The Fast Fourier Transform (FFT) is one of the

rudimentary operations in field of digital signal and image

processing. Some of the very vital applications of the fast

fourier transform include Signal analysis, Sound filtering, Data

compression, Partial differential equations, Multiplication of

large integers, Image filtering etc.Fast Fourier transform

(FFT) is an efficient implementation of the discrete Fourier

transform (DFT). This paper concentrates on the development

of the Fast Fourier Transform (FFT), based on Decimation-In-

Time (DIT) domain, Radix-2 algorithm, this paper uses VHDL

as a design entity, and their Synthesis by Xilinx Synthesis Tool

on Vertex kit has been done. The input of Fast Fourier

transform has been given by a PS2 KEYBOARD using a

testbench and output has been displayed using the waveforms

on the Xilinx Design Suite 12.1.The synthesis results show that

the computation for calculating the 32-point Fast Fourier

transform is efficient in terms of speed.