Good day Donghoon Lee,
as far as I understand your question, you would like to have the Fourier-transform of selected areas of an image.
I don't think, that you will be able to get a temporally contiuous computation but, depending on the size of the selection, a quite fast one. In any case, a macro or script will be necessary.
Please note that the Fourier-transformation algorithm that comes "native" with ImageJ is only fast for square selections with side lengths 2^x (with integer x), which is a ususal restriction known from the classic FFT-algorithm.
Furthermore, you should consider a suitable window function for your selection in order to reduce the influence of the selection borders to the Fourier-spectra.
BTW, are you changing the selection (position?) manually or by use of a macro?