EXPERIMENT - 14

AIM

To demonstrate 8 point DFT using for loop and verify it using FFT command in MATLAB.

THEORY

DFT (Discrete Fourier Transform) is very important technique used in Digital Signal Processing. N point DFT of x(n) is given by

$X(k)=\sum^{N-1}_{n=0}x(n)e^{-j2\pi k/N}$

where $k$ goes from 0 to N-1

MATLAB COMMANDS USED

* plot(x,y,color,properties)
* exp(-j*t);
* fft(x,n)
* stem(x)
* sum(x)

MATLAB CODE

% Finding 8 point DFT using a loop
N=8;
x=[ 2     -1     1     3     -2     1     2    0];
n=-0:N-1;
for k=0:N-1
    W=exp(-j*2*pi*k*n/N); % Twiddle factor
    prod=x.*W;
    X(k+1)=sum(prod);
end

subplot(2,1,1)
stem(n,abs(X),'black','filled');
title('Magnitude spectrum of 8 point DFT');

subplot(2,1,2)
stem(n,abs(fft(x,8)),'black','filled');
title('Magnitude spectrum of 8 point DFT using fft command.');

RESULT

The 8 point DFT has been using loop and verified using FFT command in MATLAB.