Quote:

Originally Posted by bigshot 

To be perfectly honest, I don't even list my equipment in my profile because you can't know anything about how it sounds by the brand name. My system sounds the way it does because of the way I have it set up and configured. I've worked on it for about 35 years now, and there are still things I'd like to tweak when I get the time. When I'm in the market to buy equipment, I rarely look at specs because with electronics, just about everything is plenty clean enough... And with speakers and headphones, the only way I can tell anything is by listening. Specs don't tell me much.

Very respectable IMHO.

Quote:

Originally Posted by xnor 
Guess that's why most speaker measurement apps don't use/recommend it.

I have to clarify that I agree with you that proper impulse response measurement and processing is probably more useful than square wave responses (square waves don't paint the full spectrum for one)...

...

I'm appreciative of you pointing out some of the issues in comparing waveform measurements given non-ideal conditions and assumptions. I've read a little about it and find it interesting.

Quote:

Originally Posted by ultrabike 

 

If you use a 5th order Butterworth maximally flat with corner at 200 Hz things might look better in the digital domain:

[...]

I welcome any piece of code but this actually is not better. The magnitude response might be flatter, but the phase is not. Even at f0 = 20 Hz the shape of the square wave still changes clearly. Just plot(filter(B, A, x)) where x is a square wave.

This would actually work with linear phase filters, but luckily that's not what headphones are.

Quote:

Originally Posted by xnor 

I welcome any piece of code but this actually is not better. The magnitude response might be flatter, but the phase is not. Even at f0 = 20 Hz the shape of the square wave still changes clearly. Just plot(filter(B, A, x)) where x is a square wave.

 

This would actually work with linear phase filters, but luckily that's not what headphones are.

Bravo my friend!

Very well xnor! I stand corrected about that filter! I didn't go all the way and devil is always in the details . Any how, IIR filters are relatively small compared to their FIR counter parts. However, they don't always play nice in the phase. And phase matters!

Here is a more elaborate piece of code you can run (select between Butterworth, Chebyshev, and Hamming windowed FIR).

Code

% clean slate
close all;
clear all;

% main parameter
sim.highpass.select = 2;        % 0: chebyshev / 1: butterworth / 2: fir1 (Hamming)

% parameters
sim.N = 5000;                   % number of samples
sim.fs = 44.1e3;                % sampling rate (Hz)
sim.sw.f = 300;                 % square wave fundamental (Hz)
sim.highpass.iir_order = 5;     % filter order (iir)
sim.highpass.fir_order = 500;   % filter order (fir)
sim.highpass.cutoff = 200;      % filter cutoff
sim.highpass.ripple = 0.5;      % filter ripple (if applicable)

% derived parameters

% square wave
sim.sw.time = (0:sim.N-1)/sim.fs;
sim.sw.data = 2*((cos(2*pi*sim.sw.time*sim.sw.f))>0)-1;

% plot square wave excitation
figure(1)
plot(sim.sw.time,sim.sw.data);
grid on;
axis tight;
xlabel('time (s)');
ylabel('au');
title('Input square wave');

% filter
switch sim.highpass.select
    case 0,
        [sim.highpass.B, sim.highpass.A]=cheby1(sim.highpass.iir_order, ...
            sim.highpass.ripple,sim.highpass.cutoff/sim.fs, 'high');
    case 1,
        [sim.highpass.B, sim.highpass.A]=butter(sim.highpass.iir_order, ...
            sim.highpass.cutoff/sim.fs, 'high');
    otherwise,
        sim.highpass.A = 1;
        sim.highpass.B=fir1(sim.highpass.fir_order, ...
            sim.highpass.cutoff/sim.fs, 'high');
end
[sim.highpass.H, sim.highpass.F]=freqz(sim.highpass.B,sim.highpass.A,1024,sim.fs);

% plot filter responce
figure(2);
subplot 211;
semilogx(sim.highpass.F,20*log10(abs(sim.highpass.H)));
grid on;
axis tight;
xlabel('Hz');
ylabel('Magnitude');
subplot 212;
semilogx(sim.highpass.F,angle(sim.highpass.H));
grid on;
axis tight;
xlabel('Hz');
ylabel('Phase');

% pass it through filter
sim.sw.output = filter(sim.highpass.B, sim.highpass.A, sim.sw.data);

% plot results
figure(3);
plot(sim.sw.time,sim.sw.output);
grid on;
axis tight;
xlabel('time (s)');
ylabel('au');
title('Output square wave');

FIRs don't have that many issues with phase and are stable at the expense of size. Also, due to the size, there will be quite a bit of group delay there. Here are the results:

Butterworth 5th order

Chevyshev 5th order

FIR1 (Hamming) 500 length:

Enjoy

Quote:

Originally Posted by xnor 

This would actually work with linear phase filters, but luckily that's not what headphones are.

Ideal is one thing. Reality is other...

BTW, I have an honest question. While I believe headphones are not linear phase filters (have not measured them to confirm or not), why do you feel that is a good thing?

Thanks for taking the time to post the plots. Phase does matter, but it's a non-issue in most headphones.

Minimum phase is ideal in my book. It doesn't have any pre-ringing due to causality (the effect happens after the event) unlike linear phase. It has an inverse, unlike linear phase, so you can make corrections with an EQ (correcting both magnitude and phase response!). And it is stable. And the phase shift / delay is minimal, unlike linear phase.

Quote:

Originally Posted by xnor 

Thanks for taking the time to post the plots. Phase does matter, but it's a non-issue in most headphones.

About the plots, your welcome . I'm really trying to learn.

Quote:

Originally Posted by xnor 

Minimum phase is ideal in my book. It doesn't have any pre-ringing due to causality (the effect happens after the event) unlike linear phase. It has an inverse, unlike linear phase, so you can make corrections with an EQ (correcting both magnitude and phase response!). And it is stable. And the phase shift / delay is minimal, unlike linear phase.

Thanks! Very good points! It makes more sense to me now:

1) "It doesn't have any pre-ringing due to causality (the effect happens after the event) unlike linear phase" = Less transient time.

2) "It has an inverse, unlike linear phase, so you can make corrections with an EQ (correcting both magnitude and phase response!)" = EQ poles inside unit circle means stable. Maybe able to do a inverse FIR approximation which minimizes the mse (lms or so) if non-minimum phase though.

3) "And the phase shift / delay is minimal, unlike linear phase." = Less delay from excitation to reproduction (group delay)... no issues with synch dialog (movie applications perhaps).

Quote:

Originally Posted by xnor 

Phase does matter, but it's a non-issue in most headphones.

The following are some more follow up questions.

Why would phase be a non-issue in most headphones? It seems it can affect the waveform there. I remember some basics about speakers and it seems sub-woofers are easier to place if crossed bellow 80 Hz since directional cues seem to happen above that frequency. If a minimum phase filter affects a 300 Hz square wave, shouldn't that result in something that is audible? Is it because this can be EQed? Or maybe phase starts to matter on a frequency range in which HP behave closer to ideal? Sorry to bombard you with more questions...

If you have a book or reference I could read I would also appreciate it

As far as I've gathered phase doesn't come into play in headphones like it does with speakers because the driver is directly on your ear AND separated from the other. So if there was a difference in arrival time it wouldn't matter because the waveforms aren't going to interact AND because your ears aren't sensitive enough to pick up on a tenth of a millisecond or whatever minuscule difference there is. 

Quote:

Originally Posted by Benny-x 

As far as I've gathered phase doesn't come into play in headphones like it does with speakers because the driver is directly on your ear AND separated from the other. So if there was a difference in arrival time it wouldn't matter because the waveforms aren't going to interact AND because your ears aren't sensitive enough to pick up on a tenth of a millisecond or whatever minuscule difference there is. 

Not so....

Phase does play a big importance in headphones. One of the problems Sony solved with the R10 was how to eliminate these problems in a novel way. Based on many headphones I have heard...phase issues are still there. A slight difference can lead to a massive loss in quality.

Audioholics talked about the audibility of phase distortion on headphones before: http://www.audioholics.com/education/acoustics-principles/human-hearing-phase-distortion-audibility-part-2

So it is audible, yet we must not forget; In headphone acoustics, a minimum amount of phase delay can be good for satisfactory bass reproduction: http://www.aes.org/e-lib/browse.cfm?elib=16014

According to this https://secure.aes.org/forum/pubs/conventions/?elib=14449, the phase issue is simply negligible above ~1kHz with headphones.

Back to the subject: 

How far can EQ really go towards truly equalizing headphones?

Take a look at these papers:

http://www.cpt.univ-mrs.fr/~briolle/11thAESpart1.pdf

http://www.cpt.univ-mrs.fr/~briolle/11thAESpart2.pdf

Even with a 200-tap FIR filter @ 44.1 kHz, which is of a rather poor quality, the author was able to match the sound quality of a poor quality headphone to that of a high quality headphone subjectively. Thus, in conclusion, as long as the filter is not a linear phase(pre-ringing) & there's no excursion issue, you can freely equalize headphones however you see them fit.