Signal Processing and Linear Systems-B.P.Lathi copy

134 i f w is t he t ransformed state vector given by

Info iconThis preview shows page 1. Sign up to view the full content.

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

Unformatted text preview: - j2w ) )_ I'S W , - (c) iw+r~;W/2 } (b) l -C:;wo' 6 .7-2 6 .8-1 (d) l_e~~-::W)T 4 .3-5 j 4sinc(w) s in 3w (c) 1r[ sinc1r(w + 10) + sinc1r(w - 1O)]e- i2 (a) ( e-' - e- 2')u(t) 4 .4-1 (c) ~e-'u(t) + ~e'u(-t) "W 4 .5-1 to ~ 3 v'2k 4 .5-2 to ~ 40!.LS 4 .6-5 B = O.!66 Hz. 4 .7-5 ( a) A = 20, ( b) A = 10, (c) A = 5 4 .8-3 BFM = 42 kHz, 4 .8-4 A F = 100 Hz, B = 2.2 kHz = 21rB ( d) No (e) Works only for even B pM ( a) No region o f convergence 2::=-00 sinc (n5") F(w - F (w) = 0 .2F(w) + ~ 5 .1-8 (a) 3 0 kHz (b) 5 .1-9 (a) 10.8 MHz (b) 5 .2-3 No = 256, T = 0.03125 by b oth c riteria. 10 b its (c) 108 M bits/s ( d) 2 e- 2'u(t) + ( -e-' + e ')u( - t) 6.1-3 ( a);12 c os(2t - 15°) (a) 7 .5u(t) (b) ( b) 2;12 s in 2t 2t)e- 2' + 4 ITe- 2' c os(t + 71.56°)]u(t) (d) . ...Le-(s+l)T ( e) ~e-(S+l)T (g) Wp c os (a), (b) ( _~)k (c)( _ elk ( d)( _ elk 8 .2-3 Aperiodic: (b) & (c); Periodic: (a) No = 4 & ( d) No = 6. 8 .2-7 . 8 .2-5 f l, a nd I fl,l a re ( b) - 0.81r, 0.81r (c) 0.6168, 0.6168 (e) 0.91r, 0.91r (a) ei (0.hk+8) (b) eiOk = 1 (c) ei4.333k ( d) ei !.3d 8 .2-8 (a) a nd ( b) 2.7778 (c) 2 .77782 8 .2-9 (a) 19 (b) 19 (c) 252 (d) 40 8 .3-2 8 .2-10 (a) 1 ( b)l (c) 0.5 ( d) 0.5 (e) 0.5 1 0cos(0.91rk-i)and5cos(0.91rk-i) (h) (b) 6 .3-1 ( a) ( e-' - e- 2')u(t) W QT s 2+wg WQ c os W QT+ssin (i)1500 Hz (ii) 1500 Hz (iii) d c (iv) 1500 Hz (v) 2000 Hz. W OT e -ST 8 .4-4 (a) I[k] = ( k + 3) (u[k + 3 ]- u[k]) + ( -k + 3) ( u[k]- u[k - 4]) s2+wg (b) (2 + 6 t)e- 2'u(t) (c) 2 + 5 .836e- 3' c os(4t - 99.86°)u(t) T hezi&zscomps. are: (b) ( 2+5t)e- 2',te- 2' (e) ;l2e-3'cos(4t-~),2+5.154e-3'cos(4t-112.83°) ( a) Y l(t) = (~ - !e-' - ie-4')u(t), Y2(t) = 6 .3-5 ( l- !e-' + 1 2e-4')u(t) Jt 9 .1-4 - 12,36 a nd - 63 9 .2-2 - (3 + 2 k)( _ l)k 9 .1-5 9 .2-3 9 .3-1 O.56[k] - 0.5( _ 2)k u [k] ( a) .2::i.~24 6 .3-6 (a) (D2 + 3 D + 8 )y(t) = ( D + 5 )/(t) (iii) ( 1.5e- 2('-5) - 2e- 3('-5) + 0 .5e- 4('-5»u(t - 5) (iv) e 20 (1.5e- 2' - 2e- 3' + 0 .5e- 4')u(t) 9 .4-1 ( v) e - 20 (1.5e- 2('-S) _ 2 e- 3(1-5) + 0 .5e- 4 ('-S»u(t - 5) * 9 .4-7 9 .2-4 2N It~S)N [2 N (0.5Jk - (0.5)N (2)k] ( b) 3 6[k]- 5<5[k - 1]- 26[k - 3] 9 .4-4 9 .3-4 2.061(5)k cos(0.923k - 0.244)u[k] 2 e"rde-(k+l) - (_2)k+l]u[k] 9 .4-3 [ (3)-k - (2)k + 5k(2)k]u[k] 9 .4-5 i 8 .5-2 p[k + 1 ]-1.02p[k] = 1.0li[k] - 5,7.667, a nd - 5.445 2 (;I2)k cos(~k) 9 .3-5 Y2(t) = 2 0;l2e- 15' c os(! - ~)u(t) (b) (vi) 600 Hz C hapter 9 ~(i::::=~:) Yl (t) = [(8 + 1 7.89-1.5' c os(! - 26.56°)]u(t), 6 .3-7 W QT-ssin 8 .2-11 (a) 8 .3-31Ocos(2jk)+vlocos(¥k-Ll07) 8 .3-4 6 .2-4 ( s+l) 6 .3-3 112.62°)u(t) (c) > f¥ei(3'-67.62°)u(t) (c) Periodic; No = 20 ( b) 0 e-('-3) c os(t - 3+ ~ ) u(t - 3) + 2 e-' sin t u(t) (c) [~e(t-l) s in 2 (t - l)]u(t - 1) + ~e' s in2tu(t) 6 .3-4 >f¥ sin(3t - 7 .7-2 8 .2-4 6 .2-3 6 .3-2 ( b) C hapter 8 ( c) s +1 (c) 2.28 cos(3t - 12.12°) xp. cos(2t + 3.69°)u(t) 5 .2-1 No = 512, zero p adding r equired. 6 .2-1 8 +1 infinite 7 .6-2 5 .2-4 (a) No = 16, T = 0.625 ( b) No = 8, T = 1.25 [to...
View Full Document

This note was uploaded on 04/14/2013 for the course ENG 350 taught by Professor Bayliss during the Spring '13 term at Northwestern.

Ask a homework question - tutors are online