pkg load signal
graphics_toolkit gnuplot
clear all; close all; clc

 M=5600;        % big number, divisible by 7 and 8
% Generate M+1 samples of a Hann window
 window = hann(M+1);
 N=8;           % actual window size, in "hops"

% Sample the window.
% Scale the abscissa. 0:M samples --> 0:7 "hops", and take 8 symmetrical hops, from 0 to 7
 sam_per_hop_7 = M/7;
 symmetric = window(1+(0:7)*sam_per_hop_7);

% Scale the abscissa. 0:M samples --> 0:8 "hops", and take 8 asymmetrical hops, from 0 to 7
 sam_per_hop_8 = M/8;
 periodic = window(1+(0:7)*sam_per_hop_8);

% Compare equivalent noise bandwidths (info only)
 ENBW_symmetric = N*sum(symmetric.^2)/sum(symmetric)^2                            % 
 ENBW_periodic  = N*sum(periodic.^2) /sum(periodic)^2                             % 

%Replace above with the equivalent formulaic versions
%This step just proves that formulas match window() array.
 symmetric = .5*(1-cos(2*pi*(0:7)/7));
 periodic  = .5*(1-cos(2*pi*(0:7)/8));     % aka "DFT Even"

%Compare equivalent noise bandwidths (info only)
 ENBW_symmetric = N*sum(symmetric.^2)/sum(symmetric)^2       % 1.7143
 ENBW_periodic  = N*sum(periodic.^2) /sum(periodic)^2        % 1.5
 
%Plot the coefficients as dots
 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
 hops = (0:M)/sam_per_hop_8;
 plot(hops, window, "color","blue")          % periodic

 hops = (0:M)/sam_per_hop_7;
 plot(hops, 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')