File:Overlap-add algorithm.svg

Summary

Description
English: A sequence of 5 plots depicts one cycle of the Overlap-add convolution algorithm. The first plot is a long sequence of data to be processed with a lowpass FIR filter. The 2nd plot is one segment of the data to be processed in piecewise fashion. The 3rd plot is the filtered segment, including the filter rise and fall transients. The 4th plot indicates where the new data will be added with the result of previous segments. The 5th plot is the updated output stream.
Date
Source Own work
Author Bob K
Permission
(Reusing this file)
I, the copyright holder of this work, hereby publish it under the following license:
Creative Commons CC-Zero This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication.
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.

Category:CC-Zero#Overlap-add%20algorithm.svg
Category:Self-published work
Other versions This file was derived from: Overlap-save algorithm.svg
Category:Derivative versions
SVG development
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The source code of this SVG is invalid due to 5 errors.
 
This W3C-invalid vector image was created with LibreOffice.
Category:Invalid SVG created with LibreOffice#0200Overlap-add%20algorithm.svg
Gnu Octave source
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click to expand

This graphic was created with the help of the following Octave script:

% Options
  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-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",[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",[10 10 912 685], "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_origin y_origin width height])

  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_origin y_origin width height])

  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_origin y_origin width height])

  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_origin y_origin width height])

  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_origin y_origin width height])

  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)
Category:Digital signal processing Category:Created with GNU Octave Category:Images with Octave source code Category:Images with Gnuplot source code Category:Overlap add
Category:CC-Zero Category:Created with GNU Octave Category:Derivative versions Category:Digital signal processing Category:Images with Gnuplot source code Category:Images with Octave source code Category:Invalid SVG created with LibreOffice Category:Overlap add Category:Pages using deprecated source tags Category:Self-published work