Homework 6

Problem 1 
Goodman problem 2-4
In part (a), you’ll end up with a result that is expressed in terms of g(x, y).

Problem 2
Goodman problem 2-11

Problem 3
Goodman problem 2-14

In part a, you can use Mathematica to help with the integral. Integrate[ ] doesn't seem to work, but it will work if you express the integral in terms of a Fourier transform.

In part b, if you are doing the integral using Mathematica, format the result in terms of the sinc[ ] function and |x|.

In part c, you can use DensityPlot[ ]. Plot both the range to +/-10 as requested and also zoom in to plot +/-0.2 to see the fine structure.

Problem 4
Goodman problem 4-7

Calculate the Fourier transform of the function shown in figure 4.18 and express the result in terms of (Subscript[f, x]) and (Subscript[f, y]).

Problem 5
Goodman problem 4-9

Calculate the Fourier transform of the function shown in figure 4.19 and express the result in terms of (Subscript[f, x]) and (Subscript[f, y]).