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A very high damping factor=Overdamping headphones?

Discussion in 'Sound Science' started by gustavmahler, Jan 17, 2015.
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  1. 71 dB
    Better in what sense? In audio only differencies that can be heard are relevant. Technical differencies such as bit depth or sampling rate which don't come out in double blind listening tests are irrelevant, just placebo effect *. Haven't we had this discussion already? The width of sinc function only shows itself in impulse-like signals which is very different from what kind of signals are present it music. As long as I listen to music instead of impulses I don't see the relevance of this.

    * 96 kHz is "unambiguously better" than 44.1 kHz, but 192 kHz is "unambiguously better" than 96 kHz, but 384 kHz is "unambiguously better" than 192 kHz, but 768 kHz is "unambiguously better" than 384 kHz, but 1.536 MHz is "unambiguously better" than 768 kHz, but… …infinite samplerate is enough so we gotta have that! Well, only differencies that can be heard are relevant so luckily we don't need infinite samplerate. Not even 96 kHz. People who really understand these things say that there is absolutely no benefits even theoretically above about 60 kHz samplerate and in practice (as demostrated by double blind listening tests) 44.1 kHz is enough.

    Nobody says you have to use brickwall filter with 44.1 kHz. You can use "causal" digital filters if you want. The material can of course be "pre-filtered". All you need is an all-pass-filter that delays the highest frequencies a bit.

    Some Japanese DACs don't have reconstruction filters at all! They output the music with a lot of ultrasound noise.
    1. The more pressure it creates, the more difficult it is to press further. And unlike simply closed cans pressure does not bounce the membrane back with same agility yet sinking in the dampening on the way back as well. Imagine a bottleneck where water starts refilling the bottle before it had the time to fully drain.
    2. Not only less sensitive but slower. You will need more power and stiffer membrane to partially overcome dampening - partially. Because air would compress instead of flowing.
  3. 71 dB
    [1] Have you ever seen a differential equation describing a damped vibrating spring-mass system? It looks like this:

    my'' + cy' + ky = r(t) ,​

    where m is mass, c is damping constant, k is spring modulus, y is the coordinate of the mass, y' = dy/dt = velocity of the mass and y'' = dy'/dt = acceleration of the mass. On the right side of the equation r(t) is the driving force as a function of time t, in other words the force on the diaphragm created by the electric current in the voice coil.

    Now, in this equation c is multiplied with velocity y'. In other words, it doesn't matter where the mass is, only the velocity matters. Non-linearities come from the fact that spring modulus k is not constant, but a function of y. That's what your "The more pressure it creates, the more difficult it is to press further" means (more or less), but that has nothing to do with damping! On the contrary, more damped systems have milder resonances which means reduction of maximum y on resonance frequencies. So, damping actually helps keeping a system linear. No need to think about missleading bottlenecks when you know the math!

    [2] "Slower" means less sensitive. Again, knowing the math tells you how it is. A 110 Hz tone needs 110 cycles per second no matter what. The only thing that can change is the amplitude of the oscillation and that's the same as sensitivity. Air doesn't care about the damping. All it cares about is the speed and frequency the diaphragm is moving. Air doesn't care if you need more electric power because of increased damping. Only your amp cares about it because it needs to generate the power without distortion!
    1. How can you fit all dampening factors in a simple equation? Particularly I mean all the materials through which air is filtered like grills foam and fabrics.
    2. If it was so simple, all headphones sounded the same (no STAX needed for speed). My amp drives dampless headphones easily, loud and clear, while dampened start sounding blurry at the same output level.
    Last edited: Oct 30, 2017
  5. SimonPac
    Yes, we're agreed it is not the technical merit of waveform fidelity per se, but what is audible that concerns most people here. But I'll say it again; your necessary brickwall filter and therefore your ADA system in total only passes indefinitely repeating signals with total accuracy. Anything else is distorted to some extent. As soon as you frequency domain convolve a periodic waveform with a square wave representing the time window, you need infinite bandwidth to reproduce it perfectly in the time domain where piecewise multiplication applies. This is because a square wave or any waveform with an infinite rise/fall time contains frequency components out to infinity. Your time window has to have infinitely fast edges to reproduce a hard stop/start. Bandlimiting messes them up. It doesn't mess up the sinewave, which is why digital meeting Nyquist criterea does in-band sine waves and combinations thereof with simple frequency relationships just fine. A soon as a waveform stops or starts even a perfect brickwall distorts it. Tell me where I'm wrong.

    Yes, of course it is desirable to eliminate any out of band output, if for no other reason than intermodulation in the amplifier.

    On headphones (oh yes, headphones!), damping equates to energy loss mechanisms, which are mechanical.acoustic in this situation of the headphone alone. I think it would be hard to alter c and k totally independently in practice, because a given suspension system would largely define both parameters. A system giving high energy loss probably would also have low compliance. That though is not uniformly reflected in your earlier figures as lower sensitivity for high DF phones.
    Last edited by a moderator: Oct 30, 2017
  6. RRod
    [nm, gregorio already said all of this]
    Last edited: Oct 30, 2017
  7. 71 dB
    [1] Can be done when we talk about the movements of a mass. Air affects the diaphragm a little bit, but the resistance air sees in grills and fabrics is linear, if it isn't, the engineering of the phones is abysmally bad.
    [2] No, it's not that simple at all. Electric part is pretty easy. Mechanical part is pretty easy. Acoustic part is hard as hell. Even if your headphone is completely linear, your frequency response can be totally wrong. How do you define a damped headphone? What is your criteria? I am talking about headphones that have large damping ratio, large c value in the equation.
  8. 71 dB
    Theoretically yes, but the magnitude of the temporal distortions related to signals typical to music is extremely small. Your amp probably generates a million times larger temporal distortions thanks to negative feedback. The good news is none of this is likely to be heard in a double blind test.

    There is no audio system in the universe to give you infinite bandwidth. Analog systems don't have a set upper limit, but in practice above a certain frequency noise is all you have. Just deal with it and concentrate on what is relevant. Perfect square waves are impossible and that's a reason why our hearing doesn't even expect them. Bandlimited versions are accepted. This is what correctly generated 2000 Hz square wave looks like at 44100 Hz samplerate:

    2000 Hz square.png

    It doesn't look very good, but it sounds to our ears the same as would sound a square wave generated at 100 times higher samplerate. The lesson is: It doesn't matter what it looks like. What matters is what it sounds like. That's one important thing in understanding digital audio.
    Last edited by a moderator: Oct 30, 2017
    1. Air is what conducts soundwaves - we can't possibly neglect it and calculate membrane movement in vacuum. Sometimes you need intense filtering to achieve the desired acoustics.
    2. I judge by how much filtering there is and how low resonances are.
  10. SimonPac
    Yes, I'm fully aware we are looking at the issue of what's relevant to perceived quality and I'm also fully aware that any real world system is band limited, especially analogue tape or vinyl and also transducers. In my youth I used to look at vinyl cartridge response graphs for relaxation and play with load capacitance! However I'm seeking to clarify some previous technical assertions.

    Digital allows solutions to filtering that analogue systems can't in practice implement. This may not be a good thing; some people say it isn't. Some would go further and say that is partly because the time domain results are not paralleled by anything occurring in the natural world. A big discussion on the nature of time and entropy might follow, but, again, we should move to another type of forum for that.

    That is all I'm saying right now.
  11. gregorio
    "Hugely faster DACs" using 16 or 24 bits per sample? Could you provide an example please.

    Yes of course, it comes down to practical implementation. You might find this paper useful and this one.

  12. 71 dB
    [1] True, but the acoustic impedance at low frequencies where the resonancies happen is small compared to the mechanical impedance of the diaphragm. When we measure the electric impedance curve of a headphone, it isn't in vacuum. Air is involved. The mechanical and acoustic impedances show in the electric impedance. So when you calculate the mechanical damping for the diaphragm, air is incorporated in it.
    [2] Low as in frequency or amplitude? How is the amount of (acoustic?) filtering judged? It is important that we are talking about real physical/technical properties instead of subjective impressions and feelings. When you measure the frequency response of a headphone, the output impedance changes the result and zero output impedance provides the largests electric damping. Impedance curves are good for calculating the properties of a headphones, because it doesn't "contain" output impedance. Headphones in general are very linear electroacoustic transducers even at dangerously high sound pressure levels. Damping simply doesn't increase distortions. On the contrary, it helps keeping distortion low as long as the amp has enough power because damping decreases sensitivity.

    I definitely agree that the normal brickwall filter is "unnatural" considering causal prosesses, but I doubt it has relevance. Selecting between 5 different filters in my CD player makes a tiny difference in the width of the sound image on suitable music, something I perhaps could hear in blind test. However, it's not as if normal filter sounds "unnatural" compared to more causal filters. A microscopic change in the width is all I can hear. But that's only me. I'm not the king of golden ears. If I use oversampling, the filter selection makes no difference for me.
  13. SimonPac
    Usually you do not want high amplitude resolution on a wideband signal (very much wider than audio) because the noise floor comes right up and there's no point. Also it is harder to get the sampling accuracy right because of settling times in the circuitry, and, because as Gregorio's second quoted paper (Larvy) points out, real sample-hold circuits actually smear energy over a finite time. That's an additional error in any A-D system. Here, all other things being equal, low sampling rate does work better, i.e. is more accurate in its instantaneous snapshot.

    The first paper you mention is simplistic, although many have agreed with the 88.4/96 with 20 or 24 conclusion. The second is mostly fine but he proves nothing about time domain issues caused by the filter. His own theorem is fine as far as I can see, and is a simple outcome of conjugate variables, but it actually tells you nothing at all about the position of the time domain sinc function other than the fact that it is positioned between minus infinity and plus infinity in time. I had sort of guessed that already.

    The Nyquist-Shannon theorem applies to perfectly brickwalled analogue, not raw analogue. In other words, yes, perfectly implemented Nyquist Shannon will work perfectly. There are a few minor mathematical caveats which I'll ignore; I actually don't really understand them. But it works perfectly (probably..) on ideal brickwalled analogue input. Brickwalled analogue input X is not the same as analogue input X.

    If you up the sample rate by *2 you can change the brickwall out by a factor of *2.
    The time domain error in energy will also be halved as far as I can see, if everything is done perfectly.

  14. gregorio
    In summary, you've stated that lower sampling rates are more accurate, higher sampling rates provide the opportunity for filters with lower error. I agree with these statements but to go a step further and implement an audio product for human beings, we can reconcile your two statements by asking; what is the lowest sample rate which can capture the audio bandwidth of human hearing and accommodate a filter with a level of error beyond human hearing? The answer to this question is NOT 192kS/s! 44.1KS/s has been demonstrated to be enough as no one has reliably demonstrated the ability to hear the level of error introduce by the filter at this rate (in music/audio) and, as Lavry has stated, even the theoretical objections disappear by the time we get to a sample rate of 60KS/s.

    We have a similar situation with bit depth. Ultimately, about 22 bits is the limit of what is physically achievable, due to thermal noise. In terms of human hearing, if we take the most extreme scenario of; dynamic levels well beyond comfort (entering the region of pain/damage), the most sensitive area of human hearing and near zero environmental noise floor, we end up with a dynamic range figure of about 118dB, which is easily attainable with 16 bits! In practice though, virtually no commercial recordings exceed about 60dB (10 bits) due to the fact that no consumer has a near zero noise floor and no one wants to create a product so far beyond comfortable.

  15. SimonPac
    Real dynamic range of CD in terms of information rather than max SNR is 96dB. You can lower the noise floor but I don't think anyone thinks there's real information to be had below -96.

    Incidentally, Dolby SR on a fast analogue tape could give you over 100dB based on SNR according to the Wikipedia article on audio dynamic range though 95dB would be a more common claim, and the information content would be real to well below the noise. And no brickwall is needed.

    Again, it all depends on how the ear works. Not on high level THD IMO. We don't listen to sine waves.
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