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

133 1 if 20 y f f t 0 a nd c o a nd f t u t xo

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Unformatted text preview: - l(l L (f) 7 .7-4 1 s S a (a) S (1 - e - S ) (c) ~ (e) 1 [ .2+(Wl+W2)2 + S"+(WI W2P ] (g) ~ (h) (s+:)2~~:;;9sin 8 ~:2 s - se- S ) (b) l~f~~s (c) ~(1 - e- s - Be- S) + '~l e -(s+l) ( a) ~(1- e( b) 3 .018e- 2' c os(3t+6.34°)u(t) (c) 6 (t)+(3.2e 3'-0.2e- 2')u(t) (g) [ e-' -(1+t+~ +~ ) e- 2t ]u(t) (h) (d) ( [ie-' + ! e2']u(t) + ~e'u(-t) (a) [ -te-' + 2 e-'/2]u(t) + ~e'/2u(-t) 8 .2-2 6 .1-2 < R e s < 0 (e) all s 705,600 b its/s C hapter 6 6 .1-1 Re s = 0 ( d) - 1 7 .5-1 5oo1r). 16 b its (c) 480,000 b its/s (d) (c) ( b) ( -e-' + e ' - 2e- 2')u( - t) (c) ( e-' + 2 e- 2')u(t) + e 'u( - t) 7 .1-1 5 .1-3 T he s ignal recoverable only in cases (b) a nd (c). (b) H(w) = T sinc 2 ( wi) (c) Minimum d elay= T 5 .1-6 < Re s < 0 ~ C hapter 7 ( a), ( b) 200 Hz (c) 120 Hz (d) 150 Hz 5 .1-5 (b) - 1 00. 6 .7-5 No. (a) ( e-' - e' + 2 e- 2 ')u(t) (a) n. C hapter 5 ( a) h (t) = u (t) - u(t - 1) 6 .4-4 Y I(t) = ( 4- ~e-' - ~e-3')u(t) Y2(t) = ( 2- ~e-' + ~e-3')u(t) K I = 2, K 2 = 25.4, a = 6.128 6 .7-3 t s c annot b e satisfied. 7 .1-2 5 .1-4 (5 - !je- 2'/3)u(t) = 38.06366 kHz. f:>.:F = 20 kHz, B = 42 kHz. 5 .1-2 6 .4-2 6 .8-4 (d) ( 1- e-')u(t) 4 .5-3 All unrealizable. (a) td = 1 !.LSec. ( b) t d " " 100 !.LSec. 4 .8-5 ~e-'sint)u(t) 6 .8-3 6 .8-5 We ( te-' - I Resl < 1 (c) (8 I lls 2) 1 < R es < 2 (f) (s -g(~2~22) 0 < R es < 1 ( b) e 2'u(t)-e 3'u(-t) (c) ( e-'+e- 2')u(t) ( d) - (e-'+e- 2')u(-t) (e) ( e-'+e- 3')u(t)-e S'u(-t) 6 .8-2 ( d) B andwidths o f Y I(t), Y2(t) a nd yet) a re 10 kHz, 5 kHz, a nd 15 kHz, respectively. 4 .7-2 (a)Yes (c) minimum 6 .4-1 (a) ~6(t) ( b) L~o u (t) 4w 2 + sinc2 ["(W~lOlJ u (t) )] Y I(t) = 7 .787e-'/6 c ost 4 It - 3LlO)u(t), v s(t) = ¥ 6(t) + [10 + 9 .045e-'/6 cost 4 It - 152.2°)u(t) 4 0e-'/Su(t) 6 .4-7 1 .716e- 2' cos(3t + 2 9°)u(t) 6 .4-8 ( 121.61e- 6.S3 , - 1.61e- 2.8')u(t) 6 .4-6 :::l.z. (cos WT + wTsinwT - 1) p, ( ) _ 2e-jW(cosw+wsinw-l) 0 6 .7-1h P O"" 3%, t r = 1.15 sees., t s = 2.67 sees., e . = 0, e r = 0.75, ep - (w5,2-2)Sin:~;+2wo'eoswo' (b) . in't:in2 ' 4 .2-4 ( a) to [ e-' + ~ cos(3t -161.56 6 .4-3 TW 4 .3-6 4 .4-3 (b) JW 841 6 .4-5 2:::'00 (Hi4ni~.:,~8.;'3+j3W) ei2n' C hapter 4 4 .1-5 Answers t o Selected problems 9 [.!j(3)k+l - (2)k+1 - i(-5)k+l]u[k] , fi[(3)k+l e os[i(k + 1) - 2.261] + 0.637(2)k+l]u[k] (a) ~[(2)k+l - (0.5)k+IJu[k] (b) 12[(2)k+l - (0.5)k+l]u[k] (c) i [(2 k - 1- (0.5)k-l]u[k - 2] 842 Answers t o Selected problems C hapter 1 2 9 .4-8 50000[(1.01)k+1 - l]u[k]- 1500(1.01)k- 4u[k - 4] 9 .5-1 2e~1 [2e( _ 2)k 9 .5-4 (~+ ~k)(-l)k - fi;(3)-k 9 .6-1 (a) A sympt. s table + e- k ] 9 .5-2 2e':r1 [ -( _ 2)k 9 .5-6 9 .4-10 N = 23, residual p mt $471.2 + e- k ] 9 .5-3 ( b) ¥( _ l)k - 1 2.1-1 ~(_2)k + ~(3)k 0 .241(0.2)k - 0.377(0.8)k + 0 .765cos(¥- - 1.393) (b) marginally stable (c) unstable (d) u nstable (e) marginally stable. 1 2.1-3 C hapter 1 0 (a) IH[ejOli = [L~~1L~':hfll'/2, L H[e + e j (0.8"k+,,/2) + e j (Lhk-,,/2) + 2 e jL6"k 1 0.1-1 2ejO.4~k 10.1-2 ~[ejO.5...
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This note was uploaded on 04/14/2013 for the course ENG 350 taught by Professor Bayliss during the Spring '13 term at Northwestern.

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