DescriptionG712 butterworth normalized.svg	English: normalized Butterworth filter approximation for CCITT G712 specification
Date	7 June 2012
Source	Own work
Author	Fcorthay
SVG development InfoField	The SVG code is valid.  This diagram was created with Inkscape, or with something else.

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

#-------------------------------------------------------------------------------
# Specifications
#
fs = 40E3;
fPass = 3000;
rPass = 0.125;
fStop1 = 4000;
rStop1 = 14;
fStop2 = 4600;
rStop2 = 32;

pointNb = 1000;
AdbMin = 40;

makeGraphics = 1;
figureIndex = 0;

#===============================================================================
# Normalized filter function
#
wLog = 2*pi*logspace(-1, 1, pointNb);
fc = 0.87;
Adb = [];
for order = 8:16
  [num, den] = butter(order, 2*pi, 's');
  while ( length(num) < length(den) )
    num = [0, num];
  endwhile;
  Adb = [Adb; 20*log10(abs(freqs(num, den, wLog)))];
endfor
Adb(Adb < -AdbMin) = -AdbMin;

figureIndex = figureIndex+1;
figure(figureIndex);

semilogx(wLog/(2*pi), Adb);
hold on;
semilogx([wLog(1)/(2*pi), fc, fc], -[rPass, rPass, AdbMin], 'r');
semilogx([fStop1*fc/fPass, fStop1*fc/fPass, fStop2*fc/fPass, fStop2*fc/fPass, wLog(length(wLog))/(2*pi)], ...
        -[0     , rStop1, rStop1, rStop2, rStop2            ], 'r');
hold off;
axis([wLog(1)/(2*pi), wLog(length(wLog))/(2*pi), -AdbMin, 0]);
grid;
xlabel('frequency [Hz]');
ylabel('amplitude [dB]');

if (makeGraphics != 0)
  print -dsvg g712_butterworth_normalized.svg
endif

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