File:Butterworth response.png

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Original file(1,240 × 880 pixels, file size: 86 KB, MIME type: image/png)


English: The frequency response of a Butterworth filter with logarithmic axes (Bode plot) and various labels. Cutoff frequency is normalized to 1 rad/s. Gain is normalized to 0 dB in the passband.

Many orders on one plot: File:Butterworth orders.png.

Version with no text available at File:Butterworth plain.png, though you should probably just modify the source code and regenerate it in your own language.

See Wikipedia graph-making tips.
Lissajous small.svg
This plot was created with Gnuplot.

Generated in gnuplot with the script below (save as butterworth.plt and then open in gnuplot). Then I opened the 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:

/LT0 { PL [] 1 0 0 DL } def
/LT1 { PL [4 dl 2 dl] 0 1 0 DL } def
/LT2 { PL [2 dl 3 dl] 0 0 1 DL } def
/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def

into this:

/LT0 { PL [] 0 0 1 DL } def
/LT1 { PL [4 dl 2 dl] 0.5 0.5 0.5 DL } def
/LT2 { PL [6 dl 3 dl] 0.3 0.3 1 DL } def
/LT3 { PL [] 0 0 0 DL } def
/LT4–/LT8 I left unchanged. (I don't know what they're used for anyway.) /LTw, /LTb, and /LTa are for the grid lines and such.

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 Butterworth response.png
Date (upload date)
Source Own work
Author Omegatron
Other versions
Derivative versions on this file
English version (SVG) 
Russian version (SVG) 
gnuplot source


I, the copyright holder of this work, hereby publish it under the following licenses:
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File history

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

current17:45, 23 July 2005Thumbnail for version as of 17:45, 23 July 20051,240 × 880 (86 KB)Omegatron (talk | contribs)split the cutoff frequency markers
16:31, 23 July 2005Thumbnail for version as of 16:31, 23 July 20051,250 × 880 (92 KB)Omegatron (talk | contribs)Better butterworth filter response curve
19:54, 26 June 2005Thumbnail for version as of 19:54, 26 June 2005250 × 220 (2 KB)Omegatron (talk | contribs)A graph or diagram made by User:Omegatron. (Uploaded with Wikimedia Commons.) Source: Created by User:Omegatron {{GFDL}}{{cc-by-sa-2.0}} Category:Diagrams\
  • You cannot overwrite this file.

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