File:Overlap-save algorithm.svg

% Options
  edge_effects_at_end_of_filter_output = true;
  frame_background_gray                = true;

  if frame_background_gray
   graphics_toolkit("qt")    % or graphics_toolkit("fltk")
   frame_background = .94*[1 1 1];
   d = 2;   % 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

  M   = 16;                     % filter length
  h   = ones(1,M)/M;          	% filter impulse response
  L   = 100;                  	% output segment length
  La  = 500;                  	% input data length
% randn("seed","reset")       	% experiment with data generator
% seed = randn("seed")        	% print value, in case want to use it again
  randn("seed", e)            	% generate same data as Overlap-add_algorithm.svg
  a   = 1 + randn(1,La)/3;    	% data to be filtered
  seg = 2;                    	% segment to be computed
  N   = L + M-1;              	% DFT size (a power-of-2 would be more efficient)
  Xa  = seg*L + (1:N);        	% indices of segment to be filtered

  if edge_effects_at_end_of_filter_output
   %Rotate the filter coefficients
   %Simple way
   %  H = fft([h(M) zeros(1,N-M) h(1:M-1)]);  
   %Fancy way
      H = fft( circshift([h zeros(1,N-M)], -(M-1)) );
      Xb = (1:L);                       % indices of good output
  else
      H = fft(h,N);
      Xb = M-1 + (1:L);                 % indices of good output
  endif

% (https://octave.org/doc/v4.2.1/Graphics-Object-Properties.html#Graphics-Object-Properties)
% Speed things up when using Gnuplot
  set(0, "DefaultAxesFontsize",10+d)
  set(0, "DefaultTextFontsize",12+d)
  set(0, "DefaultAxesYlim",[0 2])
  set(0, "DefaultAxesYtick",[0:2])
  set(0, "DefaultAxesYgrid","on")
  set(0, "DefaultAxesXlim",[0 La])
  set(0, "DefaultAxesXtick",[100:100:La])
  set(0, "DefaultAxesXgrid","on")
  set(0, "DefaultFigureColor",frame_background)
  set(0, "DefaultAxesColor","white")
%=======================================================
  hfig = figure("position",[50 30 912 650], "color",frame_background);

  x1 = .02;                     % left margin
  x2 = .02;                     % right margin
  y1 = .09;                     % bottom margin for annotation
  y2 = .08;                     % top margin for title
  dy = .05;                     % vertical space between rows

  width = 1-x1-x2;
  height= (1-y1-y2-3*dy)/4;     % space allocated for each of 4 rows

  x_origin = x1;
  y_origin = 1;                 % start at top of graph area
%=======================================================
  y_origin = y_origin -y2 -height;        % position of top row
  subplot("position",[x_origin y_origin width height])

  plot(1:La, a, "color","blue", Xa, a(Xa), "color","red", "linewidth",2)
  title("One segment of an Overlap-save algorithm", "fontsize",14+d);
  text(1, 2.2, "X[n], with segment k=2 in red", "fontsize",10+d)
%=======================================================
  y_origin = y_origin -dy -height;
  subplot("position",[x_origin y_origin width height])

  plot(1:L+M-1, a(Xa), "color","red")
  text(250, 1.6, 'X_k[n]')
%=======================================================
  y_origin = y_origin -dy -height;
  subplot("position",[x_origin y_origin width height])

% Instead of the conv() function, we demonstrate the use of circular convolution.
% Note that length(b) is different for the two implementations.  Circular convolution
% combines the edge effects into half the space of conv().

%Linear convolution
% b = conv(h,a(Xa));                 	% length(b) = N+M-1
% Circular convolution
  b = real(ifft(H .* fft(a(Xa))));   	% length(b) = L+M-1 = N
  plot(1:length(b), b, "color","blue", Xb, b(Xb), "color","red", "linewidth",2);
  text(250, 1.6, 'Y_k[n], output of FIR lowpass filter');
%=======================================================
  y_origin = y_origin -dy -height;
  subplot("position",[x_origin y_origin width height])

  c = conv(h,a);
  Xc1 = 1 : M-1 + (seg+1)*L;
  Xc2 = M-1 + seg*L + (1:L);
  plot(Xc1, c(Xc1), "color","blue", Xc2, c(Xc2), "color","red", "linewidth",2)
  text(250, 1.6, "Y[n], after segment k")
  xlabel('\leftarrow  n  \rightarrow', "fontsize",12+d)