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Unformatted text preview: (15 pts) 1. Compute the energy E<>0 and the power POO for the CT signal
ma) : 61(2t+%)l (Justify your answer.) (15 pts) 2. An LT I system has unit impulse response Mn] 2 Compute the system’s response to the input = ($714 (Justify your answer.) as
\ \\\s;{/
#6"; 3x1» _. g; (20 pts) 3. Consider the system Whose input ﬁt) is related to the output
y(t) by the equation
y(t) = a:(t A 3) + $(3 — t).
a) Check all properties that that hold for this system. (No justiﬁcation
needed.) memoryless
linear
causal
stable b) Is the above system time invariant? Answer yes/no and justify your answer . Egﬁémﬁ (15 pts) 4. Suppose we are given the following information about a Signal 1. is a real and even signal. 2. X[n] has period N : 10 and Fourier coefﬁcients ak.
3. (Lu : 5. 4. 11—0 2:20 z 50. Find (Justify your answer.) \ (1 {51%;} ‘é‘e 5/} _ (ed \ (W W??? ‘3 A “MfﬁfﬁﬁffiffiT311if?f“::f'*t::°f?7::=:iér: (15 pts) 5. Consider a continuous—time LTI system Whose frequency response
is Hm) = 00 h(t)e'jwtde : 5mg”). If the input to this system is a periodic signal 1, 0§t<4
M0:{—4,4gt<8 with period T = 8, determine the corresponding system output y(t). FWST gll’lt’i irijgmmgﬁn; SQH€$ (Mimi?) (Q On: $31—Hiyo‘; [lth The value of all may be obtained witth. ( l) ' «with n = 1; thus T 2 T/4 3T/4
a1:—1—.(Vf cosmotdt— Vf coswotdt—l— VI
1 0 cos wot dt)
T/4 3T/4 REE . 901.4. 3cooT_ . (DDT) _ . 3cooT)]
_on[sm 4 sm 4 sm 4 + smon sm 4 Since cooT = 27:, we obtain for al a1=%(1+2+1)=4—n‘5 Applying the same procedure for all n, we ﬁnd that +4", n=1,5,9,...
mt r
‘1": ‘4V, n=3,7,11,...
rm .
O, n =4 even integers
b” :2 0, all n
Thus the Fourier series is 120‘) = ill/(cos wot *7“ a} cos Scoot + gzcos Swot —— J, eds 7coot —— . . .) _m . a  2
Lei M1233“? 357 (H) W” 3% ...
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This note was uploaded on 02/13/2012 for the course ECE 301 taught by Professor V."ragu"balakrishnan during the Spring '06 term at Purdue UniversityWest Lafayette.
 Spring '06
 V."Ragu"Balakrishnan

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