pkg load signal
graphics_toolkit gnuplot

L=5600;
window = hann(L);
N=8;                            % window size, in samples

warning("off")
dx = (L-1)/(N-1);               % decimation factor for 7 hops (8 samples)
symmetric = window(1+(0:7)*dx); % take 8 of 8 symmetrical samples
dx = (L-1)/N;                   % decimation factor for 8 hops (9 samples)
periodic = window(1+(0:7)*dx);  % take 8 of 9 symmetrical samples

%Replace above with the equivalent formulaic versions
%This step just proves that formulas match window() array.
 symmetric = .5*(1-cos(2*pi*(0:N-1)/(N-1)));
 periodic  = .5*(1-cos(2*pi*(0:N-1)/N));     % aka "DFT Even"

%Compare equivalent noise bandwidths (info only)
 ENBW_symmetric = N*sum(symmetric.^2)/sum(symmetric)^2
 ENBW_periodic  = N*sum(periodic.^2) /sum(periodic)^2
 
%Plot the coefficients as dots
 hfig=figure
 plot(0:7, symmetric, 'color', 'red', '.', 'MarkerSize', 10)
 box off                                    % no border around plot
 hold on                                    % same axes for next 3 plots
 
 plot(0:7, periodic,  'color', 'blue', '.', 'MarkerSize', 10)
 
%Connect the dots
 x = (0:L-1)*N/L;
 plot(x, window, 'color', 'blue')           % periodic

x = (0:L-1)*(N-1)/L;
plot(x, window, 'color', 'red')             % symmetric
 
xlim([0 8])
set(gca,'FontSize',14)
set(gca, "yaxislocation", "origin")
set(gca, 'xgrid', 'on');
set(gca, 'ygrid', 'on');
set(gca, 'ytick', [0:.25:1]);
set(gca, 'xtick', [0:8]);
text(3.3, 0.27, 'Matlab "symmetric" \rightarrow', 'color', 'red', 'FontSize',12)

str = {'\leftarrow Matlab "periodic"','     ("DFT-even")'};
text(5.5, 0.74, str, 'color', 'blue', 'FontSize',12)

title('Two 8-point Hann window functions', 'FontSize',12);
xlabel('\leftarrow  n  \rightarrow')

% I actually used the export function on the GNUPlot figure toolbar.
print(hfig,"-dsvg", "-S620,392","-color", 'C:\Users\BobK\8-point Hann windows.svg')