Headphone FIR equalization using Foobar

Sure.

This is the B&K function:

Code:

function [b] = b_k()

% paramters
fs = 44.1e3;
fn = fs/2;
n = 450;

% target response
s = -6/(log10(20000)-log10(50));
r = log10(50):0.001:log10(fn);
p = s.*(r - log10(50));
f = 10.^r;
bk_t = [[0 f]; -[0 p]].';

% approximation
b = firls(n, bk_t(:,1).'/fn, 10.^(-bk_t(:,2).'/20.0));

% check
figure;
[h, w] = freqz(b,1,2^15,fs);
semilogx(w(2:end), 20*log10(abs(h(2:end))));
grid on;
axis([5 20000 -23 17]);

And this is the latest script using the B&K function:

Code:

% Load REW impulse responses and validate
[h, fs, nbits] = wavread('hd600_IR_4.wav');
H_left = freqz(h(:,1),1,length(h(:,1)));
H_right = freqz(h(:,2),1,length(h(:,2)));
step = (22050-5)/length(h);
f = 5:step:22050;f=f(1:end-1);
figure;
subplot(2,1,1);
semilogx(f,20*log10(abs(H_left))+90);
grid on;
axis([20 20000 65 110]);
subplot(2,1,2);
semilogx(f,20*log10(abs(H_right))+90);
grid on;
axis([20 20000 65 110]);

% hd600 impulse response sample to learn (and invert)
MatchSize = 3000;
PreCursor = 100;
MaxIndex = find(h(:,1) == max(h(:,1)));
hn = h(MaxIndex-PreCursor:MatchSize+MaxIndex-PreCursor,:);
figure;
subplot(2,1,1);
plot(hn(:,1));
grid on;
axis tight;
subplot(2,1,2);
plot(hn(:,2));
grid on;
axis tight;

% Perform LMS (least-mean-squares) on each channel and derive
% optimized filters (c)
N = 200000;                       % iterations
taps = 2000;                   % number of equalizer taps
mu = [0.0001 0.00001];  % adaptation (learning) gains
gu = 1-0.0000001;             % lossy gain
inDly = 1000;                   % delay amount for input samples
Main = 900;
i = randn(2,N);                 % input samples
o = zeros(2,N);                 % output samples
e = zeros(2,N);                 % error
id = zeros(2,N);             % delayed input samples
d = zeros(2,taps);            % adaptive filter delay line
c = zeros(2,taps);            % filter coefficients
c(:,Main) = 1;                    % filter center tap initialization
y = zeros(size(i));
for k = 1:2
  y(k,:) = filter(hn(:,k),1,i(k,:)); % convolve with hd600 response (channel to equalize)
  id(k,:) = filter([zeros(1,inDly) 1], 1, i(k,:)); % delayed input
end
for n = 1:N
    if n < N/2                   % change adaptation gear
        mup = mu(1);
    else
        mup = mu(2);
    end
  for k = 1:2
     d(k,:) = [y(k,n) d(k,1:end-1)];         % adaptive filter delay line update
     o(k,n) = d(k,:)*c(k,:).';                     % apply adaptive filter (filtering)
     e(k,n) = o(k,n) - id(k,n);               % error
     c(k,:) = gu*c(k,:) - mup*e(k,n)*d(k,:);    % lms coefficient adaptation (learning the headphone)
  end
end

% remove high frequency corrections
%[b, a] = besself(11, 0.95, 'z');
[b, a] = butter(7,0.99);
for k = 1:2
  c(k,:) = filter(b, a, c(k,:));
end

% apply b&k curve
[b] = b_k();
for k = 1:2
  c(k,:) = filter(b, 1, c(k,:));
end

% Plot errors (check convergence)
figure;
for k = 1:2
  subplot(2,1,k);
  plot(e(k,:));
  grid on;
  axis tight;
end

% Plot correction filters
figure;
for k = 1:2
  subplot(2,1,k);
  plot(c(k,:));
  grid on;
  axis tight;
end

% Plot correction filters frequency response
figure(1);
for k = 1:2
  subplot(2,1,k);
  hold on;
  C = freqz(c(k,:),1,length(c(k,:)));
  step = (22050-5)/length(c(k,:));
  f = 5:step:22050;f=f(1:end-1);
  semilogx(f,20*log10(abs(C))+90,'r');
  grid on;
  axis([20 20000 65 110]);
end

% Plot predicted impulse responses
figure;
PlotSize = 200;
corr = zeros(size(h));
for k = 1:2
  subplot(2,1,k);
  corr(:,k) = filter(c(k,:), 1, h(:,k));
  plot(h(MaxIndex-PreCursor:PlotSize+MaxIndex-PreCursor,1));
  hold on;
  plot(corr(MaxIndex-PreCursor+Main:PlotSize+MaxIndex-PreCursor+Main,k),'r');
  legend('original','corrected');
  grid on;
  axis tight;
end

% Plot predicted frequency responses
figure;
for k = 1:2
  CORR = freqz(corr(:,k),1,length(corr(:,k)));
  step = (22050-5)/length(CORR);
  f = 5:step:22050;f=f(1:end-1);
  subplot(2,1,k);
  semilogx(f,20*log10(abs(CORR))+90,'r');
  grid on;
  axis([20 20000 65 110]);
end

% Save filter
filt = c.';
wavwrite(filt, fs, nbits, 'hd600_eq.wav');

You might have to play around with the script depending on where the headphone impulse responses main peak happens. Though I might have corrected that.

 

Deleted a rogue 9 in the b_k calling. Not sure why Octave didn't complain about that. But other versions and Matlab might.

EDIT: One will need to install the signal pkg for Octave.

 

Yep!

 

A few folks were wondering if I could share the HD600 correction filter I came up with. Here is a link to it:

https://drive.google.com/file/d/0BzGhKu7Sq7bCSlczalFSZE5GVDg/view?usp=sharing

I don't think it will sound good if you just play it. Proly a blip or so. But I think one can download it and apply it as is to fb2k's convolution plugin, in which case it may sound good with an HD600 set of cans. Or one can check it out in Audacity. Or this or that.

Note this filter will give one a B&K response from an HD600 assuming my measurement rig. It will work well if one's HD600s match the response of mine closely (and if my measurement rig is not too far off).

 

I would also like to point out that there are companies that provide one with professional calibration/equalization services that can actually be tailored to your particular headphone such as these guys:

http://sonarworks.com/headphones/overview/

 

More than likely is the measurement rig. Which means this may actually help fine tuning one's measurement rig.

With my setup things open up with the HD600s. However, it does become a little brighter. Even with the B&K curve. I don't think my measurement rig is too far off, but it's not perfect.

One thing that can be done is compare results with a set of flat speakers. Perhaps experiment with different coupling materials and/or compensation.

 

BTW, how do your un-equalized HD600s measurements look?

EDIT: In some folks measurement rigs, certain headphones do look a bit way off particularly in the treble and upper mids area. Either too depressed or too peaky. If this is a short coming of the measurement rig, automatic equalization will obliviously try to correct for a problem that is not there. First step should be to get the measurement rig right.

Also, compensation should be applied to the IMPULSE RESPONSE, not the frequency response magnitude. This means that one needs to get the equivalent impulse response of the frequency response magnitude compensation. I don't know of a single measurement package that does this. Even the mega bucks ones. One would have to do this by hand.

 

Did some open air measurements on HD600s and KPPs. Interesting stuff.

Problem areas are around 7 to 10 kHz with some few dBs of discrepancy vs my measurement shack. It is not super consistent across cans. I will have to do more measurements and listen more closely.

I can also say that flat equalization or B&K equalization using my rig as reference is not perfect. It's not too far off though. As far as results after listening, I like some things and I don't like some others. But the fact that some things do improve is encouraging. I'm cool with my cans w/o eq though.

In particular, with equalization the HD600s open up. And they do so just right. But they do become a little more edgy. The KPPs on the other hand become less strident, but become more flat in dynamics. Looking at the open air measurements there are some clues as to why. But again, would have to look into it. No hurry though. Again, I'm cool with my cans the way they are.

I'm also not searching for the ultimate stuff. Just curious. And like to see for myself that things can indeed be tuned to some extent with DSP if so desired, with some positive (and not so positive) results. Other approaches obviously work as well.

 

So here is what I mean when I say there are differences between my HD600 measurement shack results and an free air measurement:



To demonstrate consistency with the measurements, I included dates. The shack rig measurements are actually years apart. The open ones are one day apart. I was not super nm careful in positioning the cans. Hell, for the open air measurements I merely held the cans with my hand.

If there is this huge change due to burn in, or whatevers, I fail to see it. At least with these cans.

Now, what the open air measurements tell me is that there is indeed a bit of mid range shoutiness due to the double hump between 3 kHz and 5 kHz. The measurement shack is perhaps injecting an artificial boost betwen 7 kHz and 10 kHz. But I fail to see the horrid mess with peaks and nulls all over the place.

The open air measurements actually correlate best with what I hear from 2 kHz and up. The two measurements correlate well between 2 kHz and 6 kHz and then they deviate a bit. But again, we are not way off the mark. Down from 2 kHz, the measurement shack pulls things together.

Can I combine the two measurements all the way to impulse responses. Proly.

Can I come up with a headphone tailred impulse response compensation from open air to shack that only applies to 2 kHz and up. Proly.

Would these be useful at all to improve things. Perhaps. It would allow me to experiment with some approaches to see if I can come up with a better equalization file. At it may help in maybe improving frequency response plots that better correlate with what we hear.

BTW, doing a similar thing with other headphones may not result in the same set of compensation curves. So it is possible that this has to be done on a headphone to headphone basis, or on a headphone type to headphone type basis.

I do not currently know if this is necessary. Hopefully experience and time will tell.

In the mean time, the equalization files that I produce should improve some things, and IMO they don't result in horrid sound. I like the corrections for the HD600s better than the KPPs. But the KPPs corrections don't sound horrid to me either. They also improve some things at the expense of others.

 

I'll give your approach a go tonite if I can because I don't have the HD600 measurements with me at the moment.

However, I think de-convolution is the equivalent of a zero-forcing filter which may be problematic on deep narrow nulls and peaks.

I didn't added a noise floor to the MMSE approach I did. But if I do, I can control the null depth in many cases.

I also wouldn't worry too much about the ringing. One might add a low pass filter or something. Though a larger filter will indeed take care of the low frequencies better. Just note many headphones are not that linear in such regions.

 

err.. I meant adding a high pass filter to the result to remove the ringing. I'm dyslexic.

 

While the response of a headphone or general driver may be mostly MP, I don't think the compensation should be.

You can obtain a MP equivalent of the NMP correction filter (google cepstrum). I do not recommend it however. The force tells me so.

Using smoothing sounds like a plan also, if you use deconvobulatation-isation.