Image:Rectified waves.png

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This file has been superseded by Image:Rectification.svg.

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

[edit] Instructions

See Wikipedia graph-making tips.

Generated in gnuplot with the following script (save as rectified_waves.plt and then open in gnuplot):

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:

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
Crop off extra whitespace (Shift+C if you can't find it in the toolbox)
Possibly need to rotate it: Click Image → Transform → Rotate 90 degrees clockwise
Filters → Blur → Gaussian 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.)
Image → Scale Image...
- Width and Height at 25%
- Cubic interpolation
You can view at normal size if you want by pressing 1, Ctrl+E
Save as Rectified waves.png

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

I, the author of this work, hereby publish it under the following licenses:

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".