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Unformatted text preview: Problem 1 (25 points) a) Given J(t) = a e-atu(t) B F(OJ) = a. . Find the bandwidth W defined as IF(W)12 = _ 2 1 a + Jm (half power bandwidth) [your result will be in terms of a]. \ F~ )12- :: Ti IbJ-Y- !.- ~ J- en. Z;:' I +-L~'~; W:=0/ I + ~)' 2-1 Ct.) BW= ~ b) Given J(t) B ~(m) and J(t- to) B G(m), what is the relation between IF(OJ)I andIG(OJ)I? Explain. _ 'LJt f- 4 UJt~ I- G(0)~ F(w) e. J ~ e.- I) 0--() I G-~)t ~ I F~)( I e--4!()~~ (I G ~)! = I f(<<»! h(t) 1 c) Given J(t) = 38(t) + 58(t-1)- 48(t- 2) , and o 1 2 t yet) = h(t) * fit). Sketchy(t). (Label axes carefully.) h(tJ= ~ ( t~) ~ [)::- 3~~)~ ~6(.G)+- z. z.-1 ~l~) S" 3 o 'f-t:--1 d) Given below are the impulse responses of two different systems. In each case, state whether or not the system is BIBO stable and causal. Explain your answers. I k(t-) i) h(t) ~ reet( ~ ) Lt::=L t 2.,~-2,'3 "J,..$"" L.J L,~}Jt :=: ~ ~ 11 (f) ~O /at tLD__ ~-~ ii) h(t) = cos mot u(t) 00 I l~wo tl ctt---s:,> ~ o l1(t)::D jot t L D ~ 4k> Problem 2 (25 points)...
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This note was uploaded on 01/26/2011 for the course ECE ece 210 taught by Professor A during the Fall '10 term at University of Illinois, Urbana Champaign.
- Fall '10