Designing and Simulation of 32 Point Fft Using Radix-2 Algorithm for Fpga

Abstract

The Fast Fourier Transform (FFT) is one of the rudimentary operations in field of digital signal and image processing. Some of the 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 VERILOG as a design entity. The input of Fast Fourier transform has been given by a keyboard using a test bench and output has been displayed using the waveforms on the Xilinx Design Suite 13.1 and synthesis results in Xilinx show that the computation for calculating the 32- point Fast Fourier transform is efficient in terms of speed. I. Introduction This proposes the design of 32-points FFT processing block. The work of the project is focused on the design and implementation of FFT for a FPGA kit. This design computes 32-points FFT and all the numbers follow fixed point format of the type Q8.23, signed type input format is used.The direct mathematical derivation method is used for this design. In this project the coding is done in VHDL (8) & the FPG synthesis and logic simulation is done using Xilinx ISE Design Suite 13.1. The Discrete Fourier Transform (DFT) plays an important role in the analyses, design and implementation of the discrete-time signal- processing algorithms and systems it is used to convert the samples in time domain to frequency domain. The Fast Fourier Transform (FFT) is simply a fast (computationally efficient) way to calculate the Discrete Fourier Transform (DFT). The wide usage of DFTs in Digital Signal Processing applications is the motivation to Implement FFTs. Almost every branch of engineering and science uses Fourier methods. The words frequency, period, phase, and spectrum are important parts of an engineer's vocabulary.The Discrete Fourier transform is used to produce frequency analysis of discrete non periodic signals. The FFT is another method of achieving the same result, but with less overhead involved in the calculations. Fig1: