A project report submitted in fulfillments of the requirements for the award of degree ofBACHELOR OF TECHNOLOGY

INELECTRONICS AND COMMUNICATION ENGINEERING

IMPLEMENTATION OF FAST FOURIERTRANSFORMATION USING LABVIEW

Prepared by

•B .SUMA 13951A0494 • R.BHAVANA 13951A0458 •A.SHAMALA 13951A0409 •B.KARTHIK 13951A0470

Under The Guidance Of

G.ANIL REDDY Assistant Professor ECE, IARE

Fast Fourier Transformation Introduction

 The Fast Fourier Transform is an algorithm optimization of the DFT—Discrete Fourier Transform. 

The “discrete” part just means that it’s an adaptation of the Fourier Transform, a continuous process for the analog world, to make it suitable for the sampled digital world.

 The results of the FFT are the same as with the DFT, the only difference is that the algorithm is optimized to remove redundant calculations

DEFINITION

The fast Fourier transform maps time-domain functions into frequency-domain representations. FFT is derived from the Fourier transform equation, which is:

where x(t) is the time domain signal, X(f) is the FFT, and ft is the frequency to analyze

Fast Fourier Transform, or FFT, is any algorithm for computing the N-point DFT with a computational complexity of O(N log N). It is not a new transform, but simply an efficient method of calculating the DFT of x(n)..

FFT ALGORITHMIF WE ASSUME THAT N IS EVEN,WE CAN WRITE THE N POINT DFT OF X(N ) AS

BUTTER FLY DIAGRAM N-POINT FFT

TWIDDLE FACTOR EQUATION

3-STAGE FFT-RADIX2 ALGORITHM

HOW IT IS APPLIED FFT is derived by cooley-tukey algorithm. It is also called

as RADIX-2 algorithm. This is a divide and conquer

algorithm that recursively breaks down a DFT of any composite size N = N1N2into many smaller DFTs of sizes N1 and N2, along with O(N) multiplications by complex  roots of unity traditionally called twiddle factors.

WHY WE ARE USING IN LABVIEW? LabVIEW is an integrated development environment

designed specifically for engineers and scientists building measurement and control systems.

LabVIEW is a flexible programming environment that can help successfully build unique application, by taking simple measurements . 

BLOCK DIAGRAM

system labview

Front panel

block diagra

m

Input and output display

LABVIEW BLOCKDIAGRAM

FRONT PANEL FOR GIVING INPUTS AND DISPLAYING OUTPUTS

APPLICATIONS OF FFTFFT's importance derives from the fact that in signal

processing and image processing it has made working in frequency domain equally computationally feasible as working in temporal or spatial domain.

FFT is a powerful signal analysis tool applicable to a wide variety of fields including spectral analysis.

Digital filtering.Medical imaging.Numerical analysis. Instrumentation and communications.

THANK YOU!!!