mige0 said:
As it turns out I do have that software. The modulated source is 2k hz/100 Hz and a midulation index of 1.0. For Doppler generated IM the modulation index can be expressed in terms of the necessary (low frequency) excursion as
MI = Pi * Fh * X / c ,
where Fh is the higher frequency.
The excursion (at 100 Hz) would thus need to be
X = MI * c / ( Pi * Fh) = 2.15"
for MI = 1.
First, I don't think you will see many tweeter reproducing 100 Hz. Second, looking at a typical tweeter (dome) Xmax is usually around 0.25mm which would yield a maximum MI of about 0.0045 at 2k Hz. At 20K hz this goes to 0.045. Since MI is much less that 1.0, this tells us that the maximum Doppler generated IM distortion in a tweeter is about 27dB down at 20K and about 47dB down at 20K.
Re: Speaking of OT
John, thanks for your maths regarding the modulation index.
Yeah 2.5" for a tweeter is slightly out of its nominal excursion, I guess.
The simus I did were in order to show the effects to be visible in the plots – I hope I have stated this clearly
Michael.
john k... said:
John, thanks for your maths regarding the modulation index.
Yeah 2.5" for a tweeter is slightly out of its nominal excursion, I guess.
The simus I did were in order to show the effects to be visible in the plots – I hope I have stated this clearly
Michael.
gedlee said:
Bad news – I already asked my sales agent to kontakt and sell them my clock.
But also good news – maybe I do a slight modification to increase jitter and have the outstanding opportunity to sell as many clocks as there are atoms in the universe
auplater said:
"We now return you to your regularly scheduled progam."
Michael
john k... said:
John, as I see it, such a typical dome tweeter of 1" you mentioned would provide the –27dB (4.5%) / -47dB (0.4%) at 20kHz / 2kHz respectively with a maximum SPL of about 100dB and a HP-XO point set to 1.8kHz
One should make sure the acoustic XO slope is 12db / octave - *at least* - as to keep IM at the specified levels above.
As can be seen in the IM barrier graph (in my spreadsheet) the tweeter *will* be operated down to 100Hz - and below – right at its IM-excursion-limit when playing the whole speaker at 100dB at that low frequencies in case of HP-XO second order slope - quite frightening though !
Michael.
While this is always the case, several studies have shown that the population in general does not have preferences or perceptions that are different from trained listeners. Trained listeners tend to have a smaller spread in the data (fewer subjects required for statistical significance), although I have seen cases where this too was not the case.
If we have to test everyone to make any statements about psychoacoustics then the whole process is doomed to failure from the start and we would have to go back to the process of design by listening. I prefer to move forward instead of backwards.
If we have to test everyone to make any statements about psychoacoustics then the whole process is doomed to failure from the start and we would have to go back to the process of design by listening. I prefer to move forward instead of backwards.
No one can ever say what any one individual will think or feel about a loudspeaker, but we can be fairly certain what "most" people will perceive. For those on the edges of "normal" I can only have sympathy, for they will most likely never be happy with any loudspeaker. None of them will ever be designed for them.
mige0 said:
You have just made the argument as to why a 12dB/octave acoustic roll off for a tweeter is insufficient in a high quality speaker.
But dare I say, IM will be the least of the problem. There would be much more serious problems from other motor nonlinearities entering the picture at that point.Actually..it may give linear thinking science folks the 'fits', but recent science has shown reality to be 30% consensus, ie, only 70% written in stone. The rest being 'variable', and existing with respect to group and individual manipulation.
Meaning: If you WISH it to be, reality is written in stone. If you wish it NOT to be....it ISN'T.
Get it?
So much for the whole 'written in stone' thing. Good riddance, IMHO. Don't let the door hit it in the behind on the way out.
I hope all the flat-earther science types break out in hives and keel over in some fashion.... Might make my day.
Meaning: If you WISH it to be, reality is written in stone. If you wish it NOT to be....it ISN'T.
Get it?
So much for the whole 'written in stone' thing. Good riddance, IMHO. Don't let the door hit it in the behind on the way out.
I hope all the flat-earther science types break out in hives and keel over in some fashion.... Might make my day.
gedlee said:
This is the fundamentals of statistical analysis in experimentation, and I truly believe that the majority of people do not understand how or why this works the way it does.
An additional issue that constantly arises among the general laymen, but is unfortunately a common problem in we scientists as well, is the ol' accepting the null hypothesis. We reject or fail to reject, and so it goes. To use your own study, you found no association between non-linearity and peoples preference (Is that correct), so in that case, you ran a regression, found in the ANOVA that the T-test was non-significant and concluded a failure to reject the null hypothesis. A suggestion that non-linearities are not associated with preference given your normed sample in your study conditions. We can't conclude that this is the case with out a doubt, its possible that there were measure sensitivity issues, sample issues, metric issues, etc. This would then be a type II error, and without some sort of confirmatory study we couldn't be sure that such an error exists, but in statistics, this is all the way it works. However the average person does not interpret data this way, and unfortunately even scientists make this mistake sometimes when it confirms their hypothesis. None the less, just because we can't be positive as to the reason for a lack of association doesn't mean its wrong to assume there is a lack of association, the evidence is that there is no association, and until we can show otherwise, we must assume this to be true. That is another problem with us Scientists and pseudo-scientists, if it goes against what we believe, then the science must be wrong.
p.s. I'm using this lack of association to confirm my own thesis hypothesis, so obviously I nor my committee sees that big a problem with it.
In order to elaborate some further on the topic of sonic patterns created by back chamber reflection, appearing as mirror sources through a loudspeaker membrane, I lined up some more simulations to proceed into the direction of quantifying the effects - as kindly suggested by John.
Ok, the main difference to the first simus is that I used a more realistic modulation index. To give a real world picture for tweeters MI was set to 0.045 translating into 5% D-IM distortion *and* to 0.0045 translating into 0.5% D-IM distortion.
Again 2Khz were modulated by 100Hz in order to show clear plots. That this still *can be* a realistic assumption for 2nd order XO filter slopes was discussed some postings ago.
First lets have a look at a Doppler intermodulation distortion of roughly 5%
What can be seen - in the time domain - is that the modulation is somewhat different to that shown in the posting before with the 100% modulation, if we take a closer look at the RED trace.
The RED trace shows us the summation of front radiated SPL overlayed by the reflected rear radiated SPL *without* any dampening in the chamber and *without* any dampening by the membrane.
The modulation does no longer drop completely to zero amplitude (as was the case in the simus with MI=1 in the posting before)
The BLUE trace shows us the summation of front radiated SPL overlayed by the reflected rear radiated SPL attenuated by –6dB due to dampening in the chamber and dampening by the membrane.
The GREE trace shows us the summation of front radiated SPL overlayed by the reflected rear radiated SPL attenuated by –20dB due to dampening in the chamber and dampening by the membrane.
In the frequency domain plot the modulation can be seen as side bands spaced by 100Hz :
For the GREEN trace - heavy –20dB absorption of the mirrored SPL – the fundamental (2kHz) is a roughly -10dB down compared to a full absorbed rear SPL.
For the BLUE trace - -6dB absorption of the mirrored SPL – the fundamental (2kHz) is a roughly -15dB down compared to a full absorbed rear SPL.
For the RED trace – no absorption of the mirrored SPL – the fundamental (2kHz) is a roughly -35dB down compared to a full absorbed rear SPL.
These values do not change that much if we calculate for a 3kHz fundamental or if the delay of the mirror source is set to be twice - except for the case of *no* absorption in the rear chamber.
This is what one would expect as sort of comb filtering effect expressed in the frequency range and of course appearing more pronounced with a strong mirror source arriving delayed.
Its interesting to note that the first side bands at 1.9kHz and 2.1kHz appear at roughly -40dB –independent of the dampening of the mirrored SPL !
The next side bands at 1.8kHz and 2.2kHz are at different levels indicating that the envelope of the side bands is different – depending on dampening of the mirrored source.
The more dampening the broader the side bands spread out.
For the case of the un-dampened rear chamber we also notice that the frst side bands generated are more or less equal in amplitude than the fundamental – meaning that we hear a 2kHz from our record at 1.9kHz / 2kHz / 2.1kHz at the same SPL simultaneously through that speaker!
Still anybody out there who is gonna tell us that couldn't be detected through our ear-brain-system *when happening*?
Next lets have a look at a Doppler intermodulation distortion of roughly 0.5%
In the time domain plot , modulation no longer is displayed clear enough to judge anything
In the frequency domain plots, the modulation can be seen as side bands more or less like at a D-IM of ten times higher (the picture discussed above).
What we can see clearly is that the side bands drop by roughly 20dB whereas the fundamentals stay roughly at the same attenuated levels
It might be worth to note that this simulations assume the rear chamber reflections occurring from an idealised mirror with a "diskrete" delay.
This is not exactly the case for most real world drivers (tweeters, compression drivers, closed mid drivers) as the back wall isn't equally spaced to the membrane in most cases.
So for measurement I would expect a more smeared behaviour than shown in the simus – never the less the effects outlined should be measurable – and will have equal sonic impacts as has correlated jitter from digital sources.
Michael
Ok, the main difference to the first simus is that I used a more realistic modulation index. To give a real world picture for tweeters MI was set to 0.045 translating into 5% D-IM distortion *and* to 0.0045 translating into 0.5% D-IM distortion.
Again 2Khz were modulated by 100Hz in order to show clear plots. That this still *can be* a realistic assumption for 2nd order XO filter slopes was discussed some postings ago.
First lets have a look at a Doppler intermodulation distortion of roughly 5%
An externally hosted image should be here but it was not working when we last tested it.
What can be seen - in the time domain - is that the modulation is somewhat different to that shown in the posting before with the 100% modulation, if we take a closer look at the RED trace.
The RED trace shows us the summation of front radiated SPL overlayed by the reflected rear radiated SPL *without* any dampening in the chamber and *without* any dampening by the membrane.
The modulation does no longer drop completely to zero amplitude (as was the case in the simus with MI=1 in the posting before)
The BLUE trace shows us the summation of front radiated SPL overlayed by the reflected rear radiated SPL attenuated by –6dB due to dampening in the chamber and dampening by the membrane.
The GREE trace shows us the summation of front radiated SPL overlayed by the reflected rear radiated SPL attenuated by –20dB due to dampening in the chamber and dampening by the membrane.
In the frequency domain plot the modulation can be seen as side bands spaced by 100Hz :
For the GREEN trace - heavy –20dB absorption of the mirrored SPL – the fundamental (2kHz) is a roughly -10dB down compared to a full absorbed rear SPL.
For the BLUE trace - -6dB absorption of the mirrored SPL – the fundamental (2kHz) is a roughly -15dB down compared to a full absorbed rear SPL.
For the RED trace – no absorption of the mirrored SPL – the fundamental (2kHz) is a roughly -35dB down compared to a full absorbed rear SPL.
These values do not change that much if we calculate for a 3kHz fundamental or if the delay of the mirror source is set to be twice - except for the case of *no* absorption in the rear chamber.
This is what one would expect as sort of comb filtering effect expressed in the frequency range and of course appearing more pronounced with a strong mirror source arriving delayed.
Its interesting to note that the first side bands at 1.9kHz and 2.1kHz appear at roughly -40dB –independent of the dampening of the mirrored SPL !
The next side bands at 1.8kHz and 2.2kHz are at different levels indicating that the envelope of the side bands is different – depending on dampening of the mirrored source.
The more dampening the broader the side bands spread out.
For the case of the un-dampened rear chamber we also notice that the frst side bands generated are more or less equal in amplitude than the fundamental – meaning that we hear a 2kHz from our record at 1.9kHz / 2kHz / 2.1kHz at the same SPL simultaneously through that speaker!
Still anybody out there who is gonna tell us that couldn't be detected through our ear-brain-system *when happening*?
Next lets have a look at a Doppler intermodulation distortion of roughly 0.5%
An externally hosted image should be here but it was not working when we last tested it.
In the time domain plot , modulation no longer is displayed clear enough to judge anything
In the frequency domain plots, the modulation can be seen as side bands more or less like at a D-IM of ten times higher (the picture discussed above).
What we can see clearly is that the side bands drop by roughly 20dB whereas the fundamentals stay roughly at the same attenuated levels
It might be worth to note that this simulations assume the rear chamber reflections occurring from an idealised mirror with a "diskrete" delay.
This is not exactly the case for most real world drivers (tweeters, compression drivers, closed mid drivers) as the back wall isn't equally spaced to the membrane in most cases.
So for measurement I would expect a more smeared behaviour than shown in the simus – never the less the effects outlined should be measurable – and will have equal sonic impacts as has correlated jitter from digital sources.
Michael
Wow - almost a full day of deeply moved silence in the auditorium / community ?
Strong tobacco, eh ?
Well - its a "rather" new and subtle topic, I admit – cutting to the bones.
Now then, next logical step could be to set up measurements.
Searching for good candidates to prove the effects outlined, what are your suggestions on drivers with back wall uniformly spaced to the diaphragm?
Can't believe *all* you are busy with running simus for verification or with filing patents ??
John – what driver did you try to measure and how did you set up your measurement ?
Ordered a cheap magnetostatic driver today as not having any suitable compression driver laying around – will see - maybe it also will do the trick...
Lynn, hope you don't mind so far – as you sometimes expressed your special interest in the modulation topic.
Michael
Strong tobacco, eh ?
Well - its a "rather" new and subtle topic, I admit – cutting to the bones.
Now then, next logical step could be to set up measurements.
Searching for good candidates to prove the effects outlined, what are your suggestions on drivers with back wall uniformly spaced to the diaphragm?
Can't believe *all* you are busy with running simus for verification or with filing patents ??
John – what driver did you try to measure and how did you set up your measurement ?
Ordered a cheap magnetostatic driver today as not having any suitable compression driver laying around – will see - maybe it also will do the trick...
Lynn, hope you don't mind so far – as you sometimes expressed your special interest in the modulation topic.
Michael
mige0 said:
Small point: with direct-radiator tweeters, the acoustical response is the vector sum of the electrical and acoustical transfer functions. When a 2 kHz, 2nd-order electrical highpass filter is combined with a tweeter's Fs at, say, 500 Hz, the net result is a 4th-order highpass filter below 500 Hz. I'm not aware of any tweeters that have an Fs much below 300~500 Hz.
With real-world tweeters, even with modest 2nd-order passive electrical filters, there is substantially more attenuation at 100 Hz than the function of the filter alone.
Michael, thanks for the interesting investigation - the apparent translation from FM to AM modulation artifacts is most interesting. It underlines why multiway systems, for all of the faults, have greater dynamic range, thanks to significant decreases in nonlinear distortion artifacts. The effective acoustical slopes of the crossover have major effects on the "area under the curve" when the excursion of the driver before and after the crossover is compared - and this "area under the curve" is the source of the artifacts we see above.
The artifacts are real and exist in the physical world; audibility, of course, is another matter.
At a given frequency SPL goes like 20 Log (X) so if the SPL is reduced by 6 dB excursion halved.
For constant SPL vs frequency, excursion goes like 1/f^2, or for constant excursion, SPL increase at 12dB/octave.
The initial argument was that for a 2nd order acoustic response with corner frequency around 2k Hz a tweeter would have the same excursion at 100 Hz as at 2k (approximately) when driven by a signal of constant anplitude vs frequency. If the tweeter had an Fs of 500 Hz and was filtered by a 2nd order electrical filter the acoustic response below 500 Hz rolls off at 24dB/octave and would be down another 24dB, more or less (two octaves), at 100 Hz compared to the 2nd order acoustic roll off (all the way to DC). The additional 24dB reduction in SPL at 100 Hz would reduct the excursion by a factor of 0.063 from that which it would be if the acoustic roll off remained 2nd order below Fs.
For constant SPL vs frequency, excursion goes like 1/f^2, or for constant excursion, SPL increase at 12dB/octave.
The initial argument was that for a 2nd order acoustic response with corner frequency around 2k Hz a tweeter would have the same excursion at 100 Hz as at 2k (approximately) when driven by a signal of constant anplitude vs frequency. If the tweeter had an Fs of 500 Hz and was filtered by a 2nd order electrical filter the acoustic response below 500 Hz rolls off at 24dB/octave and would be down another 24dB, more or less (two octaves), at 100 Hz compared to the 2nd order acoustic roll off (all the way to DC). The additional 24dB reduction in SPL at 100 Hz would reduct the excursion by a factor of 0.063 from that which it would be if the acoustic roll off remained 2nd order below Fs.