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# HW3 - ECE 301 Homework#3 due date...

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ECE 301, Homework #3, due date: 2/3/2010 http://cobweb.ecn.purdue.edu/ chihw/10ECE301S/10ECE301S.html Question 1: Consider two functions f ( t ) and g ( t ) described as follows. f ( t ) = ( 1 if - 1 t < 1 0 otherwise (1) g ( t ) = ( cos( πt ) if t < 3 0 otherwise . (2) Define a new function h ( t ) = R -∞ f ( s ) g ( t - s ) ds . Plot h ( t ) as a function of t . Question 2: Following the previous question, what are the “total energies” of the three signals f ( t ), g ( t ), and h ( t )? Are they of finite energies? What are the “(overall) average powers” of f ( t ) and h ( t )? Are f ( t ) and h ( t ) of finite powers? Question 3: Let x 1 ( t ) = e - 1 - 2 jt , x 2 ( t ) = cos( t + π/ 4), and x 3 ( t ) = e -| t - 1 | . Find the total energy and the average power of x 1 ( t ), x 2 ( t ), and x 3 ( t ). Question 4: p. 59, Problem 1.21 (e) and (f), and p. 59, Problem 1.22 (f) and (h). Question 5: p. 61, Problem 1.25 (e) and (f). Question 6: p. 61, Problem 1.26 (a,c,e) Question 7: Write down the expression of the continuous-time harmonically related complex (HRCE) for a given fundamental frequency ω = 2 π 5 . How many distinct CT HRCEs do we have? What is the common period of all HRCEs?

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HW3 - ECE 301 Homework#3 due date...

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