv [ (]( F ( (. ( ( 9. [δ(] []δ( [ ]δ(- Eg. Fi ( [] (b [ ] (c [si(] ( [(]. (Sol. ( [δ(] - []δ( iii δ( δ(. iii δ( iii ii( i( b rplc by u - b rplc by v w hv δ(v bcus δ( is v ucio. u b rplc by v b rplc by w hv iii []δ( (b [( ]F(- [ ]δ(- (c si( iii iii [si(] [ iii iii ]-i[δ(--δ(] i i[δ(-δ(-] ( ( iii iii [(] [ iii iii ][δ(-δ(]. i iii δ(-v Eg. Fi [ - ] [ - ]. (Sol. [ ]. For [ ] ( - F( [ ] Or ccorig o [ ( ] F ( 6
Eg. Drmi (Sol.. [ 成大電研 ] Eg. Fi ( [ - ] (b [ - ] (c ( ( (. [ 文化電機轉學考 ] i ( ( (Sol. [ ] [ ] ( ( ( Accorig o ( i F i i [ ] i [ ] i [ ] ( ( 6 (b [ ] (c 9 ( i i [ ] i si m ( R ( ( S ( ( ( ( Eg. Fi h Fourir rsorm o (. [7 台聯大電研 ] < (Sol. ( 7
Eg. For wo rcgulr ucios: ( g( i ( [(] (b [g(] (c 大電研 ]. (Sol. ( [ ( ] si ( i i i [ 文化電機轉學考 ] i i i si [8 成 i i ( si( i (b [ ( ] F > [ g ( ] (c ( si si i ( Accorig o ( F( ( si ( si si( si ( si 8
9 Eg. Fi ( b. (Sol. [ ] i ( i ( i. S u- u iu S u i ( F( ( [ ] ( F ( b i b Eg. Fi 9 (. (Sol. 9 9 ] [ i i ] si( [( 6 ( (...... m R. S w hv ( 5 Eg. Drmi ] [. [ 台科大電研 ] (Sol. ( [ ] ( ( F ] [ ] [ ] [ - ] [ ] sg( [ < ( u
Eg. Fi (. (Sol. u u u ( u v r No : uv rrθ o o ( F( No: ( g( r similr o ch ohr. Bu hir rspciv Fourir rsorms look qui ir! Eg. Drmi [p( ]. [ 台大光電所 ] p (Sol. /p /p - /( -p / [p( / ] p. 5
Eg. Drmi [ b ]. (Sol. ( ( u ( u u u ( u u - b (simulously h u b b b [ b ] b b ( ( F( [ ( ] si( Summry Empls - [ ] [ ] 6 [ ] c. 9 9 c. ( ( ( 6 ( 9 6 c. 5