ex1_solns - Xawxil‘ Perl/2065 Name CM Problems 1-4 are...

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Unformatted text preview: Xawxil‘ Perl/2065 Name CM Problems 1-4 are worth 4 points each. t 1. Which of the following statements is the best simplification of: bel — t0)5 (/l)d x1 —2 a)0 b) x(t—t0)5(t) x(—t0)u(t) d) x(—t0)5(t) e) none ofthese xOc'to) ; x073) 5m 2 . The average power in the signal x(t) = u(t) ~ u(—t) is “90,, “69‘; 4. 1 T” l T 2 a)0 b); @l d)00 6) none ofthese an: 53-8 \xcfil 3. Given x(t) below, which of the plots labeled (a) — (d) represents 1%(2(—-t — 2)). 'T X“) 2(_t-28=t4 -> tg'q 207143 ‘ 1 "’ i = ‘2‘5 1 4 l I I I -4 -2.5 2.5 4 (C) ] [ (C) [ l -6 -3 3 4.5 4. The signal x(t) = cos(47rt + 7r / 2) + sin(67zt) is a) not periodic LilT T 3 0" n P b periodic with fundamental period 671 seconds _ periodic with fundamental period 1 second EITT " a Tr fi’ d) periodic with fundamental period 3/2 seconds 6) none of the above 2 n r z 59’4— H W W F _ Z. Name CM 5. Graphical Convolution (29 points) Use graphical convolution to determine the intervals of integration and their corresponding integrals y(t) = x(t) * h(t) as shown in the plots below. Use x(t) as the signal to “flip and shift” (i.e. x(t-l)) for the convolution. DO NOT solve the integrals. just set them up. Mt) = u(t + z} - m 4; 1) + '2 -1 1 2 .r ‘ 1| \ A = I l x(t) e. u(t) ‘ .) ‘l | ; t x(t—x) = e 20; 3:40:13 I ‘ ‘ t '2 (+3 = o _- i > i: 4 a 'l: t l l k t A) | g f 44421 #ng 62H Ax ~z \ i: t 1 ( i 4 —1 (Jr, C 1 ' till ‘ A ‘3 -Z . t . 4—200» I ‘ I iLtéz 10¢)”an at) . -n. .54“ S t 26?)“ ' ’ I +5 (E on -----~.——_ Ill Lit. 16m... 6706‘ / , 4 ’2“ f I \ + $63 —2 Name CM 6. Impulse Response (25 points) For each of the following systems, determine the impulse response 110:) between the input x(t) and output y(t) . Be sure to include any necessary unit step functions. ,. w”. “Mama”. wry.wmmm z Wynn...” a) y(r)=x(r)+2x(t—2> We) : gm 4, 1 grew?) ,4...» m.,,.,.,... —~»-—--—--v w-«H... ,_ ,Mwegfl».m..,..,,,.m b) y'<r)—y(r)=2x(r) flagged) : E'Z‘Sta : gem 4M, A, V§:( g §i(«V2(>\)€?>0/I :Wwe 1 .~. g Sm A u A ’43:) c) For the following system, with the impulse responses of each subsystem shown, Mt)=5(t)+u(l) Determine the impulse response of the system ( relating y(t) and x(t) ). “EMA Mm ii: ti?) : Swepkzmw Name CM 7. System Properties (25 points) a) Fill in the following table with a Y (Yes) or N (No). Only your responses in the table will be graded, not any work. Assume x(t) is the system input and y(t) is the system output. Also assume we are looking at all times (positive and negative times). l Time— §ystem Linear ? Invariant? Memoryless? Causal? ya) + t2y(t) = x(t +1) J l ,u N M t y(t) = x (1 — a] r ’ at/ M N I W) = 2 ‘J A/ Y X 7 ya) =x<2r) I M w M l b) For the system described below, determine the value of “c” that will make the system time-invariant. Use a formal technique such as we used in class (and on the homework) and justify your answer. y(t) = etj'e_’1x(l)d/t C w 2; 1 fig/XHFézDAE C 6fl 6')/x(a~+DJ/‘ LY\ 2“» ) ,to «ALL 2‘ A at a mute _ tic Ermfl‘jr — it: 7((3‘3Jt' « 8 <3 €40 0&0 21:21 L; Q: 'JCO 1:be 6 m9 ‘(jrvxfi lsr QTiQQ ...
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This note was uploaded on 11/04/2008 for the course ECE 300 taught by Professor Throne during the Fall '07 term at Rose-Hulman.

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ex1_solns - Xawxil‘ Perl/2065 Name CM Problems 1-4 are...

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