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202HW1-12Sp10

# 202HW1-12Sp10 - ECE-202 HOMEWORK PROBLEMS(SET 1 SPRING 10...

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ECE-202 H OMEWORK P ROBLEMS (S ET 1) S PRING 10 TO THE STUDENT: ALWAYS CHECK THE ERRATA on the web. ANCIENT ASIAN PROVERB: If you give someone a fish, you give them food for a day; teach a person to fish and you give them food for a lifetime. The Moral of the Proverb is: learn to read the text, the class notes, and then reason your way through the HW problems rather than ask the TA to give you a solution for the day. RAY’S VIEW OF EDUCATION : The success of your education depends on your investment in that education. All investment is a risk. Investment planners always talk about the long term. Learn the material of this course for the long term, not the short term grade. Information is only part of the investment portfolio. The development of your thinking patterns constitutes the long term goal. Successful professors have thinking patterns you would do well to learn, as a musician might learn the rhythm and blues progressions of the best guitarists. Learn them and be the best you can be. Mediocrity is mostly a choice—will it be yours? ADVICE : do as many problems in each chapter as you can. Try the easy ones first. D UE F RIDAY W EEK 1 (J AN 15) 1. (Signal represenation and Laplace transforms) Recall that u ( t ) denotes the unit step function, r ( t ) = tu ( t ) the ramp function, and ! ( t ) the so-called delta function (which is NOT really a function, but rather a so-called distribution). (a) Sketch the indicated signals on graph paper or in MATLAB. (i) f 1 ( t ) = 2 u ( t ) u (2 ! t ) (ii) f 2 ( t ) = u ( t ) ! r ( t ! 1) + r ( t ! 2) . (iii) f 3 ( t ) = 4 r ( t ) u (1 ! t ) (iv) f 4 ( t ) = 2 r ( t ) u (1 ! t ) + u ( t ! 1) r (2 ! t ) (v) f 5 ( t ) = ! 2 " ( t + 1) + 4 " ( t ! 1) Hint: delta’s are represented by arrows pointing up or down with a parenthetical expression indicating the weight or area of the delta.

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