antonia_exam3 - Name TIC N 5‘ EEE 303 Signals and Systems...

Unformatted text preview: Name: TIC} N 5‘ EEE 303: Signals and Systems. Exam 3 May 1., 2003 Prof. Papandrenu—Suppappflla You must answer buth pmblcms for fufl credit. The number of points fur each part of a. problem is given. Fur full credit, Show all 51.2135 and label all axes. This area, is- fur ufi'lcial use only: ljriiblEITt—IlJ‘V;-_E£:lilllul—II1 2 ] Tug-v i E5 25 50 l _;_—____3 1. Consider the discrete—time signal = {fl.Ei}”n[n]. is.) {‘3' pts} Does the discrete—time Fourier transform {DTFT} X{e~“‘"] of 1*[n] exist? Demonstrate your answer. Prmide X {ta—i”) if it exists. Eb] {9 pts] Find the DTFT of y[n] = (REF—41:11: — 1] using DTFT properties. Show all the steps and simplify ypur result. (a) {Q ptsj Find the DTFT of gin] = {n + l][fi.fi}"n[n] using DTFT properties. Show all the steps and simplify 3mm result. _ f r "‘3 n K02) DTFT £4.er 536m. éflfli‘flifli 3% (M) :— i ’19“? .119: 1-1.4 Iflflé Ill] '5 EqFT’ ’PGLIY H“ Edi“) z: i _ “.5 d £117— J'- D'Eefiw } PM -3 “.s ,- In Ks) mew) (0.5) wart I R “is $01.04 :HLfn-ij «:4 Vie”)={g_.a)'3‘efli We ) sway WM jrfi'éé-Jh} J ail-n— kcb (atnrl; “(xiiinpl + iii-"’3 3 . . La? wwst We" i + New) Gin} .w 'I fit; 'I :J a (has?) + (Fruit ) ole) ~u_£€v“ q _ '-" :iifli * (“ME”) Us 0-6?- J (Irfi- e 2. Consider the mntinuous—time signal Edi} = whose Fourier transform is given by 51 w a: 1hr Xcfiwj = I I . We want to sample 2:513) to obtain the eontinuous and sampled signal -]1 otherwise 0Q mph) = Z: sdn’l‘flqu - nT] 1Where T is the sampling period. fl=—D(J {a} {5 pie} Plot XCULJ}. What is the largest frequency-r of :Ic{fl? [h] {5 pts] When T = 0.051 what it? the sampling frequency mg? {C} {3 pts] When T = {1.95, plot the Fourier transform Xpfljw] of :rpfl]. Does aliasing occur? Why or why.r not? [d] {1" pie) When T = Ill, plot the Fourier transform Xpfiw} of my“). Does aliasing occur? Why Xenia-3‘1 (a?) E J W- P940. B; or NAME; or Wh},r nut? T o-ns Lil}. w “JAIL-oi?” DCCLLI‘E- Sued E) 4!: fl _: Kala—Tr vague? 9‘ {will We :L _ _ J .57r-fi’ “W” r23“ -‘i—“ r'flr'i D '“E m Ho‘fi 53““ ...
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