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Potentially good idea for improving sound out of cheaper headphones

post #1 of 18
Thread Starter 
After reading about why electrostatic speakers and headphones sound better in certain areas being due to the lower inertia of the driver which translates into less severe artifacts of the driver such as resonances, quicker response, and quicker decay of energy.

If you were to model your typical headphone driver as a driven oscillator then you will get a response from the driver that mimics the driving signal but with phase delays and decayed but continueing oscillations that may not dissipate fast enough to be ignored. The ideal output of your driver would be that it exactly follows the intended driving signal (which could be achieved with approximately zero mass), however you could modify the driving signal so that you get a response equivalent to the ideal response from the original driving signal. What I am trying to say is that the response of a headphone driver may be complicated (nonlinear) but it can be modeled and will be deterministic in its response to a given input signal. Therefore you can compensate electrically in the driving signal for aspects that would be otherwise very difficult to correct by changing the design of the driver. For instance, if your drivers hold the energy too long and have decaying output from a previous signal, you can actively correct for this by driving a signal that will damp that energy faster. This kind of stuff is very common in other areas, very expensive cars can have active suspension which drive the suspension actively to cancle oscillations. Typically in these systems you need some sort of feedback (e.g. the extension of the shock in time) because the external driving signal (the roads impact on the shocks) is unknown, but for digital music you have all the information about the entire signal from the start.

Let me know if there are flaws in any of these areas but I do know this, if you were to model the headphone driver as a driven oscillator (not necassarily linear) you could model the response of the headphone (sound output) to the driving signal (the music signal) and you can see all of the error in output versus input due to artifacts of the mechanical system. It is definitely possible in this mathematical model to alter the driving signal to produce a perfect match between output and intended music driving signal. This theory is correct, I just don't know about how the application of theory to practice would fail.
post #2 of 18
What you bring up has been implemented in subwoofers (Velodyne), but I suspect that the upper frequencies go by too fast for such control, at least with current technology that I am aware of. Just buy Stax.
post #3 of 18
Thread Starter 
Quote:
I suspect that the upper frequencies go by too fast for such control, at least with current technology that I am aware of
Speed shouldn't be a problem because this conversion should be done beforehand, or at least done lets say 10 seconds in advance in a buffer. The signal itself would change.

Quote:
Just buy Stax
The idea would be to take $300 headphones and make them sound thousands of dollars better.
post #4 of 18
Given that they aren't linear, modeling them isn't going to be trivial. The information we typically measure (frequency response, THD, IMD, etc.) doesn't necessarily fully describe a pair of headphones.
post #5 of 18
Thread Starter 
Quote:
Given that they aren't linear, modeling them isn't going to be trivial. The information we typically measure (frequency response, THD, IMD, etc.) doesn't necessarily fully describe a pair of headphones.
You may still get a noticeable improvement in response by simply modeling the headphones as linear. True this wouldn't be a perfect correction but it may prove to be better than standard output. The good thing about modelling a headphone is that there is signficant damping (especially at high frequencies), therefore if you make some errors in the modeling (assume linear instead of nonlinear) these errors will not compound over time as would occur in a system without damping. Therefore in some sense your corrections to signal would have a local effect in time and their influence on the output at a later time would be minimal. Think about it this way, you are driving your headphones with your music signal assuming that your drivers are massless (hence follow the signal exactly) therefore you are driving them with an incorrect signal yet your music sounds fine and these errors certainly don't accumulate over time.

Yes, not being linear really does increase the difficulty quite a bit. If your headphones are significantly nonlinear then you can't use stuff like impulse responses and convolutions, but it is still possible to solve numerically for an approximate solution. Obtaining the parameters for each pair of headphones would be difficult (nonlinear inverse problem). The non-linear spring constant should at most be a function of displacement and the damping coefficient should be at most a function of velocity. However, it is possible to measure these by subjecting the headphone to different tests (e.g. signals at different amplitudes and monitor distortions and ring down time for the output). You could use a microphone or if you wanted to be really scientific you coud use a heterodyne interferometer (not too expensive) to measure the displacement of the driver as a function of time. Modeling the headphone driver as a 1-D nonlinear oscillator should be fully sufficient (3-D modes of oscillations are probably very insignificant). Keep in mind what I said before about the headphones being dissapative therefore we really don't require an exact solution. You could run your initial music signal through your model ODE and numerically solve for your output signal. Yes you have to be careful numerically solving nonlinear equations but with the proper scheme and small enough time step you should be fine. And in fact headphones are not what you would consider highly nonlinear (otherwise your music would sound crappy). Then with some simple criteria you can determine where and how your signal should be modified, then resolve the equation iteratively and hopefully you will converge on the solution. I'm sure there are better more established techniques for numerically solving for the proper driving signal in a 1D ODE to get a particular output.

It is true that in general solving nonlinear ODE's is difficult but if you study one particular ODE with coefficients that remain in a small range even for different headphones you can gain some insights and make some generalizations about how to correct the signals (approximately) without fully solving for every song. Therefore you could develop other methods to more efficiently "correct" your music, possibly even on the fly.
post #6 of 18
I haven't exactly read anything but how exactly are you going to change the input signals even if you do generalize the effects (in which itself has many degrees of freedom)?

These kinds of systems are imperfect and cause phase distortions and lots of power / parts.
post #7 of 18
Thread Starter 
Quote:
I haven't exactly read anything but how exactly are you going to change the input signals even if you do generalize the effects (in which itself has many degrees of freedom)?
It could be as simple as a DSP plugin in your player (e.g. foobar). To simply test if the process has potential you could modify the music itself, but in practice it would be annoying to maintain of seperate copy of music for each headphone you had.

Quote:
These kinds of systems are imperfect and cause phase distortions and lots of power / parts.
Not really sure what you are talking about here.
post #8 of 18
Quote:
Originally Posted by helicopter34234 View Post
It could be as simple as a DSP plugin in your player (e.g. foobar). To simply test if the process has potential you could modify the music itself, but in practice it would be annoying to maintain of seperate copy of music for each headphone you had.



Not really sure what you are talking about here.
I'm not sure you are familiar with digital signal processing. it will always have phase alterations, but you can minimize it but it will take a lot more processing.
post #9 of 18
Thread Starter 

DSP

Quote:
I'm not sure you are familiar with digital signal processing. it will always have phase alterations, but you can minimize it but it will take a lot more processing.
I am very familiar with the math of signal processing (convolutions, Fourier Transforms, or FFT's for digital, etc..), a little less familar with the practical applications (and problems), especially not so familiar with its application in digital audio (I mostly deal with digital image processing with matlab and photoshop). I am not sure I fully understand what you are saying about the phase alterations. I know from digital image editing that alterations are subject to quantization error but this can be mitigated by increasing the bit depth (upsampling) and by dithering. I don't understand why phase alterations are an unavoidable consequence of DSP. Also I would guess that the methods you spoke of for minimizing it are not so costly that a desktop computer could not keep up with the signal in realtime.
post #10 of 18
Quote:
Originally Posted by DoomzDayz View Post
I'm not sure you are familiar with digital signal processing. it will always have phase alterations, but you can minimize it but it will take a lot more processing.
What is your basis for saying this?

As far as I know, it is entirely possible to build a digital filter where the only "phase alteration" is a simple delay -- where phase relationships remain intact.
post #11 of 18
Not sure how big of a deal this would be, but I did think of one problem that you might encounter. If your idea works, then the process you explained may have to be repeated a few times to compensate with the change in the driver's stiffness. Over time, the driver would probably become quicker than when you first did the process (think burn-in) and you would have the same problem again.
post #12 of 18
Quote:
Originally Posted by LnxPrgr3 View Post
What is your basis for saying this?

As far as I know, it is entirely possible to build a digital filter where the only "phase alteration" is a simple delay -- where phase relationships remain intact.
here's something I googled
Phase Distortion at Passband Edges

why it's not that easy:
Linear Phase Audio Filters\
Forward-Backward Filtering

while it is possible to get around this it isn't practical
Quote:
The FIR filters are both linear-phase and minimum-phase, so they have far fewer adverse effects on the signal; in addition, the architecture of most modern DSP's is generally optimized for efficient computation of FIR filters, so that a single "tap" or computation point of an FIR filter generally takes either one or two clock cycles whereas each point in an IIR filter may take from 20 to 50 cyles. However, FIR filters also have problems at the lower audio frequencies; since the number of points to be computed increases as the inverse of the FIR "corner" frequency, if a designer tries to implement these filters at the system sample rate (as they generally do), several thousand processing cycles per sample are necessary to calculate each filter at the lower frequencies, but current technology only supports several hundred per sample per processor (at the standard sampling rates of 44.1 or 48 kilohertz), so that these filters are seldom used in real-time applications. Fast-Fourier Transforms require a high degree of frequency precision and hence a high number of sample points per transform to avoid audible distortion, so they take even more cycles than FIR filters; their much-ballyhooed "efficiency" really only takes effect when when the need is for a linear filter resolution in absolute bandwidth, but the need in an audio equalizer is for resolution as a constant percentage of bandwidth, so that the efficiency goes down dramatically for FFT-based approaches in constant-percentage-bandwidth (constant "Q") applications.
in addition, it(FIR) will create preringing due to Gibbs Phenomena
http://www.hydrogenaudio.org/forums/...showtopic=2418
http://newsgroups.derkeiler.com/Arch.../msg01178.html
http://www.hydrogenaudio.org/forums/...howtopic=13504


I've never done any kind of image processingv
post #13 of 18
One of the problems created by non-ideal headphones is distortion, which actually adds frequencies to the signal that have not been there before. I am not aware of a possibility to alter the input signal in a way that these additional frequencies are cancelled out. There are certain changes to a signal that are unfortunately not reversable.

Furthermore even an accurate model of a headphone with regard only to frequency and phase response under all input conditions would be extremely complex and probably hard to calculate in realtime. Keep in mind that for a simple stereo signal you already have ~100000 values per second to calculate, so even on modern PCs you cannot do arbitrary complex mathematics.

But you are right, for simple changes to the frequency/phase response this is already done, e.g. in some active studio monitors. But I suppose this would be something to make bad headphones acceptable, not to make good headphones great.
post #14 of 18
I don't think that a digital compensating filter based upon convolution would add any phase distortions except those that cancel out phase distortions inherent to the driver.
The only problem I see here is driver instability - it can probably be solved by recalibrating the whole system by measuring impulse response.
As for computing power, I tend to think that 4096 samples of impulse response data would be sufficient to get rid of most frequency response flaws for CD Audio quality music. That would require about 800 MIPS of computing power - not a lot for a contemporary PC or DSP.
post #15 of 18
I actually did not mean phase distortions but the waveform distortions that result from the fact, that the displacement of the membrane is not proportional to the voltage applied. If you e.g. apply an input voltage that is shaped like a sine, the displacement might not be exactly like a sine, but e.g. like a slightly compressed sine (a tad more in direction of a rectangle). These non-linear distortions can not be corrected by linear calculations like a convolution.

You are right with the convolution, with 4096 taps you can correct frequencies down to 44100/4096=10.7Hz, which is enough for CD-Audio. But I was thinking of a more complex, nonlinear model, that describes the frequency response at different amplitudes. With operations more complex than multiplications and summations the computational power quickly gets scarce. But now that I am thinking further of it, I actually am not sure how this model would look like. Someone please google some scientific papers ...
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