practiceexam2 - (15 pts) 1. Compute the energy E<>0...

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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 University-West Lafayette.

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practiceexam2 - (15 pts) 1. Compute the energy E<>0...

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