EE4150_2004_hw4sol

# EE4150_2004_hw4sol - 5.1 Since 3(a) is real, the real part...

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Unformatted text preview: 5.1 Since 3(a) is real, the real part of the DFT is even, imaginary part odd. Thus, the remaining points are {0.125+j0.0518,0,0.125+ j0.3018} 5.4 (5) 210*) = “ﬁne-W") X10) = % [5(1: — 1) +50: + 1)] also x209 '= %[5(k—1)—5(k+1)j So X30) = X1(lc)X2(lc) ' .N, = 27[6(k-1)—6(lc+1)] and 23(n) = gainﬁTvtn) (5) Ray“) = X1(’=)X§(’=) -N7 = 27[5(k—1)—5(k+1)] => 1",y(n) = —%sin(%n) .5 192 l I M‘inu —J.L:;:.Fy.h'iri.x (c) RuUc) = X1(k)Xf(k)4 N2 6/ = ——[6(k—1)+6(k+1)] => m0») = icoséNln) (d) Rum = X2(k)X5(k) 2 = §:[6(k—1)+6(k+1)] =9 Fw(n) = -];-Icos(g]%n) 5.5 (a) _ N-l lN-l 2 Emma) = 3 (MM W") n=0 in: “31 w W" = Zn=o +6 J ) - _ l N ‘ 4 .. E " 2 (b) N-1 1 Nil - ' “I gzﬁnﬁﬁn) = —4—j- i=0 (e1 + Ham) (c-J —e13¥n) '1 N—1 “a; —% :: :3 C J ) 5.8 y(n) = “(7043200 3 2 3" 1(m)mod4z3(" ’ Hm)mod4 i m=0. {17,19,22, 19} 5.9 x4») _ {7,-2—j,1.-2+J‘} =:~ X3(k) - X1(k)X2(k) x5”) = {17,19,22,19} 5.13 m (a) N—l X10) = 2 2(n)Wﬁr" n=D 3N-1 I Xauc) = Z: wows? n=0 " N—l 2N—1 3N—1 = 2 =(n)W§IG + Z =(n)W§I~}+ Z 2(n)W§ﬁ} n=0 n=N n=2N N—l N-l N—l = 2 2(n)w,';* + Z 2(n)w;w;;5 + 2 z(n)W32"W;* n=0 15:0 11:0 ‘ N-l - = Z 2(a) [I + W; + W:*] W}? n=0 ' = (I + W; + W§*)X:(Iyg (b) _X1(k) = 2 + W: X30) = 2 + W: + 2W6“ + Wé’“ + 2W3” + wg" ‘ = (2+ W?) + w:*(2 + W?) + W:*(2"+ w?) k (1+ Wat + Wau)X1(§) 5.14 (a) ‘ z ' a zi(")®32(") y(n) — {4,0,1,2,3} (b) Let. 23(11) = {20.2}, ,24}. Then, 0 4 3 2 1 :0 1 1 0 4 3 2 :1 0 2 1 0 4 3 :2 = 0 3 2 1 o 4 :3 p 4 3 2 1 0 :4 0 Solving yields sequence 23(11) = {-0.181,022.002.002.002}. 196 5.25 (a) 00 X(w) = Z :(n)e"“’" n=—oo - a“ +2er +3+2e 1'" +e 12'" = 3 + 2cos(2w) + 4cos(4w) (b) 5 . V(k) = Z woe-1"?“ n=0 = 3+2e—j15h +e—ng-2t +0+e—j3;'-4k +e-j15-5h = 3 + 4cos(%k) + 2cos(?-31k) (c) vac) = noun-5:5. . This is apparent. from t obtained by repeating :(n). he fact. that. v(n) is one period (0 _<_ n 5 7) of a periodic sequence ...
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## This note was uploaded on 02/26/2012 for the course EE 4150 taught by Professor Wu during the Fall '10 term at LSU.

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EE4150_2004_hw4sol - 5.1 Since 3(a) is real, the real part...

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