# HW3 - ECE 301, Homework #3, due date: 9/18/2008

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ECE 301, Homework #3, due date: 9/18/2008 http://www.ece.purdue.edu/ chihw/ECE301 08F.html Question 1: Consider two functions f ( t ) and g ( t ) described as follows. f ( t ) = ( 1 if 0 t < 2 0 otherwise (1) g ( t ) = ( cos(2 πt ) if - 2 t 0 otherwise . (2) Deﬁne a new function h ( t ) = R -∞ f ( s ) g ( t - s ) ds . Plot h ( 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 “(total) average powers” of the three signals? Are they of ﬁnite powers? Question 3: Let x 1 ( t ) = e 2+ jt , x 2 ( t ) = cos( πt + π/ 2), and x 3 ( t ) = e -| t | . 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. (d) and (f), and p.59, Problem 1.22. (d) and (f). Question 5: p.61, Problem 1.25 (a) and (c). Question 6:

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## HW3 - ECE 301, Homework #3, due date: 9/18/2008

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