graphics_toolkit gnuplot

M   = 16;                   % filter length
h   = ones(1,M)/M;          % filter impulse response
L   = 100;                  % output segment length
La  = 500;                  % input data length
a   = 1 + randn(1,La)/3;    % data to be filtered
seg = 2;                    % segment to be computed
N   = L + M-1;              % DFT size
Xa  = seg*L + (1:N);        % indices of segment to be filtered

frame_background = .95*[1 1 1];
%=======================================================
hfig = figure("position",[100 100 912 650], "color",frame_background);
set(gca,"color",frame_background)
set(gcf,"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() undoes all the "color" attempts above.  (gnuplot bug)
subplot("position",[x_origin y_origin width height])

set(gca,"fontsize",10)
plot(1:La, a, "color", "blue", Xa, a(Xa), "color", "red", "linewidth", 2)
set(gca, "color", "white")
title("One segment of an Overlap-save algorithm", "fontsize",14);
text(1, 2.2, "X[n], with segment k=2 in red")
xlim([0 La])
ylim([0 2])
set(gca, "ytick",[0:2])
set(gca, "xtick",[100:100:La])
grid("on")
%=======================================================
y_origin = y_origin -dy -height;
subplot("position",[x_origin y_origin width height])

set(gca,"fontsize",10)
plot(1:L+M-1, a(Xa), "color", "red")
set(gca, "color", "white")
text(250, 1.6, 'X_k[n]', "fontsize",12)
xlim([0 La])
ylim([0 2])
set(gca, "ytick",[0:2])
set(gca, "xtick",[100:100:La])
grid("on")
%=======================================================
y_origin = y_origin -dy -height;
subplot("position",[x_origin y_origin width height])

% Here we use the conv() function, to demonstrate just the "overlap & discard" part of the process.
% The efficiency of the algorithm is realized by replacing conv() with circular convolution.
% Note that length(b) is different for the two implementations.  Circular convolution "folds" 
% the trailing transition region ("fall time") back onto the "rise time" transition region.

% Circular convolution
% H = fft(h,N);
% b = real(ifft(H .* fft(a(Xa))));   % length(b) = L+M-1 = N
%Linear convolution
  b = conv(h,a(Xa));                 % length(b) = N+M-1

Xb = M-1 + (1:L);
set(gca,"fontsize",10)
plot(1:length(b), b, "color", "blue", Xb, b(Xb), "color", "red", "linewidth", 2);
set(gca, "color", "white")
text(250, 1.6, 'Y_k[n], output of FIR lowpass filter', "fontsize",12);
xlim([0 La])
ylim([0 2])
set(gca, "ytick",[0:2])
set(gca, "xtick",[100:100:La])
grid("on")
%=======================================================
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);
set(gca,"fontsize",10)
plot(Xc1, c(Xc1), "color", "blue", Xc2, c(Xc2), "color", "red", "linewidth", 2)
set(gca, "color", "white")
text(250, 1.6, "Y[n], after segment k")
xlim([0 La])
ylim([0 2])
set(gca, "ytick",[0:2])
set(gca, "xtick",[100:100:La])
grid("on")
xlabel('\leftarrow  n  \rightarrow', "fontsize",12)