File:Pwm 2.gif

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Pwm_2.gif ‎(640 × 480 pixels, file size: 590 KB, MIME type: image/gif, looped, 87 frames, 22 s)

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Summary[edit]

Description de:Pulsweitenmodulation
Source Own work
Author Mik81

en:GNU Octave[edit]

% GNU Octave / MATLAB
% Benutzer:mik81 @ de.wikipedia.org

%
% Große Frage:
%   Welche "amplitude" haben die Spektren?
%

printf("mik81 @ de.wikipedia.org\n\n");
printf("Spectrum of rectengular waveform\n\n");

stepsPerPeriod = 128; % 2^8
periods = 16; % 2^4
steps = periods*stepsPerPeriod;
timebase = 0:1:steps-1;
size(timebase)
% dutycycle = 0.05;

mkdir("./data");
axis("labelxy", "ticxy", "on");

for count=1:1:80-1

  countString = sprintf("%03i", count);
  dutycycle = count/80;
  dutycycleString = sprintf("%0.3f", dutycycle);
  realDutycycle = 0;

  %
  % set up waveform
  %

  printf("Calculating waveform: %i\n", count);

  for period=0:1:periods-1
    for step=0:1:stepsPerPeriod-1
      if ( step >= dutycycle *stepsPerPeriod)
        square = [square, 0.];
        if ( realDutycycle == 0)
          realDutycycle = step/stepsPerPeriod
          dutycycle
        endif
      else
        if (period == 0 && step == 0)
          square = [+1.];
        else
          square = [square, +1.];
        endif
      endif
    endfor
  endfor



  for step = 0:1:steps-1
    if ( step == 0)
      sinus = [sin(2*pi*0)];
    else
      sinus = [sinus, sin(2*pi*step/stepsPerPeriod)];
    endif
  endfor



  sinus = 0:1:steps-1;
  sinus = sin(2*pi*sinus/stepsPerPeriod);

  % size(sinus)
  % size(square)


  plot((0:1:steps/(0.25*periods)-1)/stepsPerPeriod
      , square(1,1:steps/(0.25*periods)), [";Tastgrad: " , dutycycleString, ";"]);
  axis ([0, 0.25*periods, -0.2, +1.2]);

  axis ("nolabel");
  axis("labely", "ticxy");
  xlabel ("");
  __gnuplot_set__ size 0.42,0.42;
  print(["./data/waveform", countString, ".png"], "-dpng");
  __gnuplot_set__ size 1.,1.;

  

  %
  % DFT
  %

  printf("Calculating DFT: %i\n", count);


  freqSteps = steps/2;

  %
  % Frequenz = freq*Samplerate*steps
  % n * Fenster

  % remove DC-part
  %square = square .- sum(square(1,:));

  for freq=0:1:freqSteps
    pad =  square .* sin(freq*2*pi*timebase/length(timebase));
    dft(1, freq+1) = sum( pad(1,:) );
    pad =  square .* cos(freq*2*pi*timebase/length(timebase));
    % cos^2 + sin^2
    dft( 1, freq+1) = dft(1, freq+1)^2 + sum( pad(1,:) )^2; 

  %  normalize = max(dft(1, freq+1), normalize);

    pad =  sinus .* sin(freq*2*pi*timebase/length(timebase));
    dftSignal(1, freq+1) = sum( pad(1,:) );
    pad =  sinus .* cos(freq*2*pi*timebase/length(timebase));
    % cos^2 + sin^2
    dftSignal(1, freq+1) = dftSignal( 1, freq+1)^2 + sum( pad(1,:) )^2;

  endfor

  dft = sqrt(dft);

  dft = dft/(periods*stepsPerPeriod);
  dftSignal = dftSignal/(periods*stepsPerPeriod);

  %envelop = dft(1,1) * abs(sinc((0:1/10:freqSteps)*dutycycle));
  envelop = dft(1,1) * abs(sinc((0:1/10:freqSteps)*realDutycycle));
  resultingEnvelop = ( 1- dft(1,1)) * abs(sinc((0:1/10:freqSteps)*(1-realDutycycle)));

%size(dft)

  %semilogx((0:1:steps-1)/stepsPerPeriod, square);
  %semilogx((1:1:freqSteps-1)/periods, dft(2:freqSteps,1));

  % plot

  plot((0:1:freqSteps)/periods, dft(1, 1:freqSteps+1), ["+1;Spektallinien;"]
      , (0:1:freqSteps)/periods, dft(1, 1:freqSteps+1), ["^1;;"]
      , (0:1/10:freqSteps), envelop, ";Einhuellende;");


  dftSelected = [dft(1,1)];
  for selected=periods+1:periods:freqSteps+1
    dftSelected = [dftSelected, dft(1,selected)];
  endfor

  %size(dftSelected)
  %size([0, (periods+1:periods:freqSteps+1)/periods])
  if ( dutycycle > 0.5)
    plot([0, (periods+1:periods:freqSteps+1)/periods-1/periods], dftSelected(1, :), ["+1;Spektallinien;"]
        ,[0, (periods+1:periods:freqSteps+1)/periods-1/periods], dftSelected(1, :), ["^1;;"]
        , (0:1/10:freqSteps), envelop, ";Einhuellende;"
        , (0:1/10:freqSteps), resultingEnvelop, ";resultiernede Einhuellende;");
  else
    plot([0, (periods+1:periods:freqSteps+1)/periods-1/periods], dftSelected(1, :), ["+1;Spektallinien;"]
        ,[0, (periods+1:periods:freqSteps+1)/periods-1/periods], dftSelected(1, :), ["^1;;"]
        , (0:1/10:freqSteps), envelop, ";Einhuellende;");
  endif


  %semilogx((1:1:freqSteps-1)/periods, dftSignal(2:freqSteps,1));
  %plot((1:1:freqSteps/8-1)/periods, dftSignal(2:freqSteps/8,1));
  axis ([0, 20, 0, 0.6]);
  axis("labelxy", "ticxy", "on");
  xlabel ("Vielfache der Grundfrequenz");
  %axis ("ticx");

 
  print(["./data/spectrum", countString, ".png"], "-dpng");

  %if ( freq == 8)
  %    fetch = pad;
  %    sum(pad(1,:))
  %    dft(1, freq+1)
  %  endif
  %plot(0:1:length(fetch)-1, fetch, [";fetch", dutycycleString ,";"] );
  %print(["./data/fetch", countString, ".png"], "-dpng");

endfor

bash/ImageMagick[edit]

#! /bin/bash


echo "Script of mik81 @ de.wikipedia.org"


#vor00()  {
#   let "${{#1}==2" && $1=0${{1}
#   let "${{#1}==1" && $1=00${{1}
#   let "${{#1}==0" && $1=000
#   echo $1
#}



#echo (vor00 5))


((i=1))
((m=79))

rm ./data/*
octave ./pulsweite.m

while ((i<=m)); do
  case $i in
  ??) composite -gravity East ./data/waveform0$i.png ./data/spectrum0$i.png ./data/composite0${i}0.png;;
  ?) composite -gravity East ./data/waveform00$i.png ./data/spectrum00$i.png ./data/composite00${i}0.png;;
  *) break;;
  esac
   ((i=$i+1))
done


((i=401))
((m=405))

while ((i<m)); do
#octave ./pulsweite.m
  cp ./data/composite0400.png ./data/composite0$i.png
   ((i=$i+1))
done


((i=791))
((m=795))

while ((i<m)); do
#octave ./pulsweite.m
  cp ./data/composite0790.png ./data/composite0$i.png
   ((i=$i+1))
done

convert -delay 25 ./data/composite*.png ./pwm.gif

Licensing[edit]

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.

File history

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Date/TimeThumbnailDimensionsUserComment
current14:28, 26 February 2008Thumbnail for version as of 14:28, 26 February 2008640 × 480 (590 KB)Mik81 (talk | contribs){{Information |Description= de:Pulsweitenmodulation |Source=self-made |Date= |Author= Mik81 |Permission= |other_versions= }} == en:GNU Octave == <source lang="matlag"> % GNU Octave / MATLAB % Benutzer:mik81 @ de.wikipedia.org

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