Fourier transformation has one very important prerequisite: I works only for linear system. If it is not, the impulse / FR relation is not necessarily maintained. This is important to observe.
A linear system must have:
and be:
.... on Linear Systems: https://www.cns.nyu.edu/~david/courses/perception/lecturenotes/linear-systems/linear-systems.html
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A linear system must have:
- Homogeneity (or the Scalar Rule)
- Additivity
- Superposition
- Shift-invariant
.... on Linear Systems: https://www.cns.nyu.edu/~david/courses/perception/lecturenotes/linear-systems/linear-systems.html
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I'm puzzled about this. You seem to be saying that flat frequency response is not very important, because musical instruments don't emit pure tones, but rather a complex mix of fundamental and harmonics. And you seem to say that a speaker which is not linear (non-flat frequency response) can still sound good because it is producing a mix of frequencies.
But none of that makes sense. A speaker needs a flat(ish) response in order to reproduce the complex mix of frequencies that you get from real instruments in something like the correct proportions. If a speaker has response anomalies, it will alter the proportions of the different tones (fundaments and harmonics) created by original instruments. So it's much less likely to sound 'real'.
But maybe I'm not following your point?
Hi,
1) From my personal experience, linearity of frequency response is highly correlated to how a speaker sounds in a way that more linear system sounds more pleasant, accurate and natural.
2) A properly designed speaker system does not distort a lot. Less than 1% is quite common and less than 0.5% is achievable without too high of a difficulty, assuming moderate listening levels of 85-95 dB or so.
3) I do not agree with the view that treats loudspeaker as an instrument. Harmonic distortion measurement is only a way to measure it's non-linearity. So where THD is high intermodulation is also typically present
4) CSD plots are commonly shown, but perhaps burst decay plots are even more useful. Both are problematic to measure under typical DIY'ers conditions as reflections ruin everything quite a lot. I see a lot of CSD measurements(some from respectable sources) that are ruined by reflected sound and can look misleading
Regards
I totally disagree with academia50. The speakers I bought with response +-3 db 54 hz 17 khz are the best I have ever heard in this flyover city. Yes, bass impulse response can be boomy or non-impulse along with with a flat response. However the designers of the system I bought figured that out too. Bass drum hits of ZZ Top Afterburner sound like the twin 30" drums I marched next to 1964=68.
Blather about actual instruments making non-linear tones is just that. I test speakers with Steinway grand top octave tracks, which have a huge energy pulse when the hammer hits the string. No problem. Double reeds where each cycle has a huge transistion when the reeds hit each other, no problem.
As far as massive speaker distortion, the ones I bought are specified at 2nd & 3rd harmonic 25 db down from fundamental 80 hz-12 khz. At 5 watts. What is that, about 5.2% HD?
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I appreciate your response and the Bazukaz
. It seems that since my English through Google Translate is insufficient to express both technical and other quite basic things in everyday speech, I withdraw my two cents, save my jugular, and decide that it is not worth participating in this thread. Thank you all, and I leave you with a reading that I found very interesting and is what motivated me to give my opinion.
https://www.linkedin.com/pulse/csd-cumulative-spectral-decay-really-important-jason-dai
I suppose the only way to know is to not only measure the FR but also the actual Impulse response. This could be hard due to the low amount of energy and background noise.
If it falls under Fourier - I think that if your stimuli was a FR sweep, any presentation with time on a scale would have used FFT.
The sheer jolt of an impulse seems to me be quite different than a sweep... I accept the math, no problem, but I'm still a bit suspicious about calculation an impulse response. Music is a lot about onset/transient/impulse and less about continuous tones. Thats why it would to me have been so much better to actually do it the other way around - measure an actual impulse (sinc or spike) and then calculate FR....
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If it falls under Fourier - I think that if your stimuli was a FR sweep, any presentation with time on a scale would have used FFT.
The sheer jolt of an impulse seems to me be quite different than a sweep... I accept the math, no problem, but I'm still a bit suspicious about calculation an impulse response. Music is a lot about onset/transient/impulse and less about continuous tones. Thats why it would to me have been so much better to actually do it the other way around - measure an actual impulse (sinc or spike) and then calculate FR....
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CSD plots are not useful at all I think
Burst decay is much better.
But why would you want to get such data with measurements further away from the speaker?
It's mostly useful for internal cabinet, port resonances and such.
All of which can be done with near-field measurements.
Other things like diffraction problems can be seen in the freq resp as well as contour/directivity plots
Hi,
I agree that burst decay is better because it keeeps the relationship between wave length and cycles into display.
In order for gated measurement to work well near field it's still needed to keep away for any hard surfaces by 2-3 meters at least. Not possible for everyone, depending on what space you have. I have observed this many times in reality and sometimes ended up making a shed from fiberglass to finally get a usefully clean burst decay plot.
Also gated near field measurements only work for mid bass/low mid range and up because half wave length should be kept small. So it can work while looking for stading wave problems in the box, but panel resonances are typically lower than this unless the box is heavily braced.
I do not want to start another discussion about diffraction but I have never seen a problem that would show up in burst decay plots due to that. What almost always appear in analysis is the first reflections from nearby surfaces like floor or back wall, and rounded edges of the box has influence to this. So it's not diffraction but reflections IMO.
Regards
I agree that burst decay is better because it keeeps the relationship between wave length and cycles into display.
In order for gated measurement to work well near field it's still needed to keep away for any hard surfaces by 2-3 meters at least. Not possible for everyone, depending on what space you have. I have observed this many times in reality and sometimes ended up making a shed from fiberglass to finally get a usefully clean burst decay plot.
Also gated near field measurements only work for mid bass/low mid range and up because half wave length should be kept small. So it can work while looking for stading wave problems in the box, but panel resonances are typically lower than this unless the box is heavily braced.
I do not want to start another discussion about diffraction but I have never seen a problem that would show up in burst decay plots due to that. What almost always appear in analysis is the first reflections from nearby surfaces like floor or back wall, and rounded edges of the box has influence to this. So it's not diffraction but reflections IMO.
Regards
@academia50 I think you may have misunderstood that article you link to. It asks whether CSD is important, and answers no, for the most part.
IME, It doesn't matter which path we take....they all give the same results. It's more a matter of exactly what we're trying to measure, that determines whether to look at impulse of freq response (complex.) ....Whether we have questions in the freq domain or the time domain.
A snip from the Smaart manual...
I use sine sweeps, temporal averaged pink noise, tone bursts, a Dirac pulse, etc etc ...with REW, Smaart, ARTA, and several other dual channel measurement programs. Results are always very close no matter which program or which stimulus...whether I went straight with FFT to freq domain, or thru impulse to freq.
It's awesome really, the simple equivalences between freq reponse (including phase) = impulse response = step response =CSD reponse =burst response....
...equaling all the various looks we find ways to debate ...hahaha
Just to answer you, actually it has been a long time since I read this other article that I attached. If CSD is not a parameter (I'm waiting for a synonym), I'm sorry, I'll put measurement, I hope it helps...) of importance, that is, if it doesn't have to be taken into account, and according to some here - too many for my taste - , it must be discarded because the "burst measurement, etc., etc., are more important
, and you have to forget about it, I don't understand why those who really know (isn't that the case?) include it in their graphs...(??) So, those guys here should respond to this guy: "You are wrong , for this and this "
His name is Joe D'Appolito, and he says the following:
Point for me. Greetings
https://audioxpress.com/article/testing-loudspeakers-which-measurements-matter-part-2
Part One
Cumulative Spectral Decay
The cumulative spectral decay (CSD) gives a detailed analysis of loudspeaker resonances. The CSD measures the frequency content of a loudspeaker’s decay response following an impulsive input. Ideally, a loudspeaker’s impulse response should die away instantly. Real loudspeakers, however, have inertia and stored energy which take a finite time to dissipate. The CSD involves a series of frequency domain calculations. It is represented by a three-dimensional plot.
On the CSD plot, frequency increases from left to right and time moves forward from the rear. The first slice analyzes the impulse response out to a fixed end point, which you can select by appropriate placement of a cursor. It is usually selected as that point in time just before the arrival of the first reflection so that the first slice is the quasi-anechoic frequency response in Fig. 3. Succeeding slices are foreshortened toward this end point, including less and less of the impulse response tail with each succeeding slice. The FFT of these slices yields the frequency content of later and later portions of the impulse response. The CSD is most useful in identifying resonances, which appear as ridges moving forward along the time axis.
Part two
" Turning to the time domain, the step response gives us qualitative information on driver polarity, time dispersion, and driver integration. Phase response is not a strong indicator of speaker quality, but we can glean more detailed information on speaker time dispersion from the excess group delay plot.
Impedance data can be used to detect cabinet vibrations and internal resonances such as standing waves. We can also judge how difficult it will be for an amplifier to drive a particular loudspeaker. Very low impedance magnitude values coupled with large phase angles produce large current demands that may be beyond the capability of an amplifier.
Unless distortion levels are very high, harmonic and IM distortions are not strong predictors of listener preference, but they are useful in assessing driver quality and can explain why speakers sound bad when played at high volume levels. The dynamic capability of a loudspeaker is a very strong predictor of its ability to produce lifelike sound. Finally, the measurements discussed here are not only useful in evaluating existing designs, but they can also be used by loudspeaker engineers as design goals.
There is one caveat in all these results. The discussions here have been limited to conventional, forward-firing dynamic loudspeaker systems. Large panel loudspeakers and line arrays present vastly different measurement challenges. In the home listening environment, you will invariably be in the near field of these speaker types. Response will vary widely with listener position in height and distance to the speaker. Defining a single response axis that characterizes one of these speakers is difficult. Also, polar response will differ substantially from conventional speakers. "
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So you have tested both ways - coming from impulse and coming from sweep and they ended up exactly the same?
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When I was specifically trying to see if an impulse taken from a pulse was any different from one taken with a sine sweep or time-averaged pink etc,
I used a Dirac pulse...figuring you can't get a cleaner / shorter pulse than that.
It's probably worth noting, the age-old acoustically generated pulse, has been a balloon pop, or a pistol firing a blank, etc.
And that it's been used for measuring rooms /acoustic space. It's probably still a better method for a room than a typical speaker's generated pulse, because a typical speaker is invariably much more directional.
But nowadays, we use an omni speaker like a dodecahedron, and sine sweeps or pink etc.
FFT gives us the same results without having the cops called for firing a gun indoors.. hahaha
Fully internalizing the equivalence between freq response and impulse response and all the derived graphs,.... step, waterfalls, CSD, bursts, etc.... has been one of the biggest audio aha moments I've had....kinda mind-blowing really. (not that I have that much of a mind to blow! )
You are aware that KEF (and probably other serious brands) used to measure with pulses some 40 years ago and that in acoustics even further back pulses were used for analysis, as mark100 states? I think the use of the obvious replacement signals has been proven valid long ago and the electrodynamic loudspeaker seems linear enough -under normal circumstances. Deviations of the linear behavior are well-known too, be they motor, cone or suspension related. We don’t have to start all over again.