% dft_ex1.m -- Some signals to compute DFT and interpret.
% Modified from dft_ex.m to produce plots for all signals.

% Rich Kozick, Spring 1997

% Instructions:  Plot each time signal and compare the signal shape with 
% the DFT basis vectors. 
% Then look at the corresponding DFT coefficients and interpret them.
% Can you explain?

N = 8;
n = 0:N-1;

% Signals to consider

x1 = ones(1,N);
x2 = cos(2*pi*n/N);
x3 = 5*cos(2*pi*2*n/N);
x4 = 0.2*sin(2*pi*n/N);
x5 = cos(2*pi*2*n/N + pi/3);
x6 = cos(2*pi*1.5*n/N);
x = [x1; x2; x3; x4; x5; x6]';
X = fft(x);

for k=1:6

figure(k)
subplot(311)
plot(n,x(:,k),'-',n,x(:,k),'o');
title(['Signal ' num2str(k)]);
subplot(312)
plot(n,real(X(:,k)),'*')
% axis([0 7 -5 8])
title('Real FFT Coeff.')
subplot(313)
plot(n,imag(X(:,k)),'*')
% axis([0 7 -5 8])
title('Imag FFT Coeff.')

end

% Effect of zero-padding signal 6

X6_16 = fft(x6, 16);
n16 = 0:.5:7.5;

figure(7)
subplot(411)
plot(n,x(:,k),'-',n,x(:,k),'o');
title('Signal 6 with zero padding to N = 16')
subplot(412)
plot(n,real(X(:,6)),'x')
hold on 
plot(n16,real(X6_16),'o')
hold off
ylabel('Real FFT')
subplot(413)
plot(n,imag(X(:,6)),'x')
hold on 
plot(n16,imag(X6_16),'o')
hold off
ylabel('Imag FFT')
subplot(414)
plot(n,abs(X(:,6)),'x')
hold on 
plot(n16,abs(X6_16),'o')
hold off
ylabel('Abs FFT')