quiz3_18085_f06

# quiz3_18085_f06 - MIT OpenCourseWare http/ocw.mit.edu...

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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 8, 2006 Professor Strang Your PRINTED name is: Grading 1 2 3 1) (30 pts.) (a) Suppose f ( x ) is a periodic function: f ( x ) = ± ² 0 for < x < 0 x e for 0 x f ( x + 2 n ) ikx Find the coeﬃcients c k in the complex Fourier series f ( x ) = c k e . What is c 0 ? What is | c k | 2 ? (b) Draw a graph of f ( x ) from 2 to 2 . Also draw a careful graph of df/dx . How quickly do the coeﬃcients of f ( x ) decay as k ± → and why ? (c) Find the Fourier coeﬃcients d k of df/dx . Do they approach a constant (or what pattern do they approach) as k ± → ? Explain the pattern from your graphs. for every integer n 1
x 2

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2) (33 pts.) (a) Can you complete this 4-step MATLAB code to compute the cyclic convolution f g = h ?
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quiz3_18085_f06 - MIT OpenCourseWare http/ocw.mit.edu...

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