% Options
frame_background_gray=true;
ifframe_background_gray
graphics_toolkit("qt")% or graphics_toolkit("fltk")
frame_background=.94*[111];
d=2;% amount to add to text sizes
else
graphics_toolkit("gnuplot")% background will be white regardless of value below
frame_background=.94*[111];
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-save_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:L);% indices of segment to be filtered
% (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",[02])
set(0,"DefaultAxesYtick",[0:2])
set(0,"DefaultAxesYgrid","on")
set(0,"DefaultAxesXlim",[0La])
set(0,"DefaultAxesXtick",[100:100:La])
set(0,"DefaultAxesXgrid","on")
set(0,"DefaultFigureColor",frame_background)
set(0,"DefaultAxesColor","white")
%=======================================================
hfig=figure("position",[1010912685],"color",frame_background);
x1=.02;% left margin
x2=.02;% right margin
y1=.08;% bottom margin for annotation
y2=.08;% top margin for title
dy=.04;% vertical space between rows
width=1-x1-x2;
height=(1-y1-y2-4*dy)/5;% space allocated for each of 5 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_originy_originwidthheight])
plot(1:La,a,"color","blue",Xa,a(Xa),"color","red","linewidth",2)
title("One segment of an Overlap-add 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_originy_originwidthheight])
plot(1:L,a(Xa),"color","red",...
L+(1:M-1),zeros(1,M-1),"color","red","linewidth",2)
text(250,1.6,'X_k[n]')
%=======================================================
y_origin=y_origin-dy-height;
subplot("position",[x_originy_originwidthheight])
H=fft(h,N);
b=real(ifft(H.*fft(a(Xa),N)));% = conv(h,a(Xa))
plot(1:N,b,"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_originy_originwidthheight])
Xc=1:seg*L;
c=conv(h,a(Xc));
x=(length(c)+1):La;
plot(1:length(c),c,"color","blue",...
x,zeros(1,length(x)),"color","blue","linewidth",2,...
seg*L+(1:N),b,"color","red","linewidth",2)
text(250,1.6,'Y_2[n-2L]')
%=======================================================
y_origin=y_origin-dy-height;
subplot("position",[x_originy_originwidthheight])
Xd=1:(seg+1)*L;
d1=conv(h,a(Xd));
x=(length(d1)+1):La;
plot(1:length(d1),d1,"color","blue",...
x,zeros(1,length(x)),"color","blue","linewidth",2)
xlabel('\leftarrow n \rightarrow',"fontsize",12+d)