A#02_Solutions

# A#02_Solutions - Assignment#02 Solutions p.1 ECSE—2410...

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Unformatted text preview: Assignment #02- Solutions - p.1 ECSE—2410 Signals & Systems — Spring 2009 Due Tue 01/20/09 1(32) Evaluate: «i (a) je “6(1- 1)dz' mjé‘étmléﬁ‘ - é‘SSC’t'DA? 7*" 3 WM) ~Q‘} , 15 't (b) [(35947 1:. S 4% :3 "6:1: -{giq z. Cg~é£)ﬁ&) “°° 2 {2 E? 35179 *3?c; m ‘1 — ‘2 ,. (die 5(7 2)dT a: a §C¢q13\$§03£2£ «2344?: “0C: “a: ’l (d) e u(’r)u(— —.r+1)dz' —.... v/Mx —oa (21) Express x(t ) in terms of step and ramp functions “‘33 “WC“? “LN-l): (tau ‘31s) (vim-n ow") tiara) :2 wiuLﬁ+um [beta-z) “ﬂouti- 2)...w L-‘wtKifléaﬁ-lei‘f: a)u&\$2ﬁ)+u€£— 2,) ma: 4% 3+aieg.z)+;t+~a + [ﬁe ‘3 ~z + also. i] 9 mt} == we} {~ng + balsa) +29%?) (C) Sketch w(t) Assignment #02- Solutions - p.2 ECSE-2410 Signals & Systems — Spring 2009 Due Tue 01/20/09 3(16). Using the basic definitions of linearity and/or time-invariance, verify that ~ 2 ~ . (a) system y(t)— t -x(t—1) is linear. 6? I Q 37f} .- {ﬁr‘é’ﬂ‘é’l} «QQ+ gag/“9‘3 tzﬁﬁ‘i) J 32%) assists-s) New tam xgazaaesssgak EMA) "TEE/pt 2. z. ' £3 a f z. 3ng e sigvgz’) —..— t [new £19.43] a a. «eggs-4)) 4-}; if: gages) 2‘ QgrxLﬁ't‘b‘sz—J 3 Fag . ism. (b) system y(t) = x20: - 2) is time—invariant. 62W 311:9 I 3%) :: Kztﬁ- 2:) 122+ gm == icing—z) Aim +51“ x7e): QC (:e— fa‘) Ttmx 323.}: 24 :&~2)- ”(Li Hegel; 2T3”: \$12/5£~a)~£>xé[email protected]“iv) LTI 012’ x(t) Use superpositipn to graph the output of this system when the input is 1 596%. X”. M} 9-} Mali): "’24; [35%) t AL: “ﬁt TM 53 saFufosﬁma tit-a =Pt~ﬁ>~ 9;; as) :7 3603M; «a, (£4) Assignment #02- Solutions — p.3 ECSE—2410 Signals & Systems — Spring 2009 Due Tue 01/20/09 5(14). In this problem you will find the approximate system response to a pulse input, p(t), as a means of understanding the derivation of the basic convolution equation. Let the impulse response of this system be: x(t)=6(t) y(t)=h(t) 1 LT] Thus, the approximate input is p(t)z 5(t)+~};5(t—%)+%5(t—%)+ﬁ§(t—~Z~). +%h(t-%)+%h(t-%) a S 2 s a succession of straight lines at every —};increment of t: L 4 t , else iuwwuh-~uukwn-w WM ”M Mu: Nam“? 42-h)”. row “MW“ ...
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