EEE 304 Test 1 NAME:

Size: px

Start display at page:

Download "EEE 304 Test 1 NAME:"

Luke Hodge
5 years ago
Views:

1 EEE 0 NME: For h oio i ih rafr fio 0.. Fi h rgio of ovrg of orrpoig o:.. a abl... a aal.. Cop h i p rpo x aig ha i i abl..: { 0. R }. : { 0. R } : 0. { aal / / 0. aal 0. aal { 0. R } {0 R } Probl : For h ir i ih rafr fio 0.. Fi h rgio of ovrg of orrpoig o:.. a abl... a aal.. Cop h i p rpo x of h aig ha i i aal..: {0. }. : { } : 0. { } { } / 9 / 9 / 9 { 0. 9{ 9 0. aal aal aal aal aal aal

2 NME SOLUIONS EEE 0 W Coir h filr ih ipl rpo h.. Fi h rafr fio. Fi h Forir rafor of h op h i x. Fi h op h i x b aig h ivr Forir rafor of or ar o par.. Rpa par a ig Lapla rafor 80 / a o R 6 R R / } {. ] [ ]* [ } { }* {i } {. }; {R. 80 / a F F F F F F x F o. i 0 o / / / / / : ; / ] /[ : } { 0} {R 0}; {R } {. L L C B C C B B C B No C B L L L x L

3 Probl : Coir h oio i aal filr ih rafr fio. Cop h rpo of h filr o x[] [].. Cop h rpo of h filr o x[] [-].. Rpa par a for a abl ih h a rafr fio. 6 ] [ 6 ] [ 6 / / / 0} R { 0} {R } R { ;. : 6 ] [ 6 6 / / / } R {0 0} {R } R { ;.: } R {. fi. - o ll } { 0} {R } {R ;. 6 6 / / / } {R 0} {R } {R ; } {R. R R 0 R R R 0 R R R 0 R Sabili Caali

4 Probl : Coir h ir i abl filr ih rafr fio 0.. Cop h rpo of h filr o x[] [].. Rpa par for a aal filr ih h a rafr fio / 0. / } { } { ; 0. } { / 0. / } { } {0. ; 0. } { Caali Sabili

5 EEE 0 Na: SOLUIONS 0. For h oio-i aal ih rafr fio op h folloig:. h apli a h pha of h a-a rpo o a ioi ip x i00 o.. h ir-i qival of a G ig h Baar Elr pproxiaio a a aplig irval of 0... For G op h apli a h pha of h a-a rpo o h ioi x apl a h i ia i.. x i0 o. h a-a rpo i 0 i0 0 0 o h apli i apl. 0 [ 0.0] [0] a a pha a. Baar Elr h biio -/ G. 0. a h a-a rpo i G i 0 G o h apli i apl. G G a a.0 pha 0 G 0...i.o a.o i a Noi ha h aplig ra 0 i o oo fa rlaiv o h ioi of frq 0ra/.6 o ha hr i appriabl rlaiv iffr b oio a ir rpo. hir abol iffr i ill all hovr i h ioi i ll-abov h baih 0.ra/.

6 EEE 0 oor SOLUIONS Coir h folloig :. rafr fio Coio i aal. rafr fio Dir i aal Cop h folloig:. Bo plo xprio graph. Rpo o i for C a i/0 for D. a 6 I a R a i 0. i a a a. Ω Ω Ω l80 a Ω Ω i Ω a o Ω i o Ω 0. o Ω i Ω i Ω a o Ω 0..8i. i Ω o Ω 0.8 i Ω ; o Ω 0.8 i Ω l # Ngaiv R par

7 Probl :. U forar a baar Elr approxiaio of rivaiv o riv h D orpar of h 0. ih rafr fio for aplig i U MLB o opar h p rpo a frq rpo of h iriaio i P.. ih h C rafr fio a i riaio ig h fio ih oh a foh opio. Brifl rib or obrvaio. Forar Elr : Baar Elr :

8 Obrvaio: Fro h bo plo h C-D frq rpo approxiaio ar rioraig abo a bfor h half-aplig frq ax Nqi ra. h Forar Elr gra a frq rpo approxiaio b h i abl. Fro h r h ZO gra h ax lag hil h FO i all o ala h b approxiaio. I h p rpo h ZO ho a o fll p bhi ara a aplig i ol a h FO ig-ag abo h oio rpo. h F-Elr iabili i lar for 0. Zoo i h plo o ail. MLB COMMND ISOR.;*[ ];ov[ -][*-];bf.;[-0.* 0.**];ov[ -][ -*];ff.;oh'oh'foh'foh' bplo pfbohfoh axi[00- ] ;oh'oh'foh'foh' ;[-0.* 0.**];ov[ -][ -*];ff ;*[ ];ov[ -][*-];bf bplo pfbohfoh axi[00- ] 0;*[ ];ov[ -][*-];bf 0;[-0.* 0.**];ov[ -][ -*];ff 0;oh'oh'foh'foh' bplo pfbohfoh axi[00- ] lf.;*[ ];ov[ -][*-];bf.;[-0.* 0.**];ov[ -][ -*];ff.;oh'oh'foh'foh' bplo bofbohfoh ;oh'oh'foh'foh' ;[-0.* 0.**];ov[ -][ -*];ff ;*[ ];ov[ -][*-];bf bplo bofbohfoh 0;*[ ];ov[ -][*-];bf 0;[-0.* 0.**];ov[ -][ -*];ff 0;oh'oh'foh'foh' bplo bofbohfoh

9 EEE 0 NME: Sppo ha a oio i igal ha Z ha i balii o 0. h igal i filr b a lo-pa orr Brorh filr ih off frq 0 /. L h op of h filr b x. -orr Brorh x SMPLING Rorio ial lo pa x Fi h aplig ra o allo prf rorio of x ih a ial lo pa filr. Explai. h Brorh filr aa frqi grar ha 0 / b i o o r h opll. I fa ig h high frq apo for h agi / - hr h off frq i 0 / h agi a 0 i approxial ¼. or xa opaio il 0.. ha i h frqi of b 0 / a 0 ar aa b a o a faor of a ao b oir a gligibl. i gral i ol gara o b balii o 0 a a Z. h for prf rorio h aplig ra hol b a la 0. Probl : Fi h larg aplig irval o allo prf rorio of h igal. i o. i i.. h Forir rafor of h pro igal i h ovolio of h Forir rafor of h iivial igal o h axi frq i 7. h h larg aplig irval i /7.. h Forir rafor of h aio igal i h aio of h Forir rafor of h iivial igal hih ha axi frq ax. h h aplig irval i /.. h Forir rafor of h igal a b fo i h abl a /. hi i o a balii igal o prf rorio i o poibl for a oro --0.

10 EEE 0 W Do Probl fro h xboo. 7.9 p / / 0 0 / p / / / / /0 0κ / /0 0 0κ /0 0 0κ 7. Coir a igal x xp ih /. h folloig h opraio i Fig.P.7.

11 x x i x i a xpoial Lopa ba ; i for a LI ih a xpoial ip x Noi ha fro h la xprio h rafr fio i /-xp- hih i o a fii iioal. Probl : Fi h larg aplig irval o allo prf rorio of h igal x* o ovolio i. i ax ig ovolio of Forir rafor. ax i. *i ax 0 ig h filrig propr a ill o. ax i. i ax. ax i. *i ax. ax

12 EEE 0 ES NME: Probl: a. Dri h igal pro if h folloig q of opraio i prfor o a igal x ha i balii o i.. 0 for.. Molaio ih a qar av arrir of frq a a o l i..: / 0 0 of prio h i a hr ohri. Bapa filrig ih a ial filr for.. Molaio ih h a qar av arrir.. Lopa filrig ih a ial filr for. b. o o h l parar aff h op igal? a.. Fro Forir abl or Forir rafor via Forir Sri xpaio S S i * i i h filrig ill allo ol half of h fir haroi o pa. I ill liia all ohr opo a h DC. [ ] ohri 0 i For vialiaio ih h al riagl for h filr igal ill b:. Molaig agai g h a xprio a b ih i h pla of. [ ] S i i i * h lo frq igal i obai for a -.

13 Vialiaio: Color o: fr lo-pa filrig h lo frq igal i i LP b. h op igal i i LP h l parar a a val i 0 / hil i /. So h i arg rag fro 0 o. h o xr h offii of i ro i i o i i ola b h ro igal a i h ohr b a oa. Boh g filr o b h bapa filr. h pa i for / for hih h op apli i / ~ 0. of h ip.

14 EEE 0 W SOLUIONS Probl 8. fro h xboo. a Wih 0 S S * fr filrig g ol h fir i-lob lipli ih : x o F b Wih 0 S S fr filrig x θ o F h axi alloabl M i ri b h o-aliaig oiio o i i /.

15 Probl 8.7 a Solio I hi probl a o oir h ff of a lo i hroiaio i pha a/or frq. h olaio a olaio ar ho i h figr blo. x[] [] [] [] LPF r[] o θ o θ For par a a b of hi probl h iffr i frq i ro a h iffr i h pha i o b θ θ - θ. a If h pr i ho i Figr P8.7b h h pr of []. h pr i a ri riagl ha i balii a frq. b Sho ha a b ho o ha h op r[] i r[] x[] o θ. I parilar ha i r[] if θ /? Solio Obrv h folloig [] x[] o θ [] [] o θ [] x[] o θ o θ [] 0. x[] o θ 0. x[] o θ θ Obrv ha i h frq oai h fir r i h qaio for [] i a al vrio of h origial igal a ha h o r i a al a hif vrio of h origial igal. hi obrvaio a b o h h rl. hr ar aall o a hr pig o h agi of h pha hif. O a ha ovrlap h ohr o o. Fiall if h arrir frq i ho orrl i i poibl o a ial lo-pa filr i h frq oai o filr o h o r i h qaio for []. I h pial a hr h pha hif i / h h op r[] i ro.

16 Probl : 8.9 of xboo a prioi o i Forir rafor i op hrogh h Forir ri xpaio. ha i / / i i 0 a a a a S a o o h a i ro for v ohr ha 0. h ola hopp x ha Forir rafor a S * ilig h ba-pa filr-hopp igal a v a a a V h axi alloabl frq o i x for hi xprio o b vali i M /. Nx V i r-ola hopp a lo-pa filr. h olaio b pro o rplia of a 0 ah lipli b / ilig a oal offii of /. h r of h rplia ar a / ha ar filr o b h lo-pa filr. So V ih h a oiio o h axi frq i x M /. b Fro h la xprio h qival gai of h ovrall i /.

17 EEE 0 Na: SOLUIONS For h fba ho blo op h rafr fio / /. r C P _ P C C P C Probl : For h fba of Probl ppo P a C K /.. Dri K o ha h roovr frq i.. For h a K fi h Pha Margi of h fba.. P C K. PM 80 PC 80 a / 0 90

18 EEE 0 W 6 SOLUIONS For h fba ho blo op h rafr fio /r / /r /. - r C P CP CP CP C r PC P PC PC r Probl : For h fba of Probl ppo / P. a. Wh C K ig K o ha h loop roovr frq i.. : PC i 0. Wha i h oribio of a oa i irba o h op? b. Wh K C / ig K o ha h roovr frq i 0 a h pha argi i.. h iffr b h loop agl a 80 a h roovr frq 80 C P i 0 o. Wha i h oribio of a oa i irba o h op? 0.09 li 0.09 /.0 /.0-80 P C 0 for abili : a.. U K K PC P K K K C P } 0 li i P C 0 for abili 7 0 : a a 90 a P C 0 : b. 7. U K K K PC P K K K C P o a

19 EEE 0 ES SOLUIONS Dri h igal pro if h folloig q of opraio i prfor o a igal x ha i balii o i.. 0 for.. Molaio ih a oi arrir of frq.. Bapa filrig ih a ial filr for.. Molaio ih a oi arrir of frq.. Lopa filrig ih a ial filr for. olaio _ / bapa -_ olaio _ / lopa _ FINL RESUL: ¼ x

EEE 0 Na: SOLUIONS Coir h folloig ih rafr fio Coio i 0. aal. Fi h apli of h a-a rpo o a ioi ip x i0 o.. Cop h ir-i qival of a G ig h Baar Elr pproxiaio a a aplig irval of 0.0.. For G op h apli of h a-a rpo o h ioi x apl a h i ia i.

6 o h iriaio i fairl ara. lo h aplig of h ioi of frq ra/ a 00 i h far ha h Nqi ra iiaig goo agr b oio a ir rpo. o a vi h rl i MLB b iig h folloig oa: f[. ];* f[. 0][. -].0;* [0:.

20 EEE 0 Na: SOLUIONS Coir h folloig ih rafr fio Coio i 0. aal. Fi h apli of h a-a rpo o a ioi ip x i0 o.. Cop h ir-i qival of a G ig h Baar Elr pproxiaio a a aplig irval of For G op h apli of h a-a rpo o h ioi x apl a h i ia i.. x i0.00 o. h a-a rpo i i 0 o h apli i 0.8 [0.].. Baar Elr h biio -/ 0.0 G h a-a rpo i G i0.0 0 G o h apli i G o0.0.i0.0 Noi ha h aplig ra 00 i fa rlaiv o h filr baih 0ra/ ~.6 o h iriaio i fairl ara. lo h aplig of h ioi of frq ra/ a 00 i h far ha h Nqi ra iiaig goo agr b oio a ir rpo. o a vi h rl i MLB b iig h folloig oa: f[. ];* f[. 0][. -].0;* [0:.0:0]; xi*; lix; plo lix; plo bo lo p i i ha MLB ipla h Bo plo i r of h oio i frq Ω /

21 EEE 0 NME: Cop h i p rpo x of h Coio i abl / / { 0. aal aiaal 0. { R 0.} {0 R } aal Probl : Cop h i p rpo x of h Dir i abl / / / { 0. aal aiaal aal {0. } { } 0.

22 EEE 0 NME: Sppo ha a oio i igal x ha ha i balii o 0. Fi h aplig ra o allo prf rorio ih ial lo pa filr of x/. Explai. x/ i a LI o i i rib b a lipliaio i h frq oai. Si i ro bo 0 o i. h for prf rorio h aplig ra hol b a la 0. Probl : Fi h larg aplig irval o allo prf rorio of h igal x* o ovolio. i o.. o *i. h Forir rafor of h opoi igal i h ovolio of h Forir rafor of h iivial igal o h axi frq i. h h larg aplig irval i /.. h Forir rafor of h opoi igal i h lipliaio of h Forir rafor of h iivial igal hih i 0. h h aplig irval i a b arbiraril larg.

EEE 304 Test 1 NAME: solutions

EEE 304 Test 1 NAME: solutions EEE 4 NAME: olio Probl : For h oio i ih rafr fio. Fi h rgio of ovrg of orrpoig o:.. a abl... a aal.. Cop h i p rpo x, aig ha i i aal. / / / / } { } {R, }; {R, } {. } {R : }, R { :. L L L L Y L Y x L Caali