%
% 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 137

nt = 512;
T = 1;
dt = T/nt;
t = 0:dt:(T-dt);
df = 1/T;
fmax = nt/(2*T);
f = 0:df:df*(nt/2-1);

f_1 = 25;
y = sin( 2*pi*f_1*t );
Y = fft(y);
Ys = zeros(1,nt/2);
Ys(1:nt/2) = (2/nt)*Y(1:nt/2);
plot( f, abs(Ys), '-b' ); hold('on');

f_2 = 30.27;
y = sin( 2*pi*f_2*t );
Y = fft(y);
Ys = zeros(1,nt/2);
Ys(1:nt/2) = (2/nt)*Y(1:nt/2);
plot( f, abs(Ys), '-r' );

f_3 = 35.49;
y = sin( 2*pi*f_3*t );
Y = fft(y);
Ys = zeros(1,nt/2);
Ys(1:nt/2) = (2/nt)*Y(1:nt/2);
plot( f, abs(Ys), '-g' );

xlabel('frequency Hz'); ylabel('abs(DFT)'); grid('on'); title('DFT direct');
legend( 'f=25', 'f=30.27', 'f=35.49', 'location', 'best' );

%saveas( gcf, '../../WriteUp/Graphics/Chapter7/c_7_p_15_orig_dft_plot.eps', 'epsc' );

% Extract the Hanning window and apply this to each sample realization: 
%
figure; 

wght = 0.5 * ( 1 - cos( 2 * pi * t / T ) );

y = sin( 2*pi*f_1*t ) .* wght;
Y = fft(y);
Ys = zeros(1,nt/2);
Ys(1:nt/2) = (2/nt)*Y(1:nt/2);
plot( f, abs(Ys), '-b' ); hold('on');

y = sin( 2*pi*f_2*t ) .* wght;
Y = fft(y);
Ys = zeros(1,nt/2);
Ys(1:nt/2) = (2/nt)*Y(1:nt/2);
plot( f, abs(Ys), '-r' );

y = sin( 2*pi*f_3*t ) .* wght;
Y = fft(y);
Ys = zeros(1,nt/2);
Ys(1:nt/2) = (2/nt)*Y(1:nt/2);
plot( f, abs(Ys), '-g' );

xlabel('frequency Hz'); ylabel('abs(DFT)'); grid('on'); title('DFT with weighting');
legend( 'f=25', 'f=30.27', 'f=35.49', 'location', 'best' );

%saveas( gcf, '../../WriteUp/Graphics/Chapter7/c_7_p_15_orig_weighted_dft_plot.eps', 'epsc' );