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 This preview has intentionally blurred sections. Sign up to view the full version. View Full Document 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. 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. This preview has intentionally blurred sections. Sign up to view the full version. View Full Document This is the end of the preview. Sign up to access the rest of the document. 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 !"#$%&’(%\$) +",+-.#!’/01’2345.02-62!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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## This note was uploaded on 12/09/2010 for the course EE ee102 taught by Professor Levan during the Spring '09 term at UCLA.

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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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