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### 20115ee102_1_hw1

Course: ELEC ENGR 102, Fall 2011
School: UCLA
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Word Count: 298

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Quarter 1 EE102 Fall 2011 Systems and Signals Jin Hyung Lee Homework #1 Due: Wednesday October 05, 2011 at 5 PM. 1. Find the even and odd decomposition of this signal: 2 1 -2 -1 x(t) 0 1 2 t 2. Given the signal x(t) shown below x(t ) 1 -2 -1 0 -1 1 2 t draw the following signals: (a) x(2(1 t)) (b) x t 2 1 3. In class we showed that any signal can be written as the sum of an evan and odd...

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Quarter 1 EE102 Fall 2011 Systems and Signals Jin Hyung Lee Homework #1 Due: Wednesday October 05, 2011 at 5 PM. 1. Find the even and odd decomposition of this signal: 2 1 -2 -1 x(t) 0 1 2 t 2. Given the signal x(t) shown below x(t ) 1 -2 -1 0 -1 1 2 t draw the following signals: (a) x(2(1 t)) (b) x t 2 1 3. In class we showed that any signal can be written as the sum of an evan and odd component, x(t) = xe (t) + xo (t). Show that the energy of x(t) is the sum of the energies of the even and odd components x2 (t) dt = x2 (t) dt + e x2 (t) dt. o 4. Periodic Signals (a) Assume that the signal x(t) is periodic with period T0 , and that x(t) is odd (i.e. x(t) = x(t)). What is the value of x(T0 )? 2 (b) Two continuous-time sequences x1 (t) and x2 (t) are periodic with T1 periods and T2 . Find values of T1 and T2 such that x1 (t)+x2 (t) is aperiodic. 5. Power and Energy Signals Plot these signals, and classify them as energy or power signals. Support your classication with an explicit calculation or an argument. In each case < t < . (a) x(t) = e2|t| (b) x(t) = 1 t t1 0 t<1 0 t0 et t < 0 (c) x(t) = (d) x(t) = e|t| 6. Review of Complex Numbers (a) Simplify the following expression ej (t+) (1 j ) 1+j and leave the result in polar form. (b) Simplify (cos t + j sin t) (cos 2t j sin 2t) and leave the result in polar form. 7. Write the following signals as a combination (sums or products) of scaled and shifted unit rectangles rect(t) and unit triangles (t). a) 2 x(t) b) 2 1 0 -2 1 -1 x(t) 1 0 2 -2 1 -1 -1 -1 -2 -2 2 t
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UCLA - ELEC ENGR - 102
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Chapter 5 The Dynamic Cell MembraneChap t er 5 , p ag e 1Chap t er 5 , p ag e 2Chap t er 5 , p ag e 3Mem b r ane Tr ansp o r t Pr o c essesI. Passiv e Pr o c essesChap t er 5 , p ag e 4Chap t er 5 , p ag e 5Chap t er 5 , p ag e 6Chap t er 5 , p a
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Chapter 6 Energy, Enzymes, and Metabolisme x e r g o n ice n d e r g o n icChap t er 6 , p ag e 1\$ \$ = ATPChap t er 6 , p ag e 2Chap t er 6 , p ag e 3Chap t er 6 , p ag e 4lac t o se - - - - - - - - - - - - - - - &gt; g alac t o se( c o l o r l e ss
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Chapter 7 Pathways That Harvest Chemical EnergyChapt er 7 , page 1Chapt er 7 , page 2Chapt er 7 , page 3Chapt er 7 , page 4NADH + H+CO22C4C6CNADH + H+CO2FADH25CATPNADH + H+NADH + H+CO24CChapt er 7 , page 5Chapt er 7 , page 6Chapt er 7
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Chapter 8 Photosynthesis: Energy from SunlightChap t er 8 , p ag e 1u se sg ener at esChap t er 8 , p ag e 2e-e-eee-e-Chap t er 8 , p ag e 3e-e-H+H+Chap t er 8 , p ag e 4Chap t er 8 , p ag e 5Chap t er 8 , p ag e 6Chap t er 8 , p ag e 7C
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