3015_Homework_8_Solutions

3015_Homework_8_Solutions - 3.5.2. Use the defining...

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Unformatted text preview: 3.5.2. Use the defining equation for the DTFI‘ to evaluate the erqueney—demain representations fer the following signals. Sketch the magnitude and phase spectra. [dime]: %_%w5{%n)’ MEN [1 otherwise 1 N (31?" + [7—31'5'11 - Yicjflw _ E Z 2 :lc—jfln n=—."i-' = lsinf2“:_,+'fl) isin(2~2+l(§1— £1} + isinii’d'g' (n + en 2 ainfigfifl) E airmail! — §}) 2 sin[%{£?— fij} a ?- 3 _ E. 2.5 - :5- = E g g _ E... 5 E i is £15 - 1 - 2- I_ :15 - 94 94 —2' ' i 4 0 (We? ['Pi-Pi] Figure P352. {0} Graph of the magnitude and phase for N = T ((1)3:[1I1]: 26:4 — 2n] fire-15‘} = % i 26[4—2n]e'jfl” = BEE?“ I-Yte'fi‘H = 3 axe-19} = an IKMH malll _. _-. __-. HI H i III E M M $- maxim“ wall A: .L .:. M // l-‘igurn 13.53. {:1} Graph 01 the magnitud-rr and 1211330 fie} as depicted in Figure P3.52f_a} . 1 :1” . Xflajfl} = a Z fl:[?1](_='3fl” 11= —-L:IL '. T! _ ' ( _' I1,3|152_ cj_fl + (I: 32.? _ E, 3152 3 cosmn} — '2} sinilifl} |X[cjfl}| = {4 (116395!) — asintdmfi J J5? : Sim-ii?) ,_X[c } arctan (mm:in N i I Him-:1 mum r: '1‘ "r1 a "Wit-mac] WWI” (HT-993 [-pim Figure P352. {(2} Graph of the magnitude and phase 3.53. "L's:- the equation describing the DTPT Iepresenmtion to determine the time—domain corresponding to the following DTPT'E. {a} X-[c—ffl) as depicted in Figure P353 {13) o _ I % _ I T["] = i — sill-(fljejmcfls‘n d5] + i Sjn(§1)€JEEIOJEE1-a dfl 21': ‘g 27: . n 1 'I' : E ? smut} [e-J'{2+“’“ +ei’~9+“1”] cm ul I D l [2 sinffl) coe:f_(2—n]fl)dfl 7" . a ir if sin(§2[—l — nj) — sinfflffl + nDdfl 2'.“— o I I 1 l—cosf_%{?1+1_}j I 1 coef_%{n—3}j—l 1T n+1 '23 n+3 to 2n n+1 Er: n+3 r _,L n— _1___3 I l l—cu5f%fn+l]} I 1 cmi[%fn+:5fl]—1 n at; l 3 M] = ' £TI' (f) X [31“) as depicted in Figure P353 [e] 0 § . 1‘31] 2 i e‘ji"+3-m"'til—l+i s—‘fifldfl 2n _, 211' u 7 _ DDE{%R]—l _ jrm coalln}—1 elm] = { —“—jm “*1 7f 0 E] n = [l- 3.60. Use the tshlm of transforms and propertiw to find the DTFT's of the following signals. (a) re] = (éf‘utn + 2] 1 1'[n] = {Ejnufii + 2] 1 1 = {El—glglfizulfil + 2] 1 n DTFT 1 l5) 1th1 <—* s[n+2] (fl. eififlstei“) T! _ gcjen W 5 ‘ : [sing—E111 t [sing—TIEEESH] sings]: FT .9 1 lfll E % SIR] = 3&9 II= I am I), I <: |S‘.!| g n Elfin] = e[ — s] M” 5119“) = e'jSflS[ejn] men) 2 Blejnl-S'lem) = “'3” lnl E e e. g -:: |n| g n 3.68. Determine the frequencyr rmponse and the impulse response for the systems described by the following differential and diflerence equations. [a] mm] + %yln — 11: arth — 2mm — 11 (1 + %s_jfl}l’l[sjfll = {1 — 2s_jfl]X{-sjflj . i — 22-?” fl _ Hie} } _ l + %e Si“ Mn] = {gm — mgr-lulu— 1] ...
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This note was uploaded on 12/20/2009 for the course EE 3015 taught by Professor Staff during the Fall '08 term at Minnesota.

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3015_Homework_8_Solutions - 3.5.2. Use the defining...

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