Wikimore

Summary

DescriptionPwm.gif	de:Pulsweiten-Modulation
Source	Own work
Author	Mik81

en:GNU Octave

% 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

#! /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

I, the copyright holder of this work, hereby publish it under the following license:

	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. CC0falsefalse

Category:CC-Zero#Pwm.gif Category:Self-published work

Category:Pulse width modulation Category:Images with BASH source code Category:Images with Octave source code Category:Animated GIF files

Wikimore

File:Pwm.gif

Summary

en:GNU Octave

Bash/ImageMagick

Licensing