% This MATLAB script is a template to
% (1) define and plot a sinusoidal sequence, x[n], n=1..N
% (2) calculate and plot its discrete-time Fourier series (DTFS) X[k], k=1..N by means of the fft algorithm.
% 
% Author: A. Muschinski
% Date:   4 March 2007

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

% Clear workspace:
clear all

% --- Define DT signal x[n]: 

% N1 = period of sinusoid;
% M  = number of full oscillations;
% P  = N - M*N1 (number of "excess samples", that is, number of samples 
%      in excess of full periods);
% N  = total number of samples.

N1 = 50;
M  = 5;
P  = 1;

N = M*N1+P;

for i = 1:N
    n(i) = i-1;
    x(i) = sin((2*pi/N1)*i);
end

% Define k array equal to n array (k = 0,..,N-1):
k = n;

% --- Calculate the DTFS by means of the MATLAB Fast Fourier Transform
% (FFT) algorithm:

X = fft(x);
mag_X = abs(X);
phi_X = angle(X);


%%%%%%%%%%%%%%% PLOT DATA %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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

% Plot DT signal x:

figure(1)
plot(n,x,'k.-','MarkerSize',12)
hold on
plot([0 N+1],[0 0],'k-')
hold off
title('Discrete-time signal')
xlabel('n')
ylabel('x[n]')
xlim([0 N+1])
ylim([-1.2 1.2])
%-------------------------------------------------

% Plot absolute value of DTFS (semilogarithmically):

figure(2)
semilogy(k,mag_X,'k.-','MarkerSize',12)
hold on
plot([0 N+1],[0 0],'k-')
hold off
title('Magnitude of DTFS')
xlabel('k')
ylabel('|X[k]|')
xlim([0 N+1])
% ylim([-0.2 1.2])
%--------------------------------------------------

% Plot absolute value of DTFS (linearly):

figure(3)
plot(k,mag_X,'k.-','MarkerSize',12)
hold on
plot([0 N+1],[0 0],'k-')
hold off
title('Magnitude of DTFS')
xlabel('k')
ylabel('|X[k]|')
xlim([0 N+1])
% ylim([-0.2 1.2])
%--------------------------------------------------


% Plot phase of DTFS:
figure(4)
plot(k,phi_X,'k.','MarkerSize',12)
hold on
plot([0 N+1],[0 0],'k-')
hold off
title('Phase of DTFS')
xlabel('k')
ylabel('\phi_x[n]')
xlim([0 N+1])
% ylim([-0.2 1.2])