Fall 2009 Exam 1 Solutions

# Fall 2009 Exam 1 Solutions - E SE 3 37 Name l C onsider t...

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ESE 337 Name l. Consider the CT signal Exam I Fall, 2009 ID no. ,(t) = -5 + 2 sin 1.8t + 3 cos 3t _ 10 cos 4.2t Is it-pe odic? What are its fundamcntal frequency and fundaotental De- riod?.What a.re its sarnpled sequences in p"in"ipuf for_ ii'ifr" .-.rriofin" period ? arc r/9. r/r, and r/1.5? undei rvhai. ."aiti"" "ii firrJt'iii sampted sequence contains all frequency components of e(r)? (20 points) Soliic'iors : O {e. , ;+ is pavioJic. f\, lA 9 -|ttrtd^uvte-"rtot fzltet1c4 -GCDCl.8, r..+.2) =_0.6 mA/s {",la^-*n,*J permd - -n/^o = T/o.6- 'o2, = (o-47 s€c @ @ r=n/1 . NFK (-T, 4..1 (-1 , ql t.9, z. +,2 Are c.tl t"itl"l, NFP. .. . x(nT) -5 r-:sin t.SnJ r- 3 au;3hT lo ce94-2^T (pric;'t*' ^f--) r\$ T--Yz rvFR (*3. 3l t.8 onrd o.{e i", NFR +.2 mod 6 =-t.B G r^ ruFR x(nTl '- -{- zsl'' t.\$vT -+ ac{93"T -tOOsC-r.8 nT) 'rq1nT) -J * zsin r.tnT +3cc\3nT -rocos r.ghT (piiciTal-f"r,_) @ T=rrlr.S NFR = (-r.s, r-sl 1.8 rnod V t.z xcnT) -s + zd^ -z XcnT)= V- 2ejn J t{JTaq>(- 4_ r Ttrrd\x=. jf EI 7 'rv1od +_zl"toJ 3-1.2 c-t 'znT) c.--i'LnT wE wcL'rl \$rvrax * +_f r> i i.> | 'Ys a - - 2_1T \ 2_T t-znT loajl.zn-i- C princi' pcl t ) (x)vnqx : *- Z we wcLu+ Nylaqy 4-z < l- \-. T T €{r lr -g'- ?-T I st

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2. Consider the sequencc r(0) = 2, ,(T) = O, .r(27) = 2. r(nT) = 0. for all n other than 0 and 2, with ? 0.5. lvhat are its nugnitudc spectruBr (5 points), aDd its phase spectrum. (b poiuts). plot the magnitutle and phase spectra for (, iu the Nyquist Flequency raDge. (10 points) SolrttianJ: ca -. ,,r.-r- {.r (w) = I y.inT ) Q-'}n v" t n? -a<l )(to) g-)owT + ((>T\ 6 -Iz"oT wb{ Ewlertg {s*n,,-lo. co3 >< : + tei*+ g -i"1 la c- '' ^ -lo'sec Xdt^l= 2 Q 2-cgs o'sL^J /'i1o'Sw'I J lXa(w)\ 4\c-c*o'S*\ 4Kccw)'= +e-lo'sN+ C -c.Sut) \ t -c.gw +rI 4 ca-i o-9ur) .f\ , rj Gcas.Sr'ur >O
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Fall 2009 Exam 1 Solutions - E SE 3 37 Name l C onsider t...

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