ABSTRACT
The aim of our project is to design an application in VLSI domain. Here we have designed using VHDL which as i hardware description language that can be used to model a digital system at many levels of abstraction ranging from the algorithmic level to the gate level. The field of digital signal processing refes heavily on operations in the frequency domain (i.e. on the Fourier transform).
The fastest known algorithms for the multiplication of large integers or polynomials are based on the discrete Fourier transform: the sequences of digits or coefficients are interpreted as vectors whose convolution needs to be computed; in order to do this, they are first Fourier-transformed, then multiplied component-wise, then transformed back.
The DFT has seen wide usage across a large number of fields. All applications of the DFT depend crucially on the availability of a fast algorithm to compute discrete Fourier transforms and their inverses, a Fast Fourier Transform.
The fast multiplications which are needed to be performed in the FFT processors will involve BOOTH'S multiplication algorithm. We have implemented and tested the MODIFIED BOOTH'S ALGORITHM on the FPGA KIT and observed the results satisfactorily. We have tried to present an overview of the complete design of the FFT processor. We have used Xilinx FPGA Spartan IIPQ 208- 5 kit, ISE 8.1 Li, and Modelsim for our project.
Various FFT processors are currently available in the market but the advantage of using FFT processor with Booth's algorithm lies in the speeds that can be attained for computation. This becomes a major factor when FFT processors form an integral part of large VLSI circuits.