3015_Homework_8_Solutions

# 3015_Homework_8_Solutions - 3.5.2. Use the deﬁning...

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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] ...
View Full Document

## This note was uploaded on 12/20/2009 for the course EE 3015 taught by Professor Staff during the Fall '08 term at Minnesota.

### Page1 / 4

3015_Homework_8_Solutions - 3.5.2. Use the deﬁning...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online