%
% Written by:
% --
% John L. Weatherwax                2009-04-21
%
% email: wax@alum.mit.edu
%
% Please send comments and especially bug reports to the
% above email address.
%
%-----

close all; clc; clear; 

% EPage 138

y = [ 0, 0.9094, 0.4251, -0.603, -0.6567, 0.2247, 0.684, 0.1217, -0.5462, ...
      -0.3626, 0.312, 0.4655, -0.0575, -0.4373, -0.1537, 0.3137, ...
      0.2822, -0.1446, -0.3164, -0.0204, 0.2694, 0.1439, -0.1702, ...
      -0.2065, 0.0536, 0.2071, 0.0496, -0.1594, -0.1182, 0.0853, ...
      0.1441, -0.0078 ];

nt = length(y);

T = 0.0625;
dt = T / nt;
t = 0:dt:(T-dt);
df = 1/T;
fmax = nt/(2*T);
f = 0:df:df*(nt/2-1);

Y = fft(y);
Ys = zeros(1,nt/2);
Ys(1:nt/2) = (2/nt)*Y(1:nt/2);
plot( f, abs(Ys) );
xlabel('frequency Hz'); ylabel('abs(DFT)'); title('DFT of original data');
grid('on');

% Notice how spread out the frequency resolution peak is
%
%saveas( gcf, '../../WriteUp/Graphics/Chapter7/c_7_p_16_orig_plot.eps', 'epsc' );

figure; 

% zero pad : 
y = [ y, zeros( 1, 480 ) ];

nt = length(y);
T = dt * nt; 
t = 0:dt:(T-dt);
df = 1/T;
fmax = nt/(2*T);
f = 0:df:df*(nt/2-1);

Y = fft(y);
Ys = zeros(1,nt/2);
Ys(1:nt/2) = (2/nt)*Y(1:nt/2);
plot( f, abs(Ys) );
xlabel('frequency Hz'); ylabel('abs(DFT)'); title('DFT of zero padded data');
grid('on');

% The frequency response is now much tigher
%
%saveas( gcf, '../../WriteUp/Graphics/Chapter7/c_7_p_16_zero_padded_plot.eps', 'epsc' );