%
% This script file verifies the "ideal reconstruction" formula of equation
% (4.28), using 6 samples (0..5) of a 1 Hz sine wave sampled at T=0.2 sec.
%
% Variables r will be the original sine wave, rk will be the samples,
% and rr will be the reconstructed signal.  Variables r and rr should be
% plotted vs time t, while sampled signal rk should be plotted vs tk.

% First create the sample to be used in reconstruction

k = [0:5]';  % Vector of sample indices from 0 to 5
T = 0.2;     % Sample period (corresponds to 5 Hz)
tk = k*T;    % Vector of sample times
rk = sin(2*pi*k*T);  % Calculate the samples of sine function

% Next calculate the reconstruction using a finer time step

t = [0:0.01:1]'; % Hi-res time vector for generating reconstruction
r = sin(2*pi*t); % Calculate continuous sine wave to compare
N = length(t);   % Number of samples in hi-res time vector
rr = zeros(N,1); % Create zero vector to hold reconstructed rr(t)

for k = 0:5  % Loop over sample points
    rr = rr + rk(k+1)*sinc(pi*(t-k*T)/T);
end;

hp = plot(t,r,'k-',tk,rk,'k*',t,rr,'r-');
grid;
ha = gca;
set(ha,'fontsize',18);
set(hp,'linewidth',2);
xlabel('Time (sec)');
legend('Original Function','Samples','Reconstruction');