File:Rectified waves.png

Original file(1,160 × 860 pixels, file size: 87 KB, MIME type: image/png)

This shows a sine wave, then half-wave and full-wave rectified versions of it.

Instructions

See Wikipedia graph-making tips.

Lissajous small.svg
This plot was created with Gnuplot:

Gnuplot code

set samples 9001
set terminal postscript enhanced landscape color solid lw 2 "Times-Roman" 20
set output "rectified_waves.ps"

# Define the four curves
sine(x) = sin(x*pi)
half(x) = sine(x)>0?sine(x):0
full(x) = abs(sine(x))

# Set up a four-pane multiplot
set size 1,1
set origin 0,0
set multiplot

set grid

# Set range of x axis
set xrange [0:6]

# Gridlines at every cycle
set ytics 1

# Ticks distract from wave shapes
set ticscale 0

# Show extents but don't waste space
set yrange [-1.5:1.5]

# No numbers needed; these are for shape comparison
set format x ""
set format y ""

set nokey

# Squish them together slightly
# (Doesn't accept fractional margins???)
set bmargin 1
set tmargin 0

# Plot each graph
# I don't understand how the labels work in multiplot, but this gives the right output

set size 1,0.333333333333
set origin 0,0.66666666
set label 1 "Sine wave" at 4.5, -0.5 c
plot sine(x) 1

set size 1,0.3333333
set origin 0,0.3333333
set label 1 "Half-wave rectified" at 4.5, -0.5 c
plot half(x) with lines 2

set size 1,0.3333333
set origin 0,0
set label 1 "Full-wave rectified" at 4.5, -0.5 c
plot full(x) with lines 3

unset multiplot

Then I opened the rectified_waves.ps file in a text editor to edit the line colors and linestyles, as per this description. This avoids needing to open in proprietary software, and really isn't that difficult (especially if you don't know the commands in the proprietary software either). ;-) Identify the lines easily by their color (the arrow is currently magenta and I want it to be black. Ah, there is the entry with 1 0 1, red + blue = magenta) or by using the gnuplot linestyle−1. (For instance, gnuplot's linestyle 3 corresponds to the ps file's /LT2.) Then you can edit the colors and dashes by hand.

I changed the original:

/LT1 { PL [4 dl 2 dl] 0 1 0 DL } def

into this:

/LT1 { PL [4 dl 2 dl] 0 0.7 0 DL } def

to make the green a little less neon.

To convert the PostScript file to PNG:

  1. Open it in the GIMP (make sure you have ghostscript installed! - Windows instructions)
    • Enter 500 under Resolution (it doesn't say "DPI" but I think that's what it means)
    • Uncheck Try bounding box (since the bounding box cuts off the edge, unfortunately. You can try with the bounding box first.)
    • Enter large values for Width and Height
    • Check Color
    • Check Strong anti-aliasing for both graphics and text
  2. Crop off extra whitespace (Shift+C if you can't find it in the toolbox)
  3. Possibly need to rotate it: Click ImageTransformRotate 90 degrees clockwise
  4. FiltersBlurGaussian blur at 2.0 px (No need to blur if you use strong anti-aliasing during conversion. I see no significant difference between end results.)
  5. ImageScale Image...
    • Width and Height at 25%
    • Cubic interpolation
  6. You can view at normal size if you want by pressing 1, Ctrl+E
  7. Save as Rectified waves.png

Created by User:Omegatron using gnuplot, possibly with post-processing in the GIMP (PNG) or Inkscape (SVG)

I, the copyright holder of this work, hereby publish it under the following licenses:
w:en:Creative Commons

attribution share alike

This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported, 2.5 Generic, 2.0 Generic and 1.0 Generic license.
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

GNU head Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.
You may select the license of your choice.

(In short, this means that you can copy and modify the image freely as long as you provide attribution; preferably in the form of a link back to this page.)

File history

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

Date/TimeThumbnailDimensionsUserComment
current01:56, 29 August 2005Thumbnail for version as of 01:56, 29 August 20051,160 × 860 (87 KB)Omegatron
The following pages on the English Wikipedia use this file (pages on other projects are not listed):

Global file usage

The following other wikis use this file: