102_1_hw01_sol

102_1_hw01_sol - -4-3-2-1 1 2 3 4 0.2 0.4 0.6 0.8 1 1.2 1 2...

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1 .// +",-./"01 "7!8/* ’4(2 9 :55 ’4(2 9 2. (a) (b) ! " # $ % ( ) 2 2 1 t x 1 2 1 -1 3 4 5 6 1 2 1 -1 -2 -1 0.5 2 1 -1 -2 - 0.5 1.5 0.5 2 1 -1 -2
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2 3. ! " ! " ! " ! " ! " ! " ! " ! " ! " ! " * + ! " ! " * + ! " ! " ! " ! " ! " ! " ! " , , , , , , , , , - - ) - - ) - - ) - - ) - - ) - - ) - - ) - - ) - - ) . / . ) / . ) / . ) ) / ) / . / ) ) . ) / . dt t x dt t x dt t x dt t x dt t x dt t x t x dt t x t x t x t x dt t x dt t x t x t x t x t x t x t x o e o e 2 2 2 2 2 2 2 2 2 2 2 2 1 2 1 2 1 2 1 2 2 4 1 4 1 2 , 2 4. (a) ! " ! " 0 0 x T x . (from periodicity) ! " 0 0 . x (from oddness) ! " 0 0 . T x (b) Any set of values 0 T and 1 T that have an irrational ratio will result in an aperiodic sum.
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3 -4 -3 -2 -1 0 0.2 0.4 0.6 0.8 1 1.2 -4 -3 -2 -1 1 2 3 4 0 50 100 150 5. (a) 2 2 4 0 1 2 2 t t E e dt e dt - - ) ) )- . . . , , Energy type signal. (b) ! " ! " 2 1 1 1 2 1 1 1 1 ln 1 1 1 lim lim ln 0 2 2 T T T E dt dt t t t P dt t T T t - - - - 0- 0- 1 2 . . . 0 - 3 4 1 2 . . . 3 4 , , , This is neither energy type or power type. (c) This case is similar to the case in part (a) for only negative t. The signal is energy type. (d) This is obviously not an energy type signal, since we have a growing-magnitude function in both directions. 2 2 2 0 1 1 lim lim lim 2 2 2 T T T t t T T T T e P e dt e T T T ) 0- 0- 0- 1 2 . . . . - 3 4 , Neither energy type or power type.
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Unformatted text preview: -4-3-2-1 1 2 3 4 0.2 0.4 0.6 0.8 1 1.2 1 2 3 4 0.2 0.4 0.6 0.8 1 1.2 4 6. (a) ! " ! " ! " ! " 2 4 4 1 2 1 2 j t j t j t j j e e j e e j e ! " # / / / ) ) ) . . / (b) ! " ! " ! " ! " 2 2 2 2 cos 2 1 1 1 1 2 4 4 2 2 j t j t j t j t t s t e e e e ) ) / . / / . / / . There are TWO frequencies present : one at 2 and one at 0. MATLAB A) -5 5-1-0.5 0.5 1 time B) -1-0.5 0.5 1-1-0.8-0.6-0.4-0.2 0.2 0.4 0.6 0.8 1 x y A = 3 , B = 4-1-0.5 0.5 1-1-0.5 0.5 1 x A = 19 , B = 20 !"#$%&(%$) +",+-.#!/012345.02-62!1)-74!.!8+1) +79:,7. ;!6<,; 1) = " >) ? " @) !"&%&&&(%() +"345.02-62=2!1) A"345.02-62?2!1)-74!.+8A1) +79:,7. ;+; 1 A79:,7. ;A; 1 !6!7,. ;= " (B 8 ? " 0&; 1)...
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102_1_hw01_sol - -4-3-2-1 1 2 3 4 0.2 0.4 0.6 0.8 1 1.2 1 2...

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