The limiting factor is not the sample rate but the length of the gate applied to the impulse response.
Or the opposite. A speaker that is very directional above 1200 Hz, even more directional above 5 Khz and much less directional below 1200 Hz.
Both these speakers need broadband treatment in order to sound right.
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Markus is right on this. The resolution of resulting frequency response data is limited by the length of a gate applied to the impulse response. The resolution is simply 1/t Hz, where t is the gate (window) length in seconds. Nothing you can do with that. Add more zero samples to the gated impulse response, it will bring you smoothness, but won't increase the resolution.
There is really no much real anechoic data below say 1 kHz if the impulse is gated to e.g. 5ms (resolution 200Hz), as it's the common limit when measuring indoors. Only much larger room can give you longer gates and it can help quite a bit.
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Not much gets said about group delay near the lower end of the desired range. The lowest frequencies expected within the gate don't always seem to come good. Does anyone separate these lower frequencies to see whether they can be properly captured within the gate?
Interestingly enough, Earl has written this paper long ago: AES E-Library Maximum Entropy, Auto Regression, Pole-Zero Modeling-On the Use of Modern Spectral Estimation in Audio Testing
I've never heard about this any more. Was it somehow pursued further or saw it any real implementaion?
I've never heard about this any more. Was it somehow pursued further or saw it any real implementaion?
Some have become confused regarding Markus's comment.
It is true that windowing in the time domain is also averaging (smoothing) in the frequency domain. He is correct.
It is true that windowing in the time domain is also averaging (smoothing) in the frequency domain. He is correct.
Yeah, obviously it's smoothing, but I was thinking the sample rate would still.. nevermind, I was being a dummy. So if 200Hz resolution, I guess that puts you at about 1/4 octave "smoothing" at the middle of the spectrum, yes?
Measure outside if an anechoic room isn't available. I've seen the use of gating not being correct and giving a false impression.
Markus is incorrect and here is why.
If one windows the impulse response to reject the reflections and then extends the data set with zeros, the resolution of the measurement is that of the data set NOT the window. I use 4096 data points over 20 kHz so the resolution is about 5 Hz. This is an insignificant amount of smoothing in the audio band above the 200 Hz limit of the window.
The window limits the low frequency at which the data is valid, 200 Hz in my case, but above 200 Hz the resolution is 5 Hz. At and below 200 Hz there is smoothing, but that is on meaningless data anyways.
A Gaussian time window that slides to narrower and narrower with frequency has a form of smoothing but it also rejects data in a way that is not valid, which is why I don't use it.
A simple thought experiment will show why what I say has to be true. Envision a measurement done in an anechoic chamber such that there is no data above 10 ms. If I window at 10 ms and zero out the data above that in makes no difference at all. The measurement is completely accurate and the windowing has no effect whatever. Now, of course, there cannot be any low frequencies below 100 Hz of the impulse response could not settle to zero in 10 ms., but that is a different issue. And there can be errors depending on how the window is implemented, but believe me I know how to do that - I am not new to this stuff.
If one windows the impulse response to reject the reflections and then extends the data set with zeros, the resolution of the measurement is that of the data set NOT the window. I use 4096 data points over 20 kHz so the resolution is about 5 Hz. This is an insignificant amount of smoothing in the audio band above the 200 Hz limit of the window.
The window limits the low frequency at which the data is valid, 200 Hz in my case, but above 200 Hz the resolution is 5 Hz. At and below 200 Hz there is smoothing, but that is on meaningless data anyways.
A Gaussian time window that slides to narrower and narrower with frequency has a form of smoothing but it also rejects data in a way that is not valid, which is why I don't use it.
A simple thought experiment will show why what I say has to be true. Envision a measurement done in an anechoic chamber such that there is no data above 10 ms. If I window at 10 ms and zero out the data above that in makes no difference at all. The measurement is completely accurate and the windowing has no effect whatever. Now, of course, there cannot be any low frequencies below 100 Hz of the impulse response could not settle to zero in 10 ms., but that is a different issue. And there can be errors depending on how the window is implemented, but believe me I know how to do that - I am not new to this stuff.
No one suggested you were new to this stuff.
Markus made a comment that windowing is a form of averaging. I believe this is correct and BTW, I did not see him discussing padding the window with zeroes. Perhapss I missed that.
A simple way to think about windowing/averaging is to note that a window can be a boxcar in the time domain that is multiplied on to time signal. In the frequency domain this is equivalent to convolving with a sin x / x function. This convolution will smear the frequency components and this ends up being a type of averaging in the frequency domain. I assume this was what Markus was trying to get accross, but maybe I should let him explain it himself.
Incidentally, I am not personally averse to some averaging.
Markus made a comment that windowing is a form of averaging. I believe this is correct and BTW, I did not see him discussing padding the window with zeroes. Perhapss I missed that.
A simple way to think about windowing/averaging is to note that a window can be a boxcar in the time domain that is multiplied on to time signal. In the frequency domain this is equivalent to convolving with a sin x / x function. This convolution will smear the frequency components and this ends up being a type of averaging in the frequency domain. I assume this was what Markus was trying to get accross, but maybe I should let him explain it himself.
Incidentally, I am not personally averse to some averaging.
That is impossible. One cannot get good information below the window frequency - time/frequency tradeoff. It is possible to extrapolate the impulse response based on the data within the window and then use that data and extend the window length. Bill at Liberty does this and it works well.
When using a window there is always the assumption that there is not enough excess group delay to allow for all energy in a frequency band to settle before the window closes. This is general not a problem, but I have seen it before. For example, when there is a resonance inside of the box, it can take a significant amount of time for this resonance to reach the microphone. Far more than the direct sound from the speakers. If this is windowed then the results are compromised.
But if one is looking for anechoic data then chopping off reflections is perfectly correct, just so long as you know it is a reflection. Since my setup is unchanging I know exactly where the reflections are so this is not an issue for me.
Padding with zero's is the defacto standard and not doing so would be pointless. So of course I assumed we were talking about padding the window. The conversation would be ridiculous otherwise. No one does not pad the data set with zero's!!
Well, if you somehow actually knew that there are no data after 5ms (only reflections), it would really make no difference, but this is pointless argument. You don't know this in advance. How could you? If there is e.g. some very high-Q resonance at 500Hz, it won't fit into 5ms and you simply won't see it from your gated impulse - not in it's real Q and no matter how many extending zeros you use, 4096 or 16 milions. It will be smoothed out / averaged, call it as you wish.
As long as your windowing is synchronous with your frequency sweeps and has a high enough sampling rate I do not see why any smoothing as it is commonly seen is the resultant. I am not saying you can't use it that way, just that it does not have to inherently produce a smoothed response curve. If you want to do that you can but that is usually a chosen end result, not a requirement of windowing or gating as I would refer to it. If you are truly looking for an accurate result you only need to increase your sampling rate to match the accuracy you are looking for. Now in a small room as Earl has pointed out there is a lower limit to this above a specific frequency that does not need to be the case. Not many have access to true anechoic chambers and even those that do for extremely low frequencies even that is still rather rare. Outdoor measurements using gating again can extend this range as long as background noise levels are low enough and proper precautions are taken for boundary conditions. An enclosure buried and flush with the ground facing up can be very accurate in this regard.
With increased sample rate you can only go higher in frequency, obviously. The frequency resolution, i.e. the smoothing/smearing is given only by the window length (in seconds), as has been already pointed out. No matter how large data set you make by adding zeroes. No zeroes will add any new information. It will give just denser data but not more precise or thruthfull.
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Thanks for posting this tidbit, Earl! This very topic of frequency resolution of gated impulse measurements has been a splinter in my mind for awhile now. I use ARTA to measure, and I will have to check to see what happens with the data when you apply gating to the measured impulse response. I am not sure the the program pads with zeros... Does anyone happen to know?
Also, while Markus was trying to be helpful with the comparison of the process using three different length windows in this post (http://www.diyaudio.com/forums/mult...directivity-how-important-58.html#post3638501) I think that it is misleading. I'm assuming the following: This was an-room measurement and the 5ms windowing has excluded all reflections. The longer windows include increasingly more reflections, and that is why there are so many changes in the frequency response.
I'd like to see plots of the frequency responses obtain under a scenario similar to that described by Earl:
1. The time domain data set is reflection free
2. Different length windows are applied
3. A comparison of the effects of zero padding versus truncating the set of time domain samples
This might be carried out by synthesizing a minimum phase frequency response that is characteristic of a driver (with broad bandpass character) and then doing an iFFT to get the time domain response. In that way the "correct answer" (in the frequency domain) would be known a priori. Something along these lines might better illustrate the concepts discussed here...2. Different length windows are applied
3. A comparison of the effects of zero padding versus truncating the set of time domain samples
-Charlie
For a high Q resonance at 500 Hz to exceed 5 ms its Q would need to be something like 100. Yes, a Q of 200 would be reduced to a Q of 100 - I don't think that is a reasonable concern. At 1000 Hz its twice as high.
The only issue is, as I said, very large non-minimum phase effects, which are pretty rare.
I think that the important point here is that some smoothing is already there if the impulse response in gated. And this smoothing is given by the gate length. If you have 5ms of time data, it will give you frequency data "for every 200Hz", as Markus said. Sure, you can make it more and more dense by padding more and more zeroes, but this doesn't increase the resolution of actual underlying data. So saying that with 4096 data points your measurement resolution is 5Hz is very misleading. Then it could be increased to 2,5Hz just by adding about twice as many zeroes...
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Mbat - except that what you are saying just isn't true.
It actually is true that the resolution can be increased at will just by padding with zero's up to any point that you want. I understand that it seems counter intuitive but it is, none the less, correct. 4096 points DOES give a 5 Hz resolution for all data above 200 Hz for a 5 ms. window. It is not misleading it is absolutely correct.
Just go look at HolmImpulse. Take a measurement and change the window The data above the cutoff does not change unless new reflection enter the window. The window length does not affect the data above the cutoff.
I am not going to argue this point any more, its a well known result. If you don't believe me go look it up.
It actually is true that the resolution can be increased at will just by padding with zero's up to any point that you want. I understand that it seems counter intuitive but it is, none the less, correct. 4096 points DOES give a 5 Hz resolution for all data above 200 Hz for a 5 ms. window. It is not misleading it is absolutely correct.
Just go look at HolmImpulse. Take a measurement and change the window The data above the cutoff does not change unless new reflection enter the window. The window length does not affect the data above the cutoff.
I am not going to argue this point any more, its a well known result. If you don't believe me go look it up.
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But it's just the resolution of the FFT algorithm. Number of data points in = number of data points out. The algorithm doesn't know or even care of what this data means. I can't imagine how what you say could be true regarding the real data resolution.
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