12. DISCRETE FOURIER TRANSFORM OF AN N-POINT SEQUENCE

DISCRETE FOURIER TRANSFORM OF AN N-POINT SEQUENCE

%to compute N-point DFT of the sequence x(n)

N=100; %length of sequence

xn=[1,1,1];  %input sequence

xk=fft(xn,N);

magxk=abs(xk);

angxk=angle(xk);

k=0:N-1;

subplot(2,1,1);

stem(k,magxk);

xlabel('k');

ylabel('|x(k)|');

subplot(2,1,2);

stem(k,angxk);

xlabel('k');

ylabel('arg(x(k))');

L=input('length of the sequence');  %length of the sequence

%checking for the length of the dft

if (N<L)

   error('N must be  >= L')

end

x1=[xn, zeros(1,N-L)];  %appending zeros

%computation of twiddle factors

for  k=0:1:N-1;

   p=exp(-i*2*pi*n*k/N);

   x2(k+1,n+1)=p

   end

end

xk=x1*x2;