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In this paper a hardware implementation of a Fast Fourier Transform (FFT) processor has been presented. Described FFT processor is implemented on a virtex-4 LX25 FPGA from Xilinx. The designed processor is a fixed-point processor which calculates a 1024-point complex FFT using radix-2 butterfly computation method with less than 1% error. This system completes the process in 26μs at operating frequency of 100MHz. The number of occupied slices on the (FPGA) is 2472 which covers 23% of the whole chip.