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hw6 - ECE220 Signals and Information Spring 2008 Homework 6...

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ECE220 Signals and Information Spring 2008 Homework 6: Due Monday, March 24, at 10:08am Drop your homework in the collection box marked ”ECE220 Spring 2008, homework” , located on the second floor 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 16-18 and Chapters 10 and 11 in the textbook. Problem 1 Find Fourier transform of the following functions (a) y ( t ) = sin(2 t ) δ ( t + 1) (b) h ( t ) = 2sin(2 π ( t - 1)) π ( t - 1) (c) x ( t ) = e - 2 t u ( t 2) e - 2 t u ( t + 2) (d) y ( t ) = d dt parenleftBig sin(2 π ( t - 2)) π ( t - 2) parenrightBig State what properties of Fourier transfrom you used to arrive at your answers. Problem 2 Find the inverse Fourier transform of the following functions (a) H (j ω ) = δ ( ω 2) ( πδ ( ω ) + πδ ( ω 4)) e 3j ω (b) Y (j ω ) = 2j ω 6+3j ω (c) Y (j ω ) = 3 2 sin ω . (d) Y (j ω ) = 1 (2 - j ω ) 2
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State what properties of Fourier transfrom you used to arrive at your answers.
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