graphics_toolkit gnuplot
#{
The gnuplot graphics toolkit is not actively maintained and has a number
of limitations that are unlikely to be fixed.  Communication with gnuplot
uses a one-directional pipe and limited information is passed back to the
Octave interpreter so most changes made interactively in the plot window
will not be reflected in the graphics properties managed by Octave.  For
example, if the plot window is closed with a mouse click, Octave will not
be notified and will not update its internal list of open figure windows.
The qt toolkit is recommended instead.
#}
% Just a bunch of defaults copied from File:Window_function_and_frequency_response_-_Rectangular.svg
set(0, "DefaultAxesFontName", "Microsoft Sans Serif")
set(0, "DefaultTextFontName", "Microsoft Sans Serif") 
set(0, "DefaultAxesTitleFontWeight", "bold")
set(0, "DefaultAxesFontWeight",      "bold")
set(0, "DefaultAxesFontSize", 14)
set(0, "DefaultAxesLineWidth", 2)
set(0, "DefaultAxesBox", "on")
set(0, "DefaultAxesGridLineStyle", "-")
set(0, "DefaultAxesGridColor", [0 0 0])  	% black
set(0, "DefaultAxesGridAlpha", 0.1)		% opaqueness of grid
set(0, "DefaultAxesLayer", "bottom")     	% grid not visible where overlapped by graph

M = 2^12;   				% interpolation factor
% An unusually large number is needed to resolve the first null of the Tukey window

DFT_length = 2^10;
window_length = DFT_length + 1;
DTFT_length = M*DFT_length;
dr = 100; 				% dynamic range
% These are the indices of the DTFT array that will be plotted logarithmically
a = M/4 : DTFT_length/2;

% These are the bin numbers to be assigned to the indices
x = (a-1)/M;

n = 2*pi*(0:DFT_length-1)/DFT_length;

%============================================
% Rectangular window
window = ones(1,DFT_length);
window(1) = 2*window(1);	% periodic summation

H = abs(fft(window, DTFT_length));
H = H(a);

H = H/max(H);
H = 20*log10(H);
H = max(-dr,H);

figure("position", [1 1 1400 600])
semilogx(x, H, "color","black", "linewidth",1)
xlim([.25 20])		% display only 20 bins
ylim([-dr 2])
set(gca,"XTick", [.5 1:10])
set(gca,"XTickLabel",[".5"; "1"; "2"; "3"; "4"; "5"; "6"; "7"; "8"; "9"; "10"])
set(gca, "ygrid", "on");

ylabel("dB", "FontSize",14, "FontWeight","bold")  
xlabel("DFT bins", "FontSize",14, "FontWeight","bold")
title("Spectral leakage of several window functions", "FontSize",20)
hold on

%============================================
% Hann window
window = 0.5 - 0.5*cos(n);
window(1) = 2*window(1);	% periodic summation
H = abs(fft(window, DTFT_length));
H = H(a);

H = H/max(H);
H = 20*log10(H);
H = max(-dr,H);
semilogx(x, H, "color","red", "linewidth",1)

%============================================
% Hamming window
window = 0.53836 - 0.46164*cos(n);
window(1) = 2*window(1);	% periodic summation
H = abs(fft(window, DTFT_length));
H = H(a);

H = H/max(H);
H = 20*log10(H);
H = max(-dr,H);
semilogx(x, H, "color","blue", "linewidth",1)

%============================================
% Tukey window
alpha = 0.5;
b = alpha*DFT_length/2;
window = ones(1,window_length);
m = 0 : b;
if( max(m) == b )
  m = m(1:end-1);
endif
M = length(m);
window(1:M) = 0.5*(1-cos(pi*m/b));
window(window_length:-1:window_length-M+1) = window(1:M);

window(1) = 2*window(1);	% periodic summation
window = window(1:end-1);
H = abs(fft(window, DTFT_length));
H = H(a);

H = H/max(H);
H = 20*log10(H);
H = max(-dr,H);
dark_green = [0 128 0]/256;
semilogx(x, H, "color",dark_green, "linewidth",2)

%============================================
% Blackman window
window = 0.42 - 0.5*cos(n) + 0.08*cos(2*n);
window(1) = 2*window(1);	% periodic summation
H = abs(fft(window, DTFT_length));
H = H(a);

H = H/max(H);
H = 20*log10(H);
H = max(-dr,H);
gold = [251 159 3]/256;
semilogx(x, H, "color",gold, "linewidth",2)

%============================================
% Flat top window
b = [0.21557895 0.41663158 0.277263158 0.083578947 0.006947368];
window = b(1) - b(2)*cos(n) + b(3)*cos(2*n) -b(4)*cos(3*n) +b(5)*cos(4*n);
window(1) = 2*window(1);	% periodic summation
H = abs(fft(window, DTFT_length));
H = H(a);

H = H/max(H);
H = 20*log10(H);
H = max(-dr,H);
semilogx(x, H, "color","magenta", "linewidth",2)

h = legend(['rectangular'],...
           ['hann'],...
           ['hamming'],...
           ['tukey'],...
           ['blackman'],...
           ['flattop'],...
           "location","west");
legend boxoff
set(h, "fontsize",16);