pkg load signal
graphics_toolkit gnuplot
clc
M=4096;
window = hann(M)';                   % row vector
N=16;                                % window size, in samples

dx = M/N;                            % decimation factor for 16 hops (17 samples)
periodic = window(1+(0:15)*dx);      % take 16 of 17 symmetrical samples

%Plot the points
 figure
 plot(0:15, periodic,  'color', 'blue', '.', 'MarkerSize',14)
 hold on
 
%Connect the dots
 x = (0:M-1)*N/M;
 plot(x, window, 'color', 'blue')    % periodic

xlim([0 16])
set(gca, 'xgrid', 'on');
set(gca, 'ygrid', 'on');
set(gca, 'ytick', [0:.25:1]);
set(gca, 'xtick', [0:16]);

title('DFT-even Hann window function');
xlabel('\leftarrow  n  \rightarrow','FontSize', 14)

%Now compute and plot the DTFT
 M=64*N;
 dr = 80;

H = abs(fft([periodic zeros(1,M-N)]));
H = fftshift(H);
H = H/max(H);
H = 20*log10(H);
H = max(-dr,H);
x = N*[-M/2:M/2-1]/M;

figure
plot(x, H, 'color', 'blue');
hold on

%Plot the 3 non-zero points
plot(-1:1, H((N/2-1:N/2+1)*M/N),  'color', 'blue', '.', 'MarkerSize',14)
ylim([-dr 0])
xlim([-N/2 N/2-1])

set(gca,'XTick', -N/2:N/2-1)
grid on
ylabel('decibels','FontSize', 14)
xlabel('DFT bins','FontSize', 12)

title('Non-zero DFT coefficients of Hann window')