File:Butterworth orders.png

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Original file (1,229 × 872 pixels, file size: 93 KB, MIME type: image/png)

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Summary

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Description
English: Butterworth filter frequency response of several orders. Cutoff frequency is normalized to 1 rad/s. Gain is normalized to 0 dB in the passband.

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This plot was created with Gnuplot by n.
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 Image → Transform → Rotate 90 degrees clockwise
  4. 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.)
  5. Image → Scale 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 Butterworth orders.png
Date 20 July 2005 (upload date)
Source Own work
Author Omegatron
Other versions
  • int .svg
    int .svg
  • English .svg
    English .svg
  • English .png
    English .png
  • Russian .svg
    Russian .svg
  • int .svg
    int .svg
  • English .pdf
    English .pdf
gnuplot source
InfoField
click to expand
 set samples 1001
 set terminal postscript enhanced landscape color solid lw 2 "Times-Roman" 20
 set output "butterworth_orders.ps"

 G(w,n) = 1 / (sqrt(1 + w**(2*n)))

 dB(x) = 20 * log10(abs(x))

 set grid

 # Set x axis to logarithmic scale
 set logscale x 10

 # Set range of x and y axes
 set xrange [0.01:100]
 set yrange [-100:10]

 # Create 10 x tick marks per decade
 set xtics 10

 set xlabel "Angular frequency (rad/s)"
 set ylabel "Gain (dB)"

 # Put legend in bottom left corner
 set key 0.1,-45

 # Plot five orders of the filter
 plot \
     dB(G(x,1)) title "1st order", \
     dB(G(x,2)) title "2nd order", \
     dB(G(x,3)) title "3rd order", \
     dB(G(x,4)) title "4th order", \
     dB(G(x,5)) title "5th order"
File:Butterworth orders.svg is a vector version of this file. It should be used in place of this PNG file when not inferior.
File:Butterworth orders.png → File:Butterworth orders.svg
For more information, see Help:SVG.
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New SVG image

File:Butterworth Filter Orders.svg is a vector version of this file. It should be used in place of this PNG file when not inferior.
File:Butterworth orders.png → File:Butterworth Filter Orders.svg
For more information, see Help:SVG.
In other languages
Alemannisch ∙ Bahasa Indonesia ∙ Bahasa Melayu ∙ British English ∙ català ∙ čeština ∙ dansk ∙ Deutsch ∙ eesti ∙ English ∙ español ∙ Esperanto ∙ euskara ∙ français ∙ Frysk ∙ galego ∙ hrvatski ∙ Ido ∙ italiano ∙ lietuvių ∙ magyar ∙ Nederlands ∙ norsk bokmål ∙ norsk nynorsk ∙ occitan ∙ Plattdüütsch ∙ polski ∙ português ∙ português do Brasil ∙ română ∙ Scots ∙ sicilianu ∙ slovenčina ∙ slovenščina ∙ suomi ∙ svenska ∙ Tiếng Việt ∙ Türkçe ∙ vèneto ∙ Ελληνικά ∙ беларуская (тарашкевіца) ∙ български ∙ македонски ∙ нохчийн ∙ русский ∙ српски / srpski ∙ татарча/tatarça ∙ українська ∙ ქართული ∙ հայերեն ∙ বাংলা ∙ தமிழ் ∙ മലയാളം ∙ ไทย ∙ 한국어 ∙ 日本語 ∙ 简体中文 ∙ 繁體中文 ∙ עברית ∙ العربية ∙ فارسی ∙ +/−
New SVG image

Licensing

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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.
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File history

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Date/TimeThumbnailDimensionsUserComment
current00:07, 20 July 2005Thumbnail for version as of 00:07, 20 July 20051,229 × 872 (93 KB)Omegatron (talk | contribs)Butterworth filter of several orders.

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