HW10 - Homework#10 Due Thursday Note Use of Matlab(or any...

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Homework #10 Due: Thursday, April 29, 2010 Note : Use of Matlab (or any other software) is not permitted. I. (see Exercise 4.2) Use Poisson’s relation to find the Fourier series for each of the following p-periodic functions on R : a. (1pt) −∞ = = m mp x e x f 2 ) ( ) ( π b. (1pt) −∞ = = m mp x a e x f | | ) (, a > 0 II. (see Exercise 4.10) Let f be a suitably regular 1-periodic function, let 0<x 0 <1 , and let m be a positive integer m=1,2,3, What can you infer about the Fourier coefficients ( c n ) n of f if you know that: a. (1pt) ) ( ) ( x f x f = b. (1pt) ) ( ) ( x f x f = c. (1pt) ) ( 1 x f m x f = + d. (1pt) ) ( 2 1 x f x f = + e. (1pt) () ) ( 0 0 x x f x x f = + f. (1pt)
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