Exactly!
The wave uncertainty principle is the simplest way I can think of to explain this: (delta omega) x (delta t) is always greater than or equal to unity for any wave, including sound. A brick wall filter has (delta omega) of zero, therefore (delta t) has to be infinity...
-Gnobuddy
Personally, I find the whole even filter versus odd filter most interesting
I've built various combinations of drivers with LR2, BW3 and LR4. For those who don't know, BW3 does NOT rely on phase alignment. But has great off-axis dispersion, aka even power response.
So to my mind, we should go for a natural musicality rather than strictly flat frequency response and phase alignment. The power response is what fills the room.
BTW, I have no idea why this thread exploded either.
I don't think it exploded. In the beginning it was nebulous and the OP's questions were sort-of avoided as implying how can you even ask.
I am also interested in what comes out the wash here, I would be interested in what System7 has to offer, "especially when we go for natural musicality".
I am always keen to learn something regarding this phenomena. It seems very complex stuff referring to Gnobuddy's wave uncertainties and delta omega and so on.
Yes, Scott I agree a switched cap filter is not brick wall but pretty steep roll of especially if there are two (or more) cascaded.
I have done some brick wall filters using PICs in the late 90s designing a software discriminator for DTMF. I never considered making cross-over filters. So go for it I am all ears.
I am also interested in what comes out the wash here, I would be interested in what System7 has to offer, "especially when we go for natural musicality".
I am always keen to learn something regarding this phenomena. It seems very complex stuff referring to Gnobuddy's wave uncertainties and delta omega and so on.
Yes, Scott I agree a switched cap filter is not brick wall but pretty steep roll of especially if there are two (or more) cascaded.
I have done some brick wall filters using PICs in the late 90s designing a software discriminator for DTMF. I never considered making cross-over filters. So go for it I am all ears.
This is my first venture into a speaker thread but thinking of how to do an active LLXO I've been over here looking around. Please forgive if this appears to be OT - It's not an intentional explosion assist.
When I look at the OP's question and mix it with the following comments I start to imagine drivers , say for eg. a tweeter and mid, abruptly starting and stopping as a frequency train (aka an idealized melody) gets handed back and forth from a driver of one dimension and material to one of another dimension and different material. It seems to me that unless they are overlapped , the continual abrupt change from one to the other would constitute added 'music' material itself . . . . and to an attentive listener there'd also be an audible source location movement as well. Is this thinking wrong here?
When I look at the OP's question and mix it with the following comments I start to imagine drivers , say for eg. a tweeter and mid, abruptly starting and stopping as a frequency train (aka an idealized melody) gets handed back and forth from a driver of one dimension and material to one of another dimension and different material. It seems to me that unless they are overlapped , the continual abrupt change from one to the other would constitute added 'music' material itself . . . . and to an attentive listener there'd also be an audible source location movement as well. Is this thinking wrong here?
That´s the point.
We talk frequency because it´s a simple idea , simple to grasp, but really we have a continuously varying voltage (or sound pressure) relative to time.
In fact, even within the same waveform cycle, even in the simplest wave of them all, a sinewave, deltaV/deltaT (sorry, don´t have Greek on this keyboard) is changing along time.
Perfect example showing OP´s question nonsense.
Note to moderators: this is not an insult but means exactly that: it does not make sense.
For argument´s sake, suppose there is a perfect brickwall crossover set to 2000Hz.
IF you have 2 nearby speakers, one reproducing 1999 Hz and another 2001 Hz they will stillinteract.
In fact, as soon as they find the first non linear element (even if slightly non linear) , they will beat against each other and give us sum and difference frequencies.
We´ll definitely hear a 2Hz Vibrato 😉
No need to go too far, air itself is nonlinear , let alone our own ears😉
It may sound unfamiliar in those terms, and the mathematics to actually prove it is complex, but I bet you already have a good handle on the concept.
For example: have you ever heard someone tune a musical instrument using a reference pitch? As the instrument gets close to being in tune, you can hear "beats". The closer to perfectly in tune, the fewer beats per second.
So, as you get closer to being in tune, you have to wait longer and longer to hear a complete beat. In other words: reduce the frequency uncertainty, and you have to increase the time it takes to measure it.
The frequency uncertainty is (delta f), or, if you consider angular frequency, it's (delta omega). The time uncertainty is (delta t). We've just shown in this simple example that as delta omega becomes smaller, delta t gets bigger.
This example is very simple, but the implications are much deeper (that's where the hard math and the brilliant minds of the people who figured all this out comes in.) It turns out the general concept is universal, something the universe dictates to us: the more tightly you try to constrain frequency, the longer you have to wait to be sure you've actually done so.
That's where the "infinite slope filter" become problematic. If the cutoff frequency is controlled to perfect accuracy (delta f is zero), then the related (delta t) has to be infinity...
-Gnobuddy
Just to add to Gnobuddy's post, think in terms of a Michelson-Morely interferometer. Same basic concept wrt interference.
I understand perfectly what you are trying to explain, but the OP posed the question and I don't think we are helping him, it remains confusing.
Beat is probably a good way to describe it but if he was not a ham radio fan beat has a different meaning in his vocabulary. Maybe inter-modulation would be a more accurate description.
But I do not think that we have given him much to go on. His question is can he uses a brick wall filter - I do not see any reason why not. What if you have two concentric drivers like the Tannoy would this be tolerant of such an arrangement?
One could argue that feeding a speaker with a "brick-wall" filter does not remove any mechanical resonances or harmonics generated by the mechanical and acoustic components. So even though the fundamental may lie on the border, there will still be higher order products generated.
Personally I think, this phenomenon should indeed be investigated rather than merely argued, there may be much merit in the suggestion.
Personally I think, this phenomenon should indeed be investigated rather than merely argued, there may be much merit in the suggestion.
Thank you very much for the exhaustive list. Looks like I'll have a ton of reading to do.
And thank you everyone for the intelligent discussion. Many of these responses are very thought provoking and interesting.
I don't believe I've ever agreed with you more.
I entered the Iron Driver competition of 2013(?) with a speaker that was flat except for the crossover point. There was a few dB peak around 1k-2k due to using odd order slopes. Even though there were speakers that were flatter, these came in first place. Also worth noting, this was a blind and level matched competition with a price limit of $200 for drivers and crossover parts.
Think you'll get a better idea if you look at DACs instead of speakers. Particularly if you look back at Wolfson DACs and the use of minimum phase and apodizing filters. Ayre used to have something but can't find it.
First off, to be a crossover by definition, drivers must overlap at a minimum of one frequency. The very existence of a crossover in the first place is just a result of the fact that drivers are imperfect; the frequency goes up or down and their output distorts or disappears all together. With that all being said, some people like the crossover range (i.e. The number of frequencies that a pair of drivers share at a certain level) to be very broad so that the transition is harder to identify. Others like the range to be small (this is accomplished with steep crossover slopes) so that the transition is harder to identify. Notice that both schools of thought are seeking the same goal: coherency. But frequency is just part of the picture as you also have phase to consider. Well, prior to the advent of DSP for the average joe, steep crossover slopes executed in the passive, analog world caused huge phase anamolies. There is no way around this one; even YG Acoustics, who actually does have a phase coherent, sweep slope crossover circuit, makes comprises to achieve this. However, we live in a modern era with DSP and that makes steeper slopes with little or no phase shift a possibility. Before DSP, the convention wisdom always said that shallower slopes sounded better and somehow that bias survived to today. That's only part of your answer though...
That is certainly my experience. And one that is rarely talked about in crossover design - harmonics. Setting the crossover at the right point for general amplitude but the wrong spot for harmonics can sound "off".
I have heard some steep crossovers, tho never brick wall. They usually don't blend well and sound artificial to me. Perhaps with DSP that could be fixed.
The term "beats" is used in music as well. I figured that most people on a DIY Audio forum would probably know something about music.
I don't think they are the same thing.Intermodulation requires nonlinearity, while beats do not, but occur even in a linear medium. If you simply add together two sine waves of slightly different frequencies, you get beats. (Addition is a linear operation.)
Well, as several of us have been trying to explain, if you have an infinitely sharp cut-off, you also get an infinitely long transient response. The woofer would ring forever after a transient, and so would the tweeter.
But if you look at the summed response of the two perfect brick-wall filters (high-pass and low-pass), it's a perfect straight line. That means it has a perfect impulse response (it rings for zero time).
How is this possible? Mathematically, it means the woofer rings forever, and so does the tweeter - but the combined output from the two drivers cancels out at all times after the transient, so that the combined response has no ringing!
This is the kind of mathematical weirdness that shows up when you start leaning too hard on concepts like infinity.
What would happen if you actually tried it? I think that's a lot like asking the classic philosopher's riddle "What happens when an irresistible force is applied to an immovable object?" The question is hard to answer in that form, because everything is infinity or zero.
A way to actually answer the question is to get away from the term "infinity". If the question is modified to "What are the pros and cons of using steeper and steeper crossover filters?", then I think a very interesting discussion might follow.
Most likely, there would be diminishing returns (and increasing complexity) after some point - I think it's very unlikely there would be any actual benefit from, say, a 10th order filter compared to an 8th order one. And maybe a 4th order filter is really all that's necessary, in practical terms.
I honestly don't know - but when I see the mathematics predicting very weird results, such as infinitely long transient ringing from both woofer and tweeter, which magically sums to zero ringing, it tells me the physical problem is extremely weird, and one would probably get better answers by re-working the question a little.
-Gnobuddy
I agree. That's the whole basis of science - someone has to do the experiments to verify (or discredit) the hypothesis. Otherwise, science would become as silly as philosophy, superstition, etc.
Keeping in mind there is no such thing as a perfect brick-wall filter, the OPs question can never be answered exactly.
But one can ask the very reasonable question: "What happens to my speaker system as I use steeper and steeper filters in the crossover?" That experiment can indeed be done, and the results studied.
Many years ago, I was peripherally involved with an active loudspeaker design, the first one for that particular manufacturer. The speaker designer got carried away and used 4th order active filters everywhere - not only in the crossover, but also to steeply roll off deep bass, to protect the woofer.
Keep in mind the woofer in it's ported enclosure already has a 4th order bass roll off. With the additional 4th order active filter, the ultimate roll-off would be very steep, 8th order.
After some work (time delay compensation), the 4th-order crossover worked very well. But the steep bass roll-off was a tragic mistake: the speakers had a nasty tendency to produce boomy, one-note bass.
I, and some others, pointed out the boomy bass to the designer at the prototype stage. But he was too caught up in all the fun he was having with active filters to pay attention to what we were trying to tell him about transient response. The product went to market, complete with boomy one-note bass.
-Gnobuddy
Newbie alert. I confess I dont understand much but am curious.
What would be the implication, if we choose a crossover slop which is little steep at beginning and gradually blends OR vice versa ?
Thanks and regards.
What would be the implication, if we choose a crossover slop which is little steep at beginning and gradually blends OR vice versa ?
Thanks and regards.
Even worse: It even takes forever until the combined response shows the actual desired input signal. OK - I have to admit that more accurately spoken it will only take half of that time. 😉
In my opinion I think 4th order is enough for most cases. Sometimes it can even be much less.
Regards
Charles
The science itself is of good use to understand better the material world we live
in but don't put philosophy in the silly bag because it is beyond any natural
science we may be talking about here. There is very little philosophers nowdays
for the modern worlds doesn't tolerate people who like and have the ability
to think about existence. The answers are spread all over around us to any
of a problem one can think of, we're just unable to see it or haven't discovered it yet.
Natural science could explain the growth of our universe but will never give an
answer why this universe had to be created.
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