AALISIS FREKUESI SIYAL DA SISTEM
AALISIS FREKUESI SIYAL DA SISTEM Alisis Siyl dlm Sptrum Frusi Alisis frusi siyl wtu otiu Alisis frusi siyl wtu disrit Sift-sift trsformsi Fourir Domi frusi sistm LTI Sistm LTI sbgi filtr
Alisis Siyl dlm Sptrum Frusi Pristiw Disprsi Alisis Frusi
Chy Prism Wr Siyl Mtmtil Tools Siyl siusoidl Sph ECG EEG Istrumt Softwr progrm Pith Dyut tug,, Trsformsi Fourir
Pd thu 8, Josph fourir, hli mtmti Pris mmu bhw Stip fugsi priodi siyl dpt dibtu dri pumlh glombggmbg sius/osius
t= os*pi*5*t +os*pi**t + os*pi**t +os*pi*5*t
Siyl wtu sbgi hsil pumlh bbrp siyl otiyu dpt diyt sbgi dim: = bilg itgr positif A = mplitudo siyl siusoid ω = frusi sudut dlm rdit/dti θ = fs siyl siusoid
Cotoh: Bri pls trhdp siyl yg trsusu dri prsm briut ii:
Jwb: Dri prsm dits didpt 3 prmtr siyl yitu: Amplitudo dlh A, A d A3 Frusi dlh, 4 d 8 rdi Fs dlh, /3 d /
Dg mob ili-ili mplitudo sprti briut ii it dpt btu siyl yg brvrisi. A =,5 A = A3 = b A = A =,5 A3 = A = A = A3 =
Siyl wtu otiyu dpt diyt dlm btu sposil ompl, yitu
Ji Didfiisi: M:
Alisis frusi siyl wtu otiu Drt Fourir utu siyl wtu otiu priodi Powr Sptrl Dsity PSD siyl priodi Trsformsi Fourir utu siyl otiu priodi Ergy Sptrl Dsity ESD siyl priodi
priod T T F t p p o t F o Drt Fourir utu siyl priodi ompls dt t T T t F p p o * yt t
t o osfo t os F t o osf t o os sif t o si t o osf t o b sif t o o o os b si t F t o
Powr Sptrl Dsity PSD dri siyl priodi T p dt t T P p Ergiy t trbts, dyy trbts b P o o sbgi fugsi dri frusi F PSD Rlsi Prsvl
4 3-4F o -3F o - 3F o -F o F o F o 3F o 4F o F Powr sptrl dsity dri siyl priodi
Cotoh Sol Ttu drt Fourir d powr sptrl dsity dri siyl puls prsgi pg di bwh ii. t A T p Tp t
Jwb : p p T T p o T A Adt T tdt T p p t F o p T T t F p o p p o F T A dt A T o o p F F p o F F si T A F T A o o
T P ttp brubh ttp T P brubh
Powr sptrl dsity :,,, F F si T A, T A o o p p
Trsformsi Fourir utu siyl priodi t XF Ft df XF t Ft dt Ergy Sptrl Dsity ESD dri siyl priodi Ergiy trbts : E t dt XF df Rlsi Prsvl F XF S ESD
Cotoh Sol Ttu trsformsi Fourir d rgy sptrl dsity dri siyl yg didfiisi sbgi : t A,, t t A t t
Jwb : XF S F A A Ft dt A si F F si F F
t XF
Alisis Frusi Siyl Wtu Disrit Drt Fourir utu siyl wtu disrit priodi Powr sptrl dsity psd siyl disrit priodi Trsformsi Fourir utu siyl disrit priodi Ergy sptrl dsity sd siyl disrit priodi
Drt Fourir utu Siyl Disrit Priodi f f s s / priod dsr /
Cotoh Sol 3 Ttu sptrum dri siyl-siyl di bwh ii.. os b.,,, 3 Jwb :. f o 6 os 3 os 6 4 6
5 6 / / 6 / 6 / 6 os 6 / / 6 5 4 3 o
5 6 o 3 4
/ 3 4 / 4 4 4,,,. b / 4 4 3 o
o 3 4 4
Cotoh Sol 4 Ttu sptrum dri siyl di bwh ii. Jwb : os os 3 3 si si 5 5 os 5 5 si 3 5 5 / 5 5 / 5 3 / 5 3 / 5 3 / 5 3 / 5 5 / 5 5 / 5
5 5 / 5 5 / 5 3 / 5 3 / 4 5 / / 5 3 3 5
/ 9 o - 9 o
Powr Sptrl Dsity PSD siyl disrit priodi P Rlsi Prsvl psd Ergi stu priod Bil yt : E *
Bil gp / / / Bil gil / / / / gp,,,, / gil,,,, /
Cotoh Sol 5 Ttu ofisi drt Fourir d powr sptrl dsity dri siyl disrit priodi di bwh ii. Jwb : / L A /
A L / AL A L / / L / / L / / L/ L / L / / / si L / si /
liy, / si L / si A,,,, AL A / L L / liy, / si L / si A,,,, AL psd
Trsformsi Fourir dri siyl disrit priodi X X Btu Drt Fourir X X d
Cotoh Sol 6 Ttu siyl disrit yg trsformsi Fouriry dlh :, X, Jwb : X d d
si si d
X X si
Ergy Sptrl Dsity ESD siyl disrit priodi E X d Rlsi Prsvl S X X X X X Sptrum mgitud Sptrum fs yt X * X X X X X
Cotoh Sol 7 Ttu rgy sptrl dsity dri siyl disrit : Jwb : u X X X S X * os S
Cotoh Sol 8 Ttu trsformsi Fourir dri siyl disrit : A, L, liy Jwb : X L A A / L A L si L / si /
L / X / si L / si A X liy, / si L / si A AL, X / si L / si L A X
A = L = 5 Sptrum mgitud Sptrum fs
Hubug Trsformsi Z dg Trsformsi Fourir Trsformsi Fourir : Xz z r [r ] z r r z z z r Xz X Trsformsi Fourir pd ligr stu = Trsformsi Z
Cotoh Sol 9 Ttu trsformsi Fourir dri : u Jwb : z Xz z z z X z z / / / / r r / / os / /
Klsifisi siyl dlm domi frusi Siyl frusi rdh :
Siyl frusi tiggi : Siyl frusi mgh bdpss sigl :
Drh frusi pd bbrp siyl sli Siyl-siyl biologi : Tip siyl Drh frusi Hz Eltrortiogrm - Eltroystgmogrm - Pumogrm - 4 Eltrordiogrm ECG - Eltrophlogrm EEG - Eltromyogrm - Aphygmomogrm - Sph - 4
Siyl-siyl sismi : Tip siyl Drh frusi Hz Wid ois - Sismi plortio sigls - Erthqu d ulr plosio sigsld. - Sismi ois, -
Siyl-siyl ltromgti : Tip siyl Drh frusi Hz Rdio brodst 3 4 3 6 Shortwv rdio sigls 3 6 3 Rdr, sttllit omuitios 3 8 3 Ifrrd 3 3 4 Visibl light 3,7 4 7,7 4 Ultrviolt 3 5 3 6 Gmm rys d -rys 3 7 3 8
Sift-Sift Trsformsi Fourir Sift-sift simtri dri trsformsi Fourir Liirits Prgsr wtu Pmbli wtu Torm ovolusi Prgsr frusi Difrsisi frusi
Sift-Sift Simtri dri Trsformsi Fourir X } {X F F{} X X F si os si os
] si os [ X ] si os [ X R I I I R R X X X R I R d X ompls ]d os X si [X ]d si X os [X I R I I R R
yt I R X X si X X X os X I I I R R R si si os os X X X X I I R R X X *
X X tg X X X X I I I R X X X X ]d si X os [X gil d si X gp d os X ]d si X os [X I R I R I R
yt d fugsi gp d os X X os X R I R yt d fugsi gil d si X X si X I R I
imir muri ]d os X si [X os X si X I R I I I I R I R
imir muri d gp d si X X si X R I I I R I I imir muri d gil d os X X os X X I I R I I I I I
Cotoh Sol Ttu d but sts X R, X I, X d X dri trsformsi Fourir : X Jwb : X os si os
R os os X I os si X I R os os os si os os X X X os si tg X
Liirits X X X F{} X } F{ X } F{ Cotoh Sol Ttu trsformsi Fourir dri :,,,, Jwb :
X X os X X X
Prgsr wtu F{ } X F{} X Pmbli wtu F{ } X F{} X
F{ } X * Torm Kovolusi F{ } X F{} X X Cotoh Sol Ttu ovolusi tr d, dg : = ={,, } Jwb : X os
3 os 4 os 3 os 4 4 os 4 os 4 os os X X X os X X 3 X } 3 {
F{ } o X Prgsr frusi F{} X o Torm Modulsi F{ } X os o o o o o F{} X X o X o
Difrsisi frusi X } { F d dx {} F } F{ d d d d d dx X
Domi Frusi Sistm LTI Fugsi rspo frusi Rspo stdy-stt d rspo trsi Rspo trhdp siyl iput priodi Rspo trhdp siyl iput priodi Hubug tr fugsi sistm d fugsi rspo frusi Komputsi dri fugsi rspo frusi
Fugsi Rspo Frusi ] [ha A ha y A ompls Iput h y AH y h H Eig futio Eig vlu
Cotoh Sol 3 Rspo impuls dri sutu sistm LTI dlh : u h Jwb : Ttu outputy bil mdpt iput : / A H H H h F /
6,6 / / 6,6 6,6 o o o 5 A 5 A AH y 5 H Amplitud Frusi Fs 3 H A A 3 y
si os h h H H H I R si os I I I R R R H H h H H H h H I I I R H H tg H H H H
A H A H y A A H y A ] os[ ] [ os ] [ ] [ A H y y y A A A ] si[ ] [ si ] [ ] [ A H y y y A A A
Cotoh Sol 4 Rspo impuls dri sutu sistm LTI dlh : h u Ttu outputy bil mdpt iput : 5si Jwb : H os
3 5 / 6,6 H H H H o os 3 4 si 5
Cotoh Sol 5 Sutu sistm LTI diyt dg prsm bd : y y b. Ttu H b. Utu H ms d,9 Ttu y bil iputy : 5 si os 4
Jwb : u b h b y y b h H os si os si os tg os si os tg b b H
b b H H ms os si os tg H H o tg H 4,9,74,9, /,53,9, H
4 os si 5 ] 4 os[ ] / si[ / 5 H H H y ] 4,6os[ ] 4,888si[ 5 y o
Rspo Stdy-Stt d Rspo Trsi y y y y A y y A A y y A
A y y A A y y A A A y y
Rspo trsi Rspo stdy stt A A y y Stbil ss AH A y y lim tr A y y
Rspo Stdy Stt trhdp siyl iput priodi / Fourir Drt / / H y H H / H y y H d d y /
Rspo Stdy Stt trhdp siyl iput priodi Tori ovolusi Y H X Y H X Y H X Y H X S H S yy Ergi: E y H S d
Cotoh Sol 6 Sutu sistm LTI mmpuyi rspo impuls : u h Ttu sptrum d sd-y bil mdpt iput : u 4 Jwb : H 4 X
4 X H Y 6 4 4 S y yy X H S os 6 7 os 4 5 S y
Hubug tr fugsi sistm d fugsi rspo frusi z H H z z h H * H H H H H HzHz z
Cotoh Sol 7 Sutu sistm LTI diyt dg : y,y,y Ttu Jwb : H Hz,5z z,z HzHz,5z z,z z,5z,z
,z,5z z,z,5z z HzHz z,z z,8z.5 z z zhz H,,8.5 H z,4 os,6 os.5 os H,8 os,6 os.45 os H os os