quiz318085f05 - MIT OpenCourseWare http/ocw.mit.edu 18.085...

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MIT OpenCourseWare http://ocw.mit.edu 18.085 Computational Science and Engineering I Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
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18.085 Quiz 3 December 9, 2005 Professor Strang Your PRINTED name is: Grading 1 2 3 1) (30 pts.) (a) Solvc this cyclic convolutior~ cyuation for tllc vcctor d. (I would trans- for111 corlvolutiorl to multiplication.) Noticc that c = (5,0,0,0) - (1,1,1,1). Thc cyuation is likc dcconvolution. (h) IVhy is thcrc no solution d if I changc c to C = ( 3 , - 1 , - 1 , l ) ? Try it. Can you find a rlonzcro D so that C O D = (0,0,0,0) ?
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2 ) (36 pts.) (a) Iff ( r c ) = e-" for 0 < rc < 27r, cxtcrldcd periodically, find its (cornplcx) Fouricr cocfficic~lt~s ck. (h) What is thc dccay ratc of thosc ck and how could you scc tllc dccay ratc from tllc fu~lctiorl f ( r c ) '! 00 (c) Corr~putc C c k 2 for tllosc C'S as a11 ordinary 11umbcr.
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