INEL495 SIGNALS AND SYSEMS FINAL EXAM: Ma 9, 8 Pro. Doigo Rodrígz SOLUIONS Probl O: Copl Epoial Forir Sri A priodi ri ar wav l ad a daal priod al o o od. i providd wi a a 5% d a.- 5 poi: Plo r ll priod ONLY o ar wav plo MUS ild priipal rgio.. b.- poi: Obai pral oii o ar..- poi: Cop a approiaio o i ar wav io ig ii o opl poial io giv blow: ~ C F rl o i approiaio i ival o rl obaid w i priodi ri ar wav i ilrd wi a idal, zropa, low-pa ilr wi ai allowd r, or -o r, al o =.5 F =.5 Hz. a.- Solio: a.- 5 poi Plo ONLY r ll priod o ar wav MUS ild priipal rgio.. plo lod b [, + ] i did a priipal rgio. Hr, = i did a daal priod o ar wav. Pag o
INEL495 SIGNALS AND SYSEMS FINAL EXAM: Ma 9, 8 Pro. Doigo Rodrígz SOLUIONS Pag o b.- poi Obai pral oii o ar. b.- Solio:,, ; C F Z C D F F F F F d d C i F F F F C F F F Z Si Si F F C ; i.- poi Cop approiaio ~ F C.- Solio: i Si i i Si i i Si
INEL495 SIGNALS AND SYSEMS FINAL EXAM: Ma 9, 8 Pro. Doigo Rodrígz SOLUIONS Pag 3 o W prod wi rird approiaio or : ~ F Si F C ~ ~, w arriv a ollowig approiaio or ar wav: o ~ W provid blow a MALAB rip o op ad plo igal wi rld a approiaio io or ri ar wav.
INEL495 SIGNALS AND SYSEMS FINAL EXAM: Ma 9, 8 Pro. Doigo Rodrígz SOLUIONS %Srip o plo approiaio io %Noralizd Sri Sar Wav Approiaio %INEL495 Fial Ea %Pro. Doigo Rodrígz lar all lo all F=; %Saplig r =/F; %Saplig i v=3; %Sigal Draio =-v/::v/-; %i dirizaio ild=ab/+/pi*o*pi*; %Approiaio igr plo,ild,, ild, '.' grid ai[-v/ v/ iild aild]; labl'i i Sod' labl'aplid' il'magid o S. Sar Wav Appro. Fir 5 Co.' Pag 4 o
INEL495 SIGNALS AND SYSEMS FINAL EXAM: Ma 9, 8 Pro. Doigo Rodrígz SOLUIONS Pag 5 o Probl wo: Ordr Ralizabl Paiv -Filr a.- poi: Uig aio giv blow, obai op w ip igal i. U = α = : b.- 5 poi: Uig liar ovolio aio giv blow, ad ipl rpo io, obai op igal w ip igal i : d a.- Solio: Sp Rpo o a Filr Sbiig or ip igal, w obai: d d, odiio a b igrad io olio: d
INEL495 SIGNALS AND SYSEMS FINAL EXAM: Ma 9, 8 Pro. Doigo Rodrígz SOLUIONS Pag 6 o b.- Solio: -Filr Copl Ep. Rpo Uig,, w obai: d d d H * Hr, H * i rl ipli opl oga o r rpo io o ilr. Rbr a r rpo io i pr or Forir raor o ipl rpo io
INEL495 SIGNALS AND SYSEMS FINAL EXAM: Ma 9, 8 Pro. Doigo Rodrígz SOLUIONS Probl r: Bai DSB-SC Coiaio S pr Forir raor o odlaig igal oi DSB-SC oiaio i giv b: i a X,, Orwi 3a.- poi: Obai a aaial orlaio or pr o op o odlaor i rair. Giv a k o pr. Fig. 3: Bai DSB-SC Coiaio S 3b.- 5 poi: Obai a aaial orlaio o pr, Y o, o al op igal o DSB-SC oiaio providd i Fig. 3 abov. Provid a k o agid o pr. Pag 7 o
INEL495 SIGNALS AND SYSEMS FINAL EXAM: Ma 9, 8 Pro. Doigo Rodrígz SOLUIONS 3a.- Solio: Covolio o Spra pr or Forir raor o op o odlaor i obaid ar prorig ollowig opraio: X X X X C X C X X X X X i rl i alo ip o al, d o ollowig a: Y i X H X X B Fig. 3a: Spr o Modlaor Op Sigal Pag 8 o
INEL495 SIGNALS AND SYSEMS FINAL EXAM: Ma 9, 8 Pro. Doigo Rodrígz SOLUIONS 3b.- Solio: Noi Cal Op Sigal Spr pr or Forir raor o op o oi al i giv b ollowig prio, ar prorig propr opraio: X Y i X C X X H X X B Y o Y N X X N i opl io N i pr o addiiv wi Gaia oi AWGN igal. Fig. 3b: Spr o Noi Cal Op Sigal o Pag 9 o
INEL495 SIGNALS AND SYSEMS FINAL EXAM: Ma 9, 8 Pro. Doigo Rodrígz SOLUIONS Probl For: Filrig Dir-i Caal Sigal op igal o a aal FIR ilr d o odl i Fig. 4 i igal [] = [][] + [][ ] + [][ ] + [3][ 3]. 4a.- poi: Cop op igal i ip i prio = {[], [], [], [3]} = {+,, +, }], ad ipl rpo io I.R.F. i dir igal [] = {[], [], [], [3]} = [] [ 4]. Pla, ollowig ovolio prio giv blow or or work: [] = k=+ [k][ k] k= 4b.- 5 poi: Cop rar io o aal FIR ilr. Fig. 4: Modlig a Fadig Cal wi a Caal FIR Filr Pag o
INEL495 SIGNALS AND SYSEMS FINAL EXAM: Ma 9, 8 Pro. Doigo Rodrígz SOLUIONS 4a.- Solio: Dir-i Liar Covolio ipl rpo o i aal FIR ilr i giv b: [] = {[], [], [], [3]} = [] [ 3] Si [] rpr dir-i p io, i giv b:, [] = {, < W vala [] or ad prod o op liar ovolio opraio i ari-vor or o obai []: [] = [] = [] = [3] = [] [] [] = H = [ ] [ ] [] [] [3] H [] [] [] [] [] [] [] [] [] [] [] = [3] [] [] [] [ ] = [3] [] [3] [] [] [4] [3] [3] [] [5] [ [3] ] [ [6]] + = [ ] = + [ ] [ +] + ] Pag o
INEL495 SIGNALS AND SYSEMS FINAL EXAM: Ma 9, 8 Pro. Doigo Rodrígz SOLUIONS 4b.- Solio: rar Fio o Dir Filr rar io o a dir-i ilr i giv b Z-raor o ipl rpo io o ilr: Hz = =+ []z = =+3 Hz = []z = = [] + []z + []z + [3]z 3 Hz = + z + z + z 3 Rprig rar io i poiiv powr o opl variabl z rl i ial prio giv blow: Hz = + z + z + z 3 z 3 Pag o