%Describe clearly how the N-point DFT performed on a signal defined
%x[n]=sin(2*pi*n/100)
%for 0=<n=<100
%for x[n]=0 for n>100
%N=100
%N=1000
N0=100;
n=0:1/50/N0:1/50-1/50/N0;
x_n=sin((2*pi*n)/100)
x_DFT=fft(x_n)
x_CTFS=1/N0*[x_DFT(4)/2,x_DFT(5:6),x_DFT(1),x_DFT(2:3),x_DFT(4)/2]
t=0:1/50/100:1/50;
x_t1=sin((2*pi*n)/100);
x_t2=0;
for nn=-N0/2:N0/2;
x_t2 = x_t2+x_CTFS(nn+N0/2+1)*exp(j*(nn)*2*pi*50*t);
end
figure(1),subplot(2,1,1),plot(t,x_t1) %original x(t)
title('f_s=f_{Nyq}'),xlabel('t'),ylabel('x(t) and x(n)'), hold on
subplot(2,1,1),stem(n,x_n,'fill'),hold off %samples x(n)
figure(1),subplot(2,1,2),plot(t,x_t2) %CTFS representation of the signal
xlabel('t'),ylabel('x(t) from CTFS'),
