I might be thinking about this wrong, at least as far as what "transient response" is. How different drivers respond to rapidly changing and dynamic signals is a whole different matter from a simple sine wave. I would probably have to do some serious studying to take this much further (iow I don't plan on it).
Ultimately any signal you can think of whether seemingly "periodic" or "changing" can be made up of a finite number of sinewaves of defined amplitudes, phase and frequency.
If you can wrap your head around that concept it goes a long way to understanding the relationship between time and frequency domains and how FFT's work...
As a couple of very basic examples. A periodic square wave, take a sinewave at the frequency of the square wave, add a 3rd harmonic in phase, then a 5th harmonic then a 7th and so on. As you add each further odd harmonic the resultant looks more and more like a square wave until you can't distinguish it. It's quite interesting to do this in a program that will add them together for you and display the result visually.
A theoretically perfect squarewave would have infinitely steep sides, but to do this you would need an infinite number of odd harmonics and an infinite bandwidth for them to reside within to reproduce it, so clearly a perfect squarewave is not possible and hence all square waves have a rise time measurement to show how closely they approximate the idea and the rise time is proportional to the bandwidth. The wider the bandwidth the faster the rise time can be.
Another example is amplitude modulation. Say you had a 1Khz sinewave, and a lower amplitude sinewave at 990 Hz, and another one at 1010 Hz, with the correct phase relationship. (I don't recall what the phase relationship is for AM sidebands, sorry, but it doesn't matter for the purpose of discussion)
The neat thing here is that if you look at the time domain waveform of this on an oscilloscope you'll see typical AM modulation, where it seems like you have only a 1Khz sinewave whose amplitude is going up and down 10 times a second. So you think you have a constantly modulating 1Khz sinewave.
But put that signal on a spectrum analyser and you have three discrete constant, unchanging periodic sinewaves... And if you mathematically sum these three constant sinewaves you will get the result you see on the scope of a "changing" 1Khz sinewave. Also a fundamental building block to understanding the relationship between frequency and time domains.
So how does this relate to the "transient" response of a speaker to "changing" signals ? The reason I give this example is to highlight that a "changing" signal is not quite what we think it is intuitively.
In particular it's actually impossible to vary the amplitude of a single tone or sinewave without producing "sidebands", the quicker you vary the amplitude of the tone the further apart in frequency the sidebands move from the fundamental.
The implication here is that for a speaker to reproduce a rapidly "changing" signal accurately it has to be able to reproduce these sidebands that are produced - and they need to be reproduced in their correct proportions. If you do anything to change these sidebands such as mucking up their phase or amplitude relationship the modulation of the original signal will not be correctly reproduced.
Again a very simplistic example - lets take our 1Khz AM modulated signal above and slap a big high Q resonance right in the middle of it at 1Khz. In the amplitude domain lets say this fundamental has been increased by 6dB in relation to the sidebands. (That's a pretty high Q resonance!)
What does it mean that the sidebands are reproduced 6dB suppressed relative to the fundamental ? It means there is less modulation, so the variation in the original signal is greatly reduced from what it should be. So the overall amplitude of the signal is higher than it should be (bad) but the amount that it modulates is less than it should be. (Also bad)
What if we modulate that signal even faster ? If we assume the peak formed by the resonance attenuates the sidebands even more as you move away from 1Khz that means the faster you try to modulate that original 1Khz signal, the less it actually modulates due to the sidebands getting more and more suppressed.
So the resonance is effectively limiting the modulation rate that the speaker can reproduce a signal around this frequency with - in the time domain it is "blurring" the modulation. I'm not expert in this but I think this is measured using something called "modulation transfer function", which is a measure how how well the "envelope" of a varying signal is preserved, and this is important for humans because we understand speech partly by analysing the "envelope" of the sound in addition to the frequency components.
So what do we get from all this ? The above is the basis for how a resonance rings out in time due to it being unable to reproduce the modulation of the signal that originally started it ringing. The high Q resonances "blur" the time domain response of a speaker around that resonance and reduce the ability of it to articulate modulating signals. In these frequency ranges it would get a poor "modulation transfer function" result.
So the best articulation of "dynamic", constantly varying signals is achieved by having a wide and flat frequency response at and either side of those signals, free of resonances.
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Effortlessness and dynamics most likely mean a speaker sounds the same at low and higher levels. That's how I see it.
It has been shown that diffraction is more audible with level. A speaker with low diffraction can be used at a higher level without the apparent stress.
Interestingly it is these time delayed, non-minimum phase components that are not considered equalisable in the ways discussed above.
Some great explanations, a lot of this is over my head. I accept that frequency response is connected to transient response.
This kind of makes sense that if two different drivers are producing the same pure tone then they will both be oscillating in sync, and basically sound the same.
So a big heavy subwoofer at 400hz might sound like a lightweight fullranger if they both have flat FR. I think my own experience bears this out for a simple tone.
However in each case there will be an equilibrium in the system as it vibrates back and forth. IOW the whole moving mass and even the amp will all reach a mechanical and electrical equilibrium.
Now heres the thing, along comes a change, which apparently are these sidebands, which I don't really know much about. But nonetheless the signal changes.
It seems intuitive to me that the lighter mass that is less mechanically damped will change its equilibrium and respond better to the change than the subwoofer.
So IOW as things get more chaotic and dynamic in the signal, lighter faster moving masses with more powerful magnets start to do better.
This kind of makes sense that if two different drivers are producing the same pure tone then they will both be oscillating in sync, and basically sound the same.
So a big heavy subwoofer at 400hz might sound like a lightweight fullranger if they both have flat FR. I think my own experience bears this out for a simple tone.
However in each case there will be an equilibrium in the system as it vibrates back and forth. IOW the whole moving mass and even the amp will all reach a mechanical and electrical equilibrium.
Now heres the thing, along comes a change, which apparently are these sidebands, which I don't really know much about. But nonetheless the signal changes.
It seems intuitive to me that the lighter mass that is less mechanically damped will change its equilibrium and respond better to the change than the subwoofer.
So IOW as things get more chaotic and dynamic in the signal, lighter faster moving masses with more powerful magnets start to do better.
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The different drivers work together to produce the full frequency range, this is why transient response it's often mentioned in crossover design due to the phase shifts caused by the filters degrading it. The high frequencies associated speed and dynamics are produced by the tweeter, the woofer only needs to produce the frequencies associated with its range. So long as the timing is correct, ie, minimal phase shifts are introduced, then the transient response will be good
I would agree with the audible effect, but is it because the diffraction is less and diffraction has some magic hitherto undiscovered effect on our hearing, or because diffraction usually makes the frequency response at any given point in space less smooth in a similar way to resonances ?
Not wanting to open yet another can of worms, (when did that ever stop me before ?) but...
If you measure the effects of cabinet diffraction they are actually minimum phase as well for a given listening/measuring point...
This is because although a multi-path signal with delayed components (the refraction from the cabinet edge) makes it possible to have a non minimum phase result it does not guarantee it will happen.Remember the measurement I posted earlier showing that apart from the whizzer cone introducing some excess phase at its 6Khz crossover frequency that the response was otherwise minimum phase ? Well that measurement naturally includes all the diffraction from the drivers and cabinet too...so why is only the whizzer cone the only non-minimum phase thing in the whole measurement ?
I'll be perfectly honest and say I don't understand the maths behind it enough to know exactly what all the ingredients necessary are to get a non-minimum phase result (I'll leave that for someone like Earl to explain) but from my observations based on measurements alone one of them seems to be that at some frequency the delayed signal needs to be stronger than the direct signal as well as out of phase with it.
If this is a requirement then its easy to see why baffle edge diffraction is minimum phase - the direct signal from the driver is always present near full strength and the signal refracted from the edge of the cabinet is always weaker. So it can modify the resulting amplitude/phase response but can't make it non minimum-phase, unless you somehow blocked the direct signal from the driver.
Another great example is room modes at bass frequencies - if you measure a variety of rooms and listening locations you'll find that its possible to measure listening setups where the bass is entirely minimum phase at a given listening location while other setups will have chunks of the bass region where it is decidedly non-minimum phase.
And the latter seems to occur when one reflection is arriving at 180 degrees and about the same amplitude causing the "direct" signal to be cancelled out, and then a 3rd and subsequent reflections arrive at other random phase shifts, when this all comes together you end up with a non-minimum phase result.
The reason you can't generally EQ diffraction is not because the are non-minimum phase, (because they aren't) but because there is a unique (but minimum phase) response for every off axis angle... so any EQ you apply will only be correct at one point in space and wrong nearly everywhere else.
So if you have a peak that looks like a resonance that only exists on axis and you apply a notch to that you cancel the ringing at that angle but you cause ringing at some other angle due to the notch being applied where it isn't wanted.
The higher in frequency you go in relation to the cabinet size the worse this gets and the more the response varies with angle. At lower frequencies EQ will be more correct over a wider range of angles. The extreme low frequency example of this is baffle step correction - baffle step is still a diffraction effect however at that low frequency it remains more consistent over a much wider range of off axis angles so it becomes possible to EQ it and have it be close enough across the listening window, as we all do when we apply baffle step correction.
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Analog minimum phase is when it can be corrected with analog means that don't require infinite energy like filling a infinite deep notch.
For example, a reflection with same impulse reponse but less level than the original gives an impulse "doublet" and a comb-filter pattern in the frequency response. Fill up the dips in that response within the bandwidth of interest and the reflection also disappears in the IR.
Digital Filters, Filter Inversion, Minimum Phase and All That (Part II )
For example, a reflection with same impulse reponse but less level than the original gives an impulse "doublet" and a comb-filter pattern in the frequency response. Fill up the dips in that response within the bandwidth of interest and the reflection also disappears in the IR.
Digital Filters, Filter Inversion, Minimum Phase and All That (Part II )
This? http://www.ejjordan.co.uk/PDFs/EJJ_1966.11_WW_titanium.pdf
It's a good read, it digs into transient response if 33Polkhigh wants to read it
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Thanks for the link - some good reading!
In a quick skim I noticed this:
I guess I must have read that somewhere before..
My point in my previous posts was that we tend to want to intuitively assign non-minimum phase properties to devices or effects such as delayed reflections or standing waves on a cone on the assumption that a multi-path signal means non-minimum phase, but more often than not its not the case.
When you actually measure a lot of devices and situations you don't actually find very many that are non-minimum phase so you should never make the assumption that something is.
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What you're saying only makes sense for something like a sine wave or a pure tone. In the case of a simple non dynamic signal then yes a flat FR with no phase shift is perfectly dynamic.
I'm not going to repost what I wrote, but I'm saying that other driver design parameters begin to matter much more with an actual complex signal.
Complex signals begin to flush out the differences in drivers, I think this is obvious to some extent though poorly documented. Also drivers aren't linear wrt volume. At lower volumes mechanical damping matters much more.
This is probably the crux of the issue you have, as explained by DBMandrake, all waveforms are comprised of sine waves of different frequencies
Actually they are surprisingly linear to very low volume. Have a look here Frequency graphs of speakers....
Yes, they are sine wave, but afaik they are of changing amplitude and duration in real music. Again, a frequency response is generated from a very simple signal that will not flush out the kinds of dynamic distortions a complex signal would.
For example everyone knows that drivers need to be broken in, but I doubt the difference between a broken in and new driver would show up on a simple test tone or FR plot from a sine wave.
Much of what is being discussed at the moment is explained quite simply here. For example, have a look at the paragraph above figure 11 Phase, Time and Distortion in Loudspeakers
He actually makes the case for intermodulation distortion which a lot of people here probably don't believe is an issue.
I agree there are many kinds of distortion, but understand what I was saying about two very different drivers with the same FR sounding the same.
This seems obvious that they would sound the same for a simple signal, but that they won't behave the same for a very dynamic complex signal. IOW there are likely peaks of nonlinear and various types of distortions that don't show up with easy test signals
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I probably need to visit that site again.
Browsing through it made me aware that the issue on phase audibility, it seems his experience is different from mine, thus I would be interested in looking at the CSD plots of the speakers he uses. This is probably one of the more critical data when comparing any kind of auditioning experiments. My experience is that lots of things are not audible until CSD of speakers are within a certain level. Recently I have been looking at CSD of USB sound cards as well. The reason I started considering this was after I listened to a seminar made by B&K which talked about masking of noise, this inspired me to look into how residual sound might effect the audibility of some things that were controversial.
Browsing through it made me aware that the issue on phase audibility, it seems his experience is different from mine, thus I would be interested in looking at the CSD plots of the speakers he uses. This is probably one of the more critical data when comparing any kind of auditioning experiments. My experience is that lots of things are not audible until CSD of speakers are within a certain level. Recently I have been looking at CSD of USB sound cards as well. The reason I started considering this was after I listened to a seminar made by B&K which talked about masking of noise, this inspired me to look into how residual sound might effect the audibility of some things that were controversial.
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But any change in amplitude of a sinewave from a lower amplitude to higher or vica versa results in the production of more sinewaves at different frequencies whose spectrum depend on the apparent rate of amplitude change of the original sinewave.
In the AM example you only get two sidebands because the modulation itself is also a sinewave. But if the modulation was a square wave approximation (the sinewave being turned "on" and "off" for example) then you get loads and loads of gradually declining sidebands trying to spread out towards infinity in either direction...
Obviously the speaker has finite bandwidth so only some of these sidebands will be reproduced - this limits the rate at which the original sinewave can "change" in amplitude. The wider the bandwidth the greater the possible modulation rate of that original signal.
What about if the frequency of a sinewave "varies", like a vibrato ? You have frequency modulation or FM. Well that too produces sidebands...
And unlike the AM case a sinewave used to frequency modulate another sinewave produces multiple sidebands spreading out at multiples of the modulation rate.
And unlike the AM example it is not at all intuitive to see why this is the case. (I still struggle to visualise it even though I know conceptually its true)
So you can't vary the amplitude of a sinewave or its frequency without producing sidebands, so it follows that to properly reproduce the amplitude or frequency modulation of the signal you have to have the bandwidth and flatness of response to correctly reproduce those sidebands.
Now if you consider an instrument with a complex harmonic structure which already consists of many individual frequencies mixed together (possibly dozens) and you then start modulating those, every one of those original sinewaves that made up the "static" version of that sound (like a constant "steady" chord) now has sidebands of its own produced.
It quickly gets really, really complicated and difficult to visualise, and is a bit of a mind bender. But all you have to keep in mind is if you reproduce those other frequency products that result from the signals "changing" in their correct proportions, then the changes will be accurately reproduced as well. The goal is not to alter the original signal.
You're probably thinking of effects such as inter-modulation distortion between high and low frequencies - for example in a two way's woofer, which incidentally produce yet more frequencies (product and difference frequencies) based on the originals signals.
These can be measured too but require two tone testing so that the interaction between them can be seen. You wouldn't see this effect if you just did a frequency sweep using a single tone for example.
I would dispute that "everyone knows drivers need to to be broken in". While I'm sure there are some things about certain kinds of drivers that may change slightly over time (paper cones that absorb moisture and change their cone damping comes to mind) on the whole I'm not a believer of "driver break-in" from new being necessary or even being a thing that exists.
If the driver is acclimatising to a change in humidity (from being unboxed after delivery from another location or country for example) then that is going to happen whether or not it is being driven by a signal...
And there are plenty of drivers that would be completely unaffected by something like humidity changes - for example a ribbon tweeter consisting only of metal parts that don't absorb moisture.
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There have been instances where I haven't been able to make something go away with equalisation, but since working on diffraction, I can equalise to a smooth curve and achieve correct reproduction. That says something to me.
Efforts I have made to reduce diffraction have increased the dynamic capability. Diffraction sources are not only temporally, but spatially displaced making them potentially localisable and potentially altering the content of reflections from that of the direct.
I feel it is more important in the upper half of the spectrum. At lower frequencies, issues become gradually less sensitive until all that seems to matter is the response, despite the fact that diffraction might be involved.
While I haven't found a need to slope the response down by 2dB like you have, (possibly due to different directivity of our respective tweeters and the fact that I'm crossing to a full range driver at 3Khz) I otherwise agree with what you describe - the balance of the treble between 1-5Khz and the top end 10Khz and up is very critical.
When I first completed building my all-new crossovers based on measurements and a lot of work in Virtuixcad to get the flat response, phase tracking etc that I showed earlier I hooked them up and listened for the first time - and marvelled at how neutral, clean and balanced they seemed right from the get go, but something wasn't quite right with the imaging, and I just couldn't put my finger on it at first. It was good but didn't provide a convincing illusion.
In fact it took me a week of listening and a bit of tinkering with active EQ before I started to realise that the balance of the treble wasn't quite right, but I still wasn't sure in what way it was wrong.
The presence region seemed slightly recessed, and I initially tweaked the L-Pad's for the tweeters to give them a half dB increase, but that seemed to make it worse if anything, and resulted in over bright symbols etc as you describe.
I quickly reverted the change as it became unpleasant to listen to on some recordings that already had a lot of treble and sounded slightly "thin" overall. (Yes, from a half dB increase across just 2.5 octaves) It was quite a bit later that I thought to increase the first cap in the high pass filter slightly - not much, I changed it from 3.4uF to 3.6uF.
According to virtuixcad (confirmed by measurement) that would lift the bottom end of the treble from about 2-5Khz by 0.4dB gradually tapering off to no effect by 10Khz.
0.4dB doesn't sound like much does it... but that 0.4dB change in slope was what was missing. The presence region now sounds nicely balanced - alive with a good sense of realism but not over bright and never harsh or fatiguing even on "bad" recordings. The change in slope has made the top end of the tweeter sound a little bit more laid back and "natural", but still with air and sparkle.
As for other frequency ranges, I disagree a bit when you say they're not as fussy - there are specific ranges where I find there is a similar degree of fussiness - the low mid-range 200-400 region is one.
My cabinets are 39cm wide so have their baffle step rollover point at about 280Hz, my initial baffle step correction was based on a theoretical 6dB at 280Hz, however that also didn't seem quite right when I first started listening.
I realised fairly quickly that the values I'd chosen in the sim were based on free standing measurements, but I only have the speakers about 40-60cm from the front wall.
Also the simulated design was based on a driver measurement that spliced together a gated measurement and a near-field measurement of driver and ports - and I'd had some difficulty splicing them together accurately so there was a little bit of uncertainty about just how valid the spliced response was, so I realised there could be an error here.
It was just slightly on the "wooly" side so I increased the baffle step coil value quite a bit to reduce the lower mid-range response centred around 250Hz by about 1dB. Too much as it turned out! It improved the imaging but with the speakers 60cm out from the wall it actually sounded a bit over bright and pushy...
I eventually settled on a coil value that dropped the lower midrange by 0.5dB from the original calculated response and that after a few weeks listening seems to be spot on. So even in that frequency range I found there was a very obvious change in the imaging and presentation for a +/- 0.5dB shift over only one octave.
I'm still pretty happy with how close the original theoretical crossover design was though - I haven't touched the baffle step attenuation level (resistor value) or the L-Pad for the tweeter from the original starting point, I've only tweaked two component values slightly to lift the low treble by 0.4dB and drop the lower midrange by 0.5dB.
As I said earlier, attention to detail is key in getting that last mile...
Exactly!
And btw I actually agree with you on the 200-400 hz region as well. Im not sure that i can claim .5db discernment here (did not get as serious on thi one) BUT I totally agree that gettig this level right was a sensative area as well.
In the system I mentioned the drivers were well behaved enough with a 500 hz cross that you could easily taylor the level of the 200-400 hz range with the crossover values. Quite small changes made noticable improvments in as you say "realism".
This is why I say many of us miss this. The exact levels across the range are so small there easily missed.
I actualy keep the FR measurments from these events and compare them. I see this same basic pattern each time and going back to these measurments helps me any system taylored into focus much more quickly. Knowing where to tweek is power.
Basically I am postulating that its the complexity of a real signal that causes incidents of distortion and apparent performance differences in real drivers, even if they have the same frequency response.
Now if a simple sine wave or test signal is just as mechanically and electrically stressful for a driver to respond to as a real complex signal then what I am saying doesn't hold up.
Now if a simple sine wave or test signal is just as mechanically and electrically stressful for a driver to respond to as a real complex signal then what I am saying doesn't hold up.