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A#02_Solutions

# A#02_Solutions - Assignment#02 —— Solutions —{1.1...

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Unformatted text preview: Assignment #02 —— Solutions — {1.1 130832410 Signals & Systems — Fall 2006 Due Tue (BIOS/06 1(20). Given x(t) m :4: +1) + W) m w m 1) w “(I m 2), sketch (a) By Mn} and (b) Od{x(1)}. 960) Answer Answer Assignment #02 — Solutions ~+ p.2 ECSE—2410 Signais & Systems - Fail 2006 Due Tue 09/05/06 2(21). Given the sigma} shown, A x(I) (21) Express x(r) in terms of step functions. (Any form is ﬁne. Be carefuﬁ) d2?) in terms of step and delta functions. (13) Find the equation for Mr) 2 (0) Sketch w(t) . (a) :60) = r[u(t) m u(r w 2)]+1[u(t — 2) - u(t — 3)]— (z m 4)[u(t m 3) _ “(t e 4)] Or x(t) m ru(t) — (I — 2)u(r w 2) -~ u(t m 2) — (I — 3)u(t ~ 3) + (t w 4)u(r w 4) (b) 0 0 0 0 05‘“) =1: t)+u(z)—[(z7zaﬁ:—2)+u(t—2)]m5(:»-2)—[(z—3 (t—3)+u(rW3)}+[(t—})6€—4)+u(t—4)} dz muU)—u(r——2)w~§(tm2)—u(I—3)+u(t—4) (e) mm 5 2 i E Assignment #02 — Solutions -- p.3 ECSE~24E O Signals & Systems “ Pal} 2006 Due Tue 09/05/06 4(10). Find the value (a number) of the integral}, If u(r)u(—r + 2)dr . M a. ﬁfm 3 a. i '2... 9 93 i? n 5(18). Evaluate (a) §[k] (b) 6ch (Some may be constants, others sequences of n.) w :40 :36 MW 3 w w chsmazgém .2 2 sag: :1. g 9:: m w ﬁg: .- % 3g, ’5:— my? a it. .1}. ‘ r‘ m. is) Z G) to; as: Z we»; a ago; = we K "in. HQ) F2: “up FL; “W 6(21).Eva1uate (a) je‘r§(r~1)dr (b) je"u(r)dr (e) Te‘fukyz’r (Some may be constants, others functions of t.) ‘t t t “I W 5 ééxﬁs~a)d¢=§ gigs-0M a e‘j SMM z- 3, my ma) ._.w —a-9 4: é- “ r J?“ ,.. -- (*5 Se¢udezgeldT=~€ {:4 E: a. (we Mi“) “‘® 0 W» i} if“ {13%; {23\$ €250 ...
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