hw6ans_1

# hw6ans_1 - Homework 6 Answers 1(a x(t = 2(t 0.4 0.6e#0.3 t...

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Homework 6: Answers 1. (a) x ( t ) = 2 " ( t # 0.4) # 0.6 e # 0.3( t # 0.4) u ( t # 0.4) (b) x ( t ) = 3 " ( t ) # " ( t # 1) # " ( t + 1) (c) x ( t ) = e " 2 t " e " 5 t ( ) u ( t ) (d) " 1 # sin(17 # t ) 2. X ( j " ) = j " e # j 2 " u " + 6 \$ ( ) # u " # 6 \$ ( ) [ ] 3. x ( t ) = 4 te " 2 t " 2 e t u ( " t ) 4. (a) (b)

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5. (a) X ( j " ) = 2 #\$ ( " % n 2 # ) n = %& & (b) H ( j " ) = 4 u " + " co ( ) # u " # " co ( ) [ ] (c) y ( t ) = 8 cos(4 " t ) + 8 cos(2 " t ) + 4 (d) Choose " co such that 0 < " co < 2 # . This will filter out all frequencies except the DC term and the result will be y ( t ) = 4 . 6. (P 12.4) b)
c) d) The output signal consists of only one copy of each half of the original spectrum. 7. (P-12.6) a) b) c) The system places the positive frequency portion on the negative frequency portion and the negative frequency portion on the positive frequency portion by translating the pos. freq. portion

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Unformatted text preview: to the left by m w and the neg. freq. portion to the right by m w . d) 8. (P-12.12) a) ! 160 " s w For 160 = s w , 80 1 = s T , b) For 100 = s w , 50 1 = s T , For one period 50 50 " " # w , 50 20 , 20 , 20 , 20 50 , ) ( 4 3 80 80 4 3 " " " " " " # # " " # \$ \$ % \$ \$ & ’ + # + = w w w w w w jw X s s s s s s T A T A T A T A T A T A s c) 9. (P-12.14ab) a) ! 2000 2 " s T b) ) 10 ( ) ( s T t x t y ! =...
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