cos(2*PI/60*X)*cos(2*PI/60*Y)
    


                                                        Fourier Transform[ cos(2*PI/60*X)*cos(2*PI/60*Y) ]
                                                        This has a large range (from 0 to ~ 10000)
      
    



                                                        Fourier Transform[ cos(2*PI/60*X)*cos(2*PI/60*Y) ]
                                                        The range of the image is clamped from 0 to ~ 600
                                                        to better visualize the nonzero portions of the spectrum
    


                                           
                                                        abs( cos(2*PI/60*X)*cos(2*PI/60*Y) )
                                                        This is the abs of the original
    


                                                       Fourier Transform[ abs( cos(2*PI/60*X)*cos(2*PI/60*Y)) ]
                                                        This has a large range (from 0 to ~ 10000)
 
    


                                                        Fourier Transform[ abs( cos(2*PI/60*X)*cos(2*PI/60*Y) ) ]
                                                        The range of the image is clamped from 0 to ~ 600
                                                        to better visualize the nonzero portions of the spectrum
    


                                                        This is the filtered abs function (filtered with a box function)
                                                        The three curves show the function filtered with three different
                                                        widths.

                                                        The next sets of images are the result of using the abs with the
                                                        three different widths (and frequency plots, clamped and unclamped)
    


                                               
                                                        Using the 0.1 width abs
                                                        filtered_abs( cos(2*PI/60*X)*cos(2*PI/60*Y) , 0.1)

    


                                                      Fourier Transform[  filtered_abs( cos(2*PI/60*X)*cos(2*PI/60*Y) , 0.1) ]
                                                      fourier transform (unclamped) of 0.1 width 
    


                                                      Fourier Transform[  filtered_abs( cos(2*PI/60*X)*cos(2*PI/60*Y) , 0.1) ]
                                                      fourier transform (clamped to 600) of 0.1 width
    


                                               
                                                        Using the 0.5 width abs
                                                        filtered_abs( cos(2*PI/60*X)*cos(2*PI/60*Y) , 0.5)
    


                                                      Fourier Transform[  filtered_abs( cos(2*PI/60*X)*cos(2*PI/60*Y) , 0.5) ]
                                                      fourier transform (unclamped) of 0.5 width
    


                                                      Fourier Transform[  filtered_abs( cos(2*PI/60*X)*cos(2*PI/60*Y) , 0.5) ]
                                                      fourier transform (clamped to 600) of 0.5 width

    

                                              
                                                        Using the 1.0 width abs
                                                        filtered_abs( cos(2*PI/60*X)*cos(2*PI/60*Y) , 1.0)
    


                                                      Fourier Transform[  filtered_abs( cos(2*PI/60*X)*cos(2*PI/60*Y) , 1.0) ]
                                                      fourier transform (unclamped) of 1.0 width
    


                                                      Fourier Transform[  filtered_abs( cos(2*PI/60*X)*cos(2*PI/60*Y) , 1.0) ]
                                                      fourier transform (clamped to 600) of 1.0 width
    

  
  

               side by side comparison of the original (abs(cos...)) and the three filtered versions.
               Top left is original. Top right is 0.1. Bottom left is 0.5, and Bottom right is 1.0.

    
              width = 0.1


    
              width = 0.5
    
    
              width = 1.0
    
    These are the differences between the filtered and unfiltered  versions
    for each of the three widths