soln_ex1

soln_ex1 - ECE320 Solutions to First Examination Cornell...

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ECE320 Solutions to First Examination Spring 2006 Cornell University T.L.Fine FAILURE TO FOLLOW INSTRUCTIONS WILL RESULT IN A LOSS OF POINTS. CLOSED BOOK, NO NOTES, CALCULATORS, OR SCRAP PAPER. TURN OFF CELLPHONES. ALLOTTED TIME IS 1 hour and 30 min. SHOW YOUR WORK, GIVE REASONS, NOT JUST ANSWERS. Place your three-digit ID number, not your name, on each sheet. Work each problem on a separate sheet of paper so that the individual questions can be separated for grading. 1. (a)(6pts) Consider the function f specified by D = { a, b, & } = R , graph( f ) = { ( a, b ) , ( b, &) , (& , a ) } . Let g = f ( f ) be the composition of f with itself. What are the domain, codomain, and graph of g ? Its domain is D and its codomain is R . As g ( x ) = f ( f ( x )) we have g ( a ) = f ( f ( a )) = f ( b ) = & , g ( b ) = f ( f ( b )) = f (&) = a, g (&) = f ( f (&)) = f ( a ) = b. graph( g ) = { ( a, &) , ( b, a ) , (& , b ) } . (b)(2pts) In a signal g ( t ) = (1 + μf ( t )) cos( ω c t ) , what qualitative effect does varying μ have on the bandwidth of g ? There is no change in bandwidth for this AM signal so long as μ = 0.

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