HW10 - Homework #10 Due: Tursday, May 7, 2009 Note: Use of...

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Homework #10 Due: Tursday, May 7, 2009 Note : Use of Matlab (or any other software) is not permitted. I. (Exercises 7.34) Simplify the following expressions. The parameters a,b, are real, and m,n=0,1,2,… You can freely use rules from Fourier transform calculus, as well as operations with distributions. 1. (1pt) ) ( ) ( ) ( b a x b x a x δ ; 2. (1pt) [] ) ( " " ) ( 2 ax a ax ; a 0 3. (1pt) ) ( ) ( ) ( ) ( ) ( ) ( x x x n m n m + II. (Exercise 7.38) Find the Fourier transform of each of the following generalized functions assuming that a>0, - <b< , and n=1,2,… . 4. (1pt) ) ( ) ( ) ( b ax x f n + = ; 5. (1pt) n n b x b x x f + = ) ( ) ( ) (; 6. (1pt) n ia x x f + = ) ( ) ( III. (Exercise 7.56) Solve the following convolution equations over the space of
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