graphics_toolkit gnuplot
pkg load signal

symmetric8 = exp(-.5*(((0:7)-7/2)/(.4*7/2)).^2);   % 8-points of an 8-point window
periodic8  = exp(-.5*(((0:7)-8/2)/(.4*8/2)).^2);   % 8-points of a  9-point window

 ENBW_symmetric8 = 8*sum(symmetric8.^2)/sum(symmetric8)^2                            % 1.6233
 ENBW_periodic8  = 8*sum(periodic8.^2) /sum(periodic8)^2                             % 1.4533

%Now compute and plot the DTFTs and DFTs
 N = 8;         % DFT size
 M = 64*N;      % DTFT size
 dr = 80;       % dynamic range (decibels)
%------------------------------------------------------------------
% DTFT of symmetric window
H = abs(fft([symmetric8 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("position", [100 200 700 400])
plot(x, H, "color","red", "linewidth",1);
hold on
ylim([-dr 0])

% Compute a DFT to sample the DTFT 8 times
H = abs(fft(symmetric8));
H = fftshift(H);
H = H/max(H);
H = 20*log10(H);
H = max(-dr,H);
plot(-N/2:(N/2-1), H, "color","red", ".", "markersize",14)

%------------------------------------------------------------------
% DTFT of periodic window
H = abs(fft([periodic8 zeros(1,M-N)]));
H = fftshift(H);
H = H/max(H);
H = 20*log10(H);
H = max(-dr,H);
plot(x, H, "color","blue", "linewidth",1);

% Compute a DFT to sample the DTFT 8 times
H = abs(real(fft(periodic8)));   % real() is redundant... just to illustrate a point
H = fftshift(H);
H = H/max(H);
H = 20*log10(H);
H = max(-dr,H);
plot(-N/2:(N/2-1), H, "color","blue", ".", "markersize",14)

set(gca,"XTick", -N/2:N/2-1)
grid on
text(-1.17,-64, "Equivalent Noise Bandwidths", "fontsize",10, "fontweight","bold")
h = legend("", num2str(ENBW_symmetric8,'%5.3f'),...
           "", num2str(ENBW_periodic8, '%5.3f'), "location","south");
set(h, "fontsize",10)
%legend boxoff

text(-2.84, -11.66, {"        DTFT";'symmetric8 \rightarrow'}, "color","red",...
        "fontsize",10, "fontweight","bold")
set(gca,"XTick", -N/2:N/2-1)
grid on
ylabel("decibels", "fontsize",14)
xlabel("DFT bins", "fontsize",12, "fontweight","bold")
title('"Spectral leakage" from two 8-point Gaussian windows','FontSize', 14)

% After this call, the cursor units change to a normalized ([0,1]) coordinate system
annotation("textarrow", [.132 .132], [.675 .51],...
        "color", "blue", "string", {"   DTFT";"periodic8"}, "fontsize",10,...
        "linewidth",1, "headstyle","vback1", "headlength",5, "headwidth",5)