the meantime the fast fourier transform has the duality property the duality property is the property that when x m is referred to as an fft result of x n an fft result of x m becomes the x n if the fast fourier transform is done with the interpolation that four times repeats the 1024 input data of time domain data of 3 zeros is inserted and distributed between the 1024 input data in frequency domain according to the fft duality property refer to fig2 b the application of the interpolation according to such a duality property is described below in order for an fft processor to perform the same radix 4 algorithm on diverse input data modes such as 2048 1024 256 and 512 the address generator 300 generates the same addresses from 0 to 4095 for 2048 1024 256 and 512 input data according to this the memory controller 450 interpolates the diverse input data to 4096 data that is the memory controller 450 repeats the interpolation on the input data twice for the 2048 mode four times for the 1024 mode 16 times for the 256 mode and 8 times for the 512 mode accordingly the memory 410 capable of storing 2048 data stores data corresponding to the addresses from 0 to 2047 from the data addressed 0 to 4095 at this time the memory controller 450 stores in a virtual memory data corresponding to the addresses from 2048 to 4095 that is the data substantially stored in the memory 410 are data addressed from 0 to 2047 and the rest of the data addressed from 2048 to 4095 is not stored in the memory 410 but acknowledged by the memory controller 450 only as.