MATLAB Programme 01: Implement DFT Without using inbuilt function

DFT Implementation

DFT is used to convert a signal sample array x(n) of size 1 x N to signal spectral component array X(k) of size 1 x N.

 

 

 

%programme

 

clc;close all;

clear all;

xn = input('Enter the sequence');

 

 

ln = length(xn);

xk = zeros(1,ln);

ixk = zeros(1,ln);

 %Calculating DFT

for k=0:ln-1

   for n=0:ln-1

xk(k+1) = xk(k+1)+(xn(n+1)*exp((-i)*2*pi*k*n/ln));

 

   end

end
%hear xk(k+1); because of in matlab array index start form 1

 

t = 0:ln-1;
subplot(3,2,1);
stem(t,xn);

title ('Input Sequence x(n)');
xlabel('Time Index');
ylabel('Amplitude');

 

t = 0:ln-1;
subplot(3,2,2);
stem(t,xk);

ylabel ('Amplitude');
title ('X(K)');
xlabel ('K');

 

 

t = 0:ln-1;
subplot(3,2,3);
stem(t,abs(xk));

 

 

ylabel ('Amplitude');

xlabel ('K');

title ('Magnitude Response');

 

 

t = 0:ln-1;

subplot(3,2,4);

stem(t,angle(xk));

 

ylabel('Phase');

xlabel('K');

title ('Phase Response');


%-------------------------------------------------------------------%

%Output
%Enter the sequence[ 1 2 3 3 2 1]