Implementation of FFT of a given sequence 

AIM: To implementation of  Fast Fourier Transform.  

EQUIPMENTS:  

Operating System - Windows XP

Constructor - Simulator

Software - CCStudio 3 & MATLAB 7.5

Fast Fourier Transform:

The Fast Fourier Transform (FFT) isa computationally fast way to calculate the DFT.

Determine the Fourier transform of the following sequence. Use the FFT (Fast Fourier

Transform) function, using inbuilt function

x (n) = {4 6 2 1 7 4 8}

MATLAB Code:     

%for defined sequence  using inbuilt function

n = 0:6;

x = [4 6 2 1 7 4 8];

a = fft(x);

mag = abs(a);

pha = angle(a);

subplot(2,1,1);

plot(mag);

grid on

title('Magnitude Response');

subplot(2,1,2);

plot(pha);

grid on

title('phase Response');

Implementation of FFT of given sequence in matlab  n-point fft  WITHOUT USING INBUILT FUNCTION

PROGRAM:

clear all;

close all;

clc;

x=input('Enter the sequence x[n]= ');

N=input('Enter the value N point= ');

L=length(x);

x_n=[x,zeros(1,N-L)];

for i=1:N

   for j=1:N

       temp=-2*pi*(i-1)*(j-1)/N;

       DFT_mat(i,j)=exp(complex(0,temp));

   end

end

X_k=DFT_mat*x_n';

disp('N point DFT is X[k] = ');

disp(X_k);

mag=abs(X_k);

phase=angle(X_k)*180/pi;

subplot(2,1,1);

stem(mag);

xlabel('frequency index k');

ylabel('Magnitude of X[k]');

axis([0 N+1 -2 max(mag)+2]);

subplot(2,1,2);

stem(phase);

xlabel('frequency index k');

ylabel('Phase of X[k]');

axis([0 N+1 -180 180]);

PROGRAM:   for user defined sequence

%fast fourier transform  

clc;  

clear all;  

close all;  

tic;  

x=input('enter the sequence');  

n=input('enter the length of fft'); %compute fft  

disp('fourier transformed signal');

X=fft(x,n)  

subplot(1,2,1);stem(x); title('i/p signal');  

xlabel('n --->');  

ylabel('x(n) -->');grid;  

subplot(1,2,2);stem(X);  

title('fft of i/p x(n) is:');  

xlabel('Real axis --->');  

ylabel('Imaginary axis -->');grid;

OUTPUT:-

enter the sequence[1 .25 .3 4]

enter the length of fft4

fourier transformed signal

X =

 5.5500             0.7000 + 3.7500i  -2.9500             0.7000 - 3.7500i

 Graph output

RESULT:  The Fast Fourier Transform  of given sequence  is obtained. Hence the theory and practical value are proved.

VIVA QUESTIONS:

? FFT is in complex domain how to use it in real life signals optimally?

? What is the difference between FFT and IFFT?

? Explain using convolution the effects of taking an FFT of a sample with no windowing  

? What is the need of FFT ?

? What’s the difference between FFT and DFT?

? Why do we need Fourier transform in DSP?

? Give any practical application of fft in daily life?

? What  is the importance of fft in  OFDMA technology?

? In STB  DVB  how many point fft is currently using?

? Give FFT & IFFT  formulae and calculate for any sequence?

? What is "decimation-in-time" versus "decimation-in-frequency"?

? What is "bit reversal"?

? How does the FFT work?