# 1 - x T\^a,r lJsFrnl LlOn G-^rt\lt(Jt l I fcl...

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T\^a ,r' - lJsFrnl LlOn : G):-^rt ) \lt (Jt l) + I fcl,: El, x frequeny - ?e:ponse An{;sis * Steody stote Qe.sBr"5s 7|- o sgste.,-1 to qSinusoidoL input. input lieq',rc,.,. q Jl ,.+a: L-: t c{Le-qifi ;4J1 ;f" ggt ) " ( c.! | u[*tr r5.:iern -r t 3 l.-, 6*..11 p'ut Jl Tro.sFer tuncti,:',Jl .:(S; &rJ.*:r: eilJq- gqffil i ..(t)= Asin<'rt - xgl_ _. z l-{ cD \ r t**--'----*-F ,€'*:l-l , i,t€ uri tl At sfeadi """ sterdl-stote reTWe b: j* S ia N4 ,r rtC olp _ 1.4 I x(i) X(ul P(s] G(5) = 1{:; !J(>] P(sl ltsl stote P(:) [s+ s 115"5r; - - - (s+s.,) ; Y(s)_. L [as;" "'t] w,_. .'" /L>,: .----\_---v/-"v---'r-r d is cr cr:rnplex = *]j.g5tu * J /^ /. \ Kespon5e 3 \t(lcd) = IJ omplitvde roti6 "F 6"" ond i/p Sincrsoids - GG) xG) * G(s) ud ;-":* '.r -.. * -. ::+j'r"J [ -j* {he ofp ernd i/p X sinosoids. - r.r2 t -'.* -- "l- _.. - J?_.4 LA J ho:e -J (rJL c" !(t\ - o'3 -ts l-\. P I bcl|{fcf b" -t -*--- 5 -t 5n a+' bnC {t>o1 lcrJ L- cCa -+

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fst-hie <- 5q\$em i-".1 gd LRe"l Sgstern =,,- - rri' t' f*?,,t i,i*rt?i"'] -.'l 1,c.r 4;{,i* Z f +-:y 1 - %rt] -:t ;;\$ s, rtl. , --- .,:,',, f;-:J ""' |.. , [-of o St-oble tJ Jte of t -+ co -5.tt ol I terrn: * ," -->Zeta [[:':l --]tr -j*t Jurt 5rr.= oe- + ad -l I ltr rl-" .!-r' -i0 = lGti-116'' : JQv" -o l turt+ O) -j (*tr*f) -l ^ -^. I ar-,)PgD d* (JYJ o = Jitl (s-j,,) G(:) ;:?-:.J : -A-=1!Jg i31rt * = h,-g*j-; Gcs) *!e8- = - 49-cJ-) i'ry- S " /crir) = ron': Ji;'":;.'-it.r:_l-'] . -i cb atrr..,r-jd :, A= 4leg-llej+ -'. q -- -5- lbruurrlE 't ..: - Zi ' 1J q61-;-tl e js J hi.;t r G(-1.'r) = .!1, i.^ In L9: .x 5r, = A \GU,")l -e"-.*.= e--- - .' 2j - A lGtl")l sin('ut*P) = r,,_, . sinmoid ol olp jt^, s;" (u:t+cP) i-,itn phns. d iFFerent omplif"dei3 5h; Ft '(@) ff The rrP G(j,.r)
\Gtior\ = \+iil * r x(jd i" lgP = G(i,r)-+ X(jt') , r- +ft j Phase leod xQ{ ' L.-ve : phase \T colled sinusoidal tro'nsGer F.rnction (c-omplex qucrifiU ) KXt^l (rs"')C+'*) Y0-) Xu) St+.r)a r-l<.I\ | \J-tTl s. Y(st = Gts) - x[s) = =+ ' -T-S +l br o +# -t : -J t^r 5*j_ Q= A GC.i."l 2j A Gti.) j-t L. - t/r 6e + +e _Llr. I p \- --'>t llfo -i"'t iwt e- * de- **'* a= - ( *,u+":t xl< XK z1 G(,--) ( t+jwT)(zj) (r --;.,rrXzj)

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'; G(ju:) = " (\= w"- t f- 64lttb ...1:-ljt ,i-Jeb.i- ti nblr ui-s t" J+ a44JlJ.ije4rl L,';+ -,-- \!rltJl -:-::y't uh"st'<,\$ l-,-tfif Gr:ro ,rr,-ir 1"j-f fg' ,r, xl ) ,-__,f _ <^rTl + g): .ron t _f_J = - ton '(.,tf) imj port -.loi;' L-(L"j in phose) e'* 2J ij-\t-,rr lec"1*r1 I io zJ {'.Gt' e Yss. . / L | -l -\ Sro(a/L - ton (^rl / sgstemotic 1r;" ;r,i.r:."- .,"3,--- &€r,tP - ,,b * o-rrf, Vla: e,-i" 3i Oul*-s jU-gLaIo) P{dl OJ €r G(s) - x(t) - x Firnl ons,^jer, -l \r::_ J -t- lr J 1' -i' IL >tn Crl L t, Sin[i.tt *ton'It-r t -l .-r \ - ton ts.JJ) I + (u,rT)' Xlz
,f) , ,-\.

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