File:Processing losses for 3 window functions.svg

pkg load signal
% Options
  frame_background_gray = true;

  if frame_background_gray
   graphics_toolkit("qt")         % has "insert text" option
%  graphics_toolkit("fltk")       % has cursor coordinate readout
   frame_background = .94*[1 1 1];
   d = 4;                         % amount to add to text sizes
  else
   graphics_toolkit("gnuplot")    % background will be white regardless of value below
   frame_background = .94*[1 1 1];
   d=0;
  endif

% (https://octave.org/doc/v4.2.1/Graphics-Object-Properties.html#Graphics-Object-Properties)
% Speed things up when using Gnuplot
  set(0, "DefaultFigureColor",frame_background)
  set(0, "DefaultAxesFontsize",10+d)   % size of numeric tick labels
  set(0, "DefaultLineLinewidth",1)
  set(0, "DefaultTextFontsize",10+d)

  hfig= figure("position",[100 50 574 609]);
 
  N = 256;                % sams_per_fft;
  window1 = rectwin(N)'/sum(rectwin(N));
  window2 = hann(N)'/sum(hann(N));
  window3 = blackmanharris(N)'/sum(blackmanharris(N));
%
  Fs = N;                 % sams_per_sec;
  HzPerBin = Fs/N;
  F1 = -20.0*HzPerBin;    % bin -20
  F2 = +20.5*HzPerBin;    % bin 20.5
%
  L = 100000;
  n = 1:L;
  x = exp(j*2*pi*F1/Fs*n) + exp(j*2*pi*F2/Fs*n);
  x = x + (randn(1,L) +j*randn(1,L))*1.4;
%
  sams_per_offset = 0.75*N;    % overlap = 25%
%
% number of samples available beyond just one FFT
  excess_sams = length(x) - N;
%
  j1 = floor( excess_sams / sams_per_offset );
  sams_per_offset = floor( excess_sams / j1 );
  num_ffts = 1 + j1;
%
% define the first block of data
  samples = 1:N;
%
  amplitude1 = zeros(1,N);
  amplitude2 = zeros(1,N);
  amplitude3 = zeros(1,N);
%
% Loop over all the available blocks
  for j1 = 1 : num_ffts
    amplitude1 = amplitude1 + abs(fft( x(samples) .* window1 ));
    amplitude2 = amplitude2 + abs(fft( x(samples) .* window2 ));
    amplitude3 = amplitude3 + abs(fft( x(samples) .* window3 ));
    samples = samples + sams_per_offset;
  end
%
  amplitude1  = 20*log10(fftshift(amplitude1/num_ffts));
  amplitude2  = 20*log10(fftshift(amplitude2/num_ffts));
  amplitude3  = 20*log10(fftshift(amplitude3/num_ffts));
% 
  abscissa = -40:40;
  set(gca,"fontsize",8)
  subplot(3,1,1);
  h = area(abscissa, amplitude1(abscissa +N/2+1), ...
  "facecolor", [.871 .49 0], "edgecolor", [.871 .49 0]);
  set(h,"basevalue",-20)
  set(gca, "xtick", [-20 0 20.5], "xticklabel",[" "; " "; " "], "ygrid","on", "color", "white")
  xlim([-40 40])
  ylim([-20 2])
  ylabel("decibels")
  text(-40, 3.5, "Rectangular window")
  text(-12.0, -8.1, "X dB")
  text(3.6, -8.1, "X - 3.92 dB")
  text(-28.7, -22.7, "No scallop loss")
  text(9.8, -22.7, "Maximum scallop loss")
  title({"Processing losses for sinusoids in additive noise"; ""; ""}, "fontsize",12+d);
%
  subplot(3,1,2);
  h = area(abscissa, amplitude2(abscissa +N/2+1), ...
  "facecolor", [.871 .49 0], "edgecolor", [.871 .49 0]);
  set(h,"basevalue",-20)
  set(gca, "xtick", [-20 0 20.5], "xticklabel",[" "; " "; " "], "ygrid","on", "color", "white")
  xlim([-40 40])
  ylim([-20 2])
  ylabel("decibels")
  text(-40, 3.5, "Hann window")
  text(-12.4, -8.1, "X - 1.76 dB")
  text(3.6, -8.1, "X - 3.18 dB")
  text(-28.7, -22.7, "No scallop loss")
  text(20, -22.7, 'frequency  \rightarrow')
%
  subplot(3,1,3);
  h = area(abscissa, amplitude3(abscissa +N/2+1), ...
  "facecolor", [.871 .49 0], "edgecolor", [.871 .49 0]);
  set(h,"basevalue",-20)
  set(gca, "xtick", [-20 0 20.5], "xticklabel",[" "; " "; " "], "ygrid","on", "color", "white")
  xlim([-40 40])
  ylim([-20 2])
  ylabel("decibels")
  text(-40, 3.5, "Blackman-Harris")
  text(-12.0, -8.1, "X - 3.01 dB")
  text(3.6, -8.1, "X - 3.85 dB")
  text(-28.7, -22.7, "No scallop loss")
  text(9.8, -22.7, "Maximum scallop loss")

% After this call, the cursor units change to a normalized ([0,1]) coordinate system, spanning all plots
  annotation("line", [.334 .5], [.906 .906])
  annotation("line", [.52 .7], [.87 .87])
  annotation("doublearrow", [.388 .388], [.906 .727],...
      "head1style","vback1", "head2style","vback1",...
      "head1length",5, "head1width",5, "head2length",5, "head2width",5)
  annotation("doublearrow", [.545 .545], [.87 .727],...
      "head1style","vback1", "head2style","vback1",...
      "head1length",5, "head1width",5, "head2length",5, "head2width",5)

  annotation("line", [.334 .5], [.602 .602])
  annotation("line", [.52 .7], [.589 .589])
  annotation("doublearrow", [.388 .388], [.602 .438],...
      "head1style","vback1", "head2style","vback1",...
      "head1length",5, "head1width",5, "head2length",5, "head2width",5)
  annotation("doublearrow", [.545 .545], [.589 .438],...
      "head1style","vback1", "head2style","vback1",...
      "head1length",5, "head1width",5, "head2length",5, "head2width",5)

  annotation("line", [.334 .5], [.3 .3])
  annotation("line", [.52 .7], [.292 .292])
  annotation("doublearrow", [.388 .388], [.3 .147],...
      "head1style","vback1", "head2style","vback1",...
      "head1length",5, "head1width",5, "head2length",5, "head2width",5)
  annotation("doublearrow", [.545 .545], [.292 .147],...
      "head1style","vback1", "head2style","vback1",...
      "head1length",5, "head1width",5, "head2length",5, "head2width",5)