If an image is seen from afar, your perception is dominated
  by the low-frequency spatial frequencies of the image. At close
  range, high-frequency elements dominate. Here I tried to compose
  an image consisting of low-frequency 'welcome to STAR' and
  high-frequency 'welcome to PHENIX'. COuld not make it work.

    http://www.imagemagick.org/Usage/fourier/#blurring
http://www.imagemagick.org/Usage/compose/#math

Convert a sharp circle mask to a blurred circle mask (low-pass filter):
 convert circle_r14.png -blur 0x4 -auto-level gaussian_r14.png

Do a FFT using this mask:
  convert lena.png -fft \
       \( -clone 0 gaussian_r14.png -compose multiply -composite \) \
       \( +clone -evaluate log 10000 -write lena_gblur_r14_spec.png +delete \) \
       -swap 0 +delete -ift lena_gblur_r14.png