I’ve been playing with signal processing and I would like to apply an “equal loudness filter” to a track, as is done during calculation of Replay Gain values. I’ve been using this Replay Gain documentation as a guide.  At this point I have not been able to figure out how to reproduce the “average inverse equal loudness curve” shown. I think it should be possible to use the equations of the yulewalk and butter functions, along with the filter coefficients given here, to generate the curve. So far I’ve just been using the yulewalk equation thinking that:

B(z)/A(z) = Amplitude    and,
z = Frequency 

But somehow I don’t get the expected curve shape (the one with a good fit on the right side), never mind the units.

Anyone know where I’m fooling up?

function [a1,b1,a2,b2]=equalloudfilt(fs)
% Design a filter to match equal loudness curves
% 9/7/2001

% If the user hasn't specified a sampling frequency, use the CD default
if nargin<1,
   fs=44100;
end

% Specify the 80 dB Equal Loudness curve
if fs==44100 | fs==48000,
   EL80=[0,120;20,113;30,103;40,97;50,93;60,91;70,89;80,87;90,86;100,85;200,78;300,76;400,76;500,76;600,7
6;700,77;800,78;900,79.5;1000,80;1500,79;2000,77;2500,74;3000,71.5;3700,70;4000,70.5;5000,74;6000,79
;
7000,84;8000,86;9000,86;10000,85;12000,95;15000,110;20000,125;fs/2,140];
elseif fs==32000,
   EL80=[0,120;20,113;30,103;40,97;50,93;60,91;70,89;80,87;90,86;100,85;200,78;300,76;400,76;500,76;600,7
6;700,77;800,78;900,79.5;1000,80;1500,79;2000,77;2500,74;3000,71.5;3700,70;4000,70.5;5000,74;6000,79
;
7000,84;8000,86;9000,86;10000,85;12000,95;15000,110;fs/2,115];
else
   error('Filter not defined for current sample rate');
end

% convert frequency and amplitude of the equal loudness curve into format suitable for yulewalk
f=EL80(:,1)./(fs/2);
m=10.^((70-EL80(:,2))/20);

% Use a MATLAB utility to design a best bit IIR filter
[b1,a1]=yulewalk(10,f,m);

% Add a 2nd order high pass filter at 150Hz to finish the job
[b2,a2]=butter(2,(150/(fs/2)),'high');

EL80=

f=EL80(:,1)./(fs/2);

m=10.^((70-EL80(:,2))/20);