File:Overlap-add algorithm.svg

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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.

Other versions This file was derived from: Overlap-save algorithm.svg
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.
Gnu Octave source
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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)

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14 January 2020

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File history

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Date/TimeThumbnailDimensionsUserComment
current13:57, 25 January 2020Thumbnail for version as of 13:57, 25 January 2020855 × 619 (140 KB)Bob Kreplace version with spurious arrow at the top
01:11, 25 January 2020Thumbnail for version as of 01:11, 25 January 2020855 × 619 (136 KB)Bob KReverted to version as of 20:09, 24 January 2020 (UTC)
22:31, 24 January 2020Thumbnail for version as of 22:31, 24 January 2020855 × 619 (136 KB)Bob Kslightly darker shade of gray, because previous shade is ignored (i.e. replaced by white)
20:09, 24 January 2020Thumbnail for version as of 20:09, 24 January 2020855 × 619 (136 KB)Bob Kchange frame background from white to gray
14:31, 19 January 2020Thumbnail for version as of 14:31, 19 January 2020855 × 630 (111 KB)Bob Kchange seed value to "e"
22:01, 18 January 2020Thumbnail for version as of 22:01, 18 January 2020855 × 630 (110 KB)Bob Kuse same waveform as File:Overlap-save method.svg
22:34, 14 January 2020Thumbnail for version as of 22:34, 14 January 2020855 × 630 (102 KB)Bob KUser created page with UploadWizard
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