hw7 - ECE220 Signals and Information Spring 2008 Homework...

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ECE220 Signals and Information Spring 2008 Homework 7: Due Monday, April 7, at 10:08pm Drop your homework in the collection box marked ”ECE220 Spring 2008, homework” , located on the second foor oF Phillips at the south entrance to 219 Phillips. Print your name, NetId, and lab section in the top right corner on all pages. NOTE: This homework is based on lectures 20-66 and Chapter 12 in the textbook. Problem 1 Consider the system in ±igure 1. LTI system H(j ω ) x(t) w(t) y(t) m(t) ±igure 1. Assume that the input signal x ( t ) has a bandlimited ±ourier transForm X ( ) as graphed in ±igure 2. X(j ω ) 10π 15π -5π -10π -15π ω ±igure 2. (a) The signal w ( t ) is de²ned by w ( t ) = x ( t ) cos(5 πt ), that is m ( t ) = cos(5 πt ). Make a sketch oF the ±ourier transForm W ( ) oF w ( t ). (b) The Frequency response oF the LTI ²lter in ±igure 1 is H ( ) = b 1 | ω | < 5 π 0 | ω | > 5 π Plot the ±ourier transForm Y ( ) oF the output y ( t ).
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hw7 - ECE220 Signals and Information Spring 2008 Homework...

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