File:Pwm.gif

From Wikimedia Commons, the free media repository
Jump to navigation Jump to search

Pwm.gif (640 × 480 pixels, file size: 268 KB, MIME type: image/gif, looped, 44 frames, 11 s)

Captions

Captions

Add a one-line explanation of what this file represents

Summary

[edit]
Description de:Pulsweiten-Modulation
Source Own work
Author Mik81
% 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=1:1:40

  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));
  
%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])
  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;");

  %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=40))

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.png;;
  ?) composite -gravity East ./data/waveform00$i.png ./data/spectrum00$i.png ./data/composite00$i.png;;
  *) break;;
  esac
   ((i=$i+1))
done

((i=41))
((m=45))

while ((i<m)); do
#octave ./pulsweite.m
  cp ./data/composite040.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

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current14:16, 26 February 2008Thumbnail for version as of 14:16, 26 February 2008640 × 480 (268 KB)Mik81 (talk | contribs){{Information |Description= de:Pulsweiten-Modulation |Source=self-made |Date= |Author= Mik81 |Permission= |other_versions= }} == en:GNU Octave == <source lang="c"> % GNU Octave / MATLAB % Benutzer:mik81 @ de.wikipedia.org % % %

The following page uses this file: