File:Butterworth poles 3.svg
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Size of this PNG preview of this SVG file: 469 × 600 pixels. Other resolutions: 187 × 240 pixels | 375 × 480 pixels | 600 × 768 pixels | 800 × 1,024 pixels | 1,601 × 2,048 pixels | 512 × 655 pixels.
Original file (SVG file, nominally 512 × 655 pixels, file size: 8 KB)
This is a file from the Wikimedia Commons. The description on its description page there is shown below. |
Summary
DescriptionButterworth poles 3.svg |
English: pole location for a 3rd order Butterworth lowpass filter |
Date | |
Source | Own work |
Author | Fcorthay |
SVG development InfoField | This vector image was created with Inkscape, or with something else. |
Source code
This graphics has been realized with the help of the following Octave script:
#------------------------------------------------------------------------------- # Specifications # order = 3; fc = 1; pointNb = 100; axesLength = 1.25; textOffset = 0.05; wLog = logspace(-2, 2, pointNb); AdbMax = 10; AdbMin = -60; makeGraphics = 1; figureIndex = 0; #=============================================================================== # Butterworth filter # [zeroes, poles, gain] = butter(order, fc, 's'); [num, den] = butter(order, fc, 's'); while ( length(num) < length(den) ) num = [0, num]; endwhile; #------------------------------------------------------------------------------- # Poles plot # figureIndex = figureIndex+1; figure(figureIndex); angle = linspace(pi/2, 3*pi/2, pointNb); plot(cos(angle), sin(angle)); hold on; plot([-axesLength, axesLength-1], [0, 0], 'k'); plot([0, 0], [-axesLength, axesLength], 'k'); plot(axesLength-1+textOffset*[0, 2, 0, 0], textOffset*3/4*[-1, 0, 1, -1], 'k'); plot(textOffset*3/4*[-1, 0, 1, -1], axesLength+textOffset*[0, 2, 0, 0], 'k'); plot(poles, 'xr'); hold off; axis("equal", "off"); text(axesLength-1+textOffset, 1.5*textOffset, "re(s)"); text(textOffset, axesLength+1.5*textOffset, "im(s)"); for index = 1:order if imag(poles(index)) > 0 text(real(poles(index))-textOffset, imag(poles(index))+textOffset, ... sprintf("p%i", index), "horizontalalignment", "right"); elseif imag(poles(index)) == 0 text(real(poles(index))-textOffset, imag(poles(index))+textOffset, ... "pr", "horizontalalignment", "right"); endif endfor if (makeGraphics != 0) print -dsvg butterworth_poles_3.svg endif #------------------------------------------------------------------------------- # Amplitude plot # Adb = 20*log10(abs(freqs(num, den, wLog))); figureIndex = figureIndex+1; figure(figureIndex); semilogx(wLog, Adb); hold on; for index = 1:order if imag(poles(index)) > 0 numP = [0, 0, 1]; denP = [1, -2*real(poles(index)), abs(poles(index))^2]; Adb = 20*log10(abs(freqs(numP, denP, wLog))); semilogx(wLog, Adb, 'g'); elseif imag(poles(index)) == 0 numP = [0, 1]; denP = [1, -real(poles(index))]; Adb = 20*log10(abs(freqs(numP, denP, wLog))); semilogx(wLog, Adb, 'g'); endif endfor hold off; axis([wLog(1), wLog(length(wLog)), AdbMin, AdbMax]); xlabel('Frequency'); ylabel('Amplitude responses'); grid; if (makeGraphics != 0) print -dsvg butterworth_amplitudes_3.svg endif #------------------------------------------------------------------------------- # Phase plot # phase = arg(freqs(num, den, wLog)); figureIndex = figureIndex+1; figure(figureIndex); semilogx(wLog, phase); hold on; for index = 1:order if imag(poles(index)) > 0 numP = [0, 0, 1]; denP = [1, -2*real(poles(index)), abs(poles(index))^2]; phase = arg(freqs(numP, denP, wLog)); semilogx(wLog, phase, 'g'); elseif imag(poles(index)) == 0 numP = [0, 1]; denP = [1, -real(poles(index))]; phase = arg(freqs(numP, denP, wLog)); semilogx(wLog, phase, 'g'); endif endfor semilogx([wLog(1), wLog(length(wLog))], -pi/2*[1, 1], 'c'); semilogx([wLog(1), wLog(length(wLog))], 0 *[1, 1], 'c'); semilogx([wLog(1), wLog(length(wLog))], pi/2*[1, 1], 'c'); hold off; axis([wLog(1), wLog(length(wLog)), -pi, pi]); xlabel('Frequency'); ylabel('Phase responses'); if (makeGraphics != 0) print -dsvg butterworth_phases_3.svg endif
Licensing
I, the copyright holder of this work, hereby publish it under the following licenses:
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported 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.
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.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
You may select the license of your choice.
7 June 2012
image/svg+xml
d5355d1f9fac51306e2e66e3622568a723f3be21
8,346 byte
655 pixel
512 pixel
File history
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 14:37, 7 June 2012 | 512 × 655 (8 KB) | Fcorthay | removed indexes which don't display properly | |
14:36, 7 June 2012 | 512 × 655 (8 KB) | Fcorthay | {{Information |Description ={{en|1=pole location for a 3rd order Butterworth lowpass filter}} |Source ={{own}} |Author =Fcorthay |Date =2012-06-07 |Permission = |other_versions = }} [[Category:Signal ... |
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Metadata
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Image title | Produced by GNUPLOT 4.2 patchlevel 5 |
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