Homework Set # 12 - Not Due – Solutions Available on December 4

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1) 15.3.2

2) 15.3.3

3) 15.3.5

4) 15.3.8

5) 15.3.9

6) 15.4.3

7) 15.4.4


8)  a) Consider he function f(x)=1 for |x|<1 and 0 otherwise.

         1) Can you expand f(x) in terms of a sine Fourier transform? Why?

         2) What Fourier transform should you use? Calculate this FT for f(x).

     b) Now consider f(x)=1 for a<x<b with a>0 and b>0 and f(x)=0 otherwise.

         1) Can you expand f(x) in terms of a sine FT? Why?

         2) If the answer to the previous question is yes perform the FT.

         3) For what values of x is your sine transform appropriated?

         4) What assumption are you making about f(-x)?

         5) Can you expand f(x) as a cosine FT? What assumption do you need to make about f(-x)?

         6) If you wanted to obtain a FT of f(x) valid for all x what FT should you use? Why? Find the coefficients .