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Unformatted text preview: EGM 4313 Summer 2007 NAME:____________________________________ Final Exam Part A 60 minute time limit. Closed notes Open book No calculators 1) Using contour integration find the inverse Fourier transform of ( 29 1 , 0. f a a i = + (Hint: you will need to handle x>0 and x<0 differently.) ( 29 ( 29 1 1 1 1 2 2 2 i x i x i x i f x f e dx e dx e dx a i ia ---- = = = +- If x>o, then consider the following contour: On the curved part ( 29 ( 29 ( 29 sin cos R x iR i x e e e - = so the integral on the curved part goes to 0 as R . Therefore for x>0, ( 29 ( 29 ( 29 2 Re 2 2 2 2 i ia x ax i i f x i sidue at ia i e e --- = = = = If x<0, then we must close the contour in the lower half plane so that the integral is zero on the curved part as R , that is we need sin( ) negative in the expression ( 29 ( 29 ( 29 sin cos R x iR i x e e e - = ....
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This note was uploaded on 12/15/2011 for the course EGM 4313 taught by Professor Mei during the Fall '08 term at University of Florida.
- Fall '08