File:Butterworth amplitudes 6.svg

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Original file(SVG file, nominally 512 × 384 pixels, file size: 14 KB)

Summary[edit]

Description
English: Amplitude response of a 6th order reference Butterwort filter, with the amplitudes of the internal second order sections
Date
Source Own work
Author Fcorthay

Source code[edit]

This graphics has been realized with the help of the following Octave script:

#-------------------------------------------------------------------------------
# Specifications
#
order = 6;
pointNb = 100;
axesLength = 1.25;
textOffset = 0.05;
wLog = logspace(-1, 1, pointNb);
AdbMax = 10;
AdbMin = -40;

#===============================================================================
# Butterworth filter
#
[zeroes, poles, gain] = butter(order, 1, 's');

[num, den] = butter(order, 1, 's');
while ( length(num) < length(den) )
  num = [0, num];
endwhile;

#-------------------------------------------------------------------------------
# Poles plot
#
figure(1);
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");
  endif
endfor

#-------------------------------------------------------------------------------
# Normalized filter, transfer functions plot
#
Adb = 20*log10(abs(freqs(num, den, wLog)));

figure(2);
semilogx(wLog, Adb);
hold on;
for index = 1:order
  if imag(poles(index)) > 0
    num = [0, 0, 1];
    den = [1, -2*real(poles(index)), abs(poles(index))^2];
    Adb = 20*log10(abs(freqs(num, den, wLog)));
    semilogx(wLog, Adb, 'g');
  endif
endfor
hold off;

axis([wLog(1), wLog(length(wLog)), AdbMin, AdbMax]);
xlabel('Frequency');
ylabel('Amplitude responses');
grid;

print -dsvg butterworth_amplitudes_6.svg

Licensing[edit]

I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution share alike
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You are free:
  • to share – to copy, distribute and transmit the work
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Under the following conditions:
  • attribution – You must attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work).
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File history

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Date/TimeThumbnailDimensionsUserComment
current14:39, 11 August 2011Thumbnail for version as of 14:39, 11 August 2011512 × 384 (14 KB)Fcorthay (talk | contribs)
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