Why Some Audiophiles Fear Measurements
- Thread starter Jeff Fritz
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I am just getting caught up here again. Your example is still not clear to me. If you have a narrow time-domain impulse in the original analog signal, that may violate the sampling theorem. The sampling theorem does not say you can reconstruct any signal from its samples. The sampling theorem only says that you can recover a strictly bandlimited signal from its samples. In that context, "strictly bandlimited" means the Fourier transform of the signal has a magnitude of zero for all frequencies greater than some frequency fmax. In practical terms, this means putting the signal into a brick-wall low-pass filter before digitizing it. All correctly implemented A/D converters do this. Said filter will spread out the impulse in time and smooth it out, thus making the "narrow pulse" argument null and void. If you don't like that, then the answer will be an outcome of the "analog vs. digital" debate and not of the "measurement vs. listening" one. It's an inescapable consequence of proper application of the sampling theorem.
Regarding your later quotes of Kaiser, an important distinction needs to be made, and that is one of signal analysis vs. system analysis. In signal analysis, one might want to find the spectrum of a signal, or go backwards and find a signal from its spectrum. This is the domain of the DFT and inverse DFT. Nowhere in this analysis does nonlinearity come into play. But if you have a system that corrupts a signal in a nonlinear way, that's a different story altogether. Without having a complete mathematical description of such a system, which in general involves knowing an infinite number of terms in its Volterra series representation, we cannot know everything about how it affects that signal. But this is entirely different from, and irrelevant to obtaining the spectrum of a signal, and the reverse process of obtaining a signal from its spectrum.
So in the context of recovering a signal from its spectrum and vice versa, nonlinear system theory and related considerations are irrelevant.
As Colombo would say, "just one more thing...". What you're saying is also mixing up the time and frequency domains. For a time domain sequence, the "real spectrum" (for lack of a better term) is a continuous function of frequency. It's called the DTFT, the discrete-time Fourier transform. It is the same as the z-transform with z=ejp(j*2*pi*f*T)
where f = frequency in Hz and T = 1/(sample frequency in Hz) and j = sqrt(-1)
The DFT ends up being a sequence which consists of samples of the DTFT. And the FFT is just a specific algorithm for computing the DFT. In order for this frequency-domain sequence to give an accurate representation to the continuous-frequency spectrum of the time-domain sequence, the frequency points of the DFT must be chosen to be dense enough so they don't miss the needed detail of the spectrum. If, for example, we had a very short time-domain sequence, say 4 samples, this might seem to be an obstacle. But the answer is to pad the sequence with many zeros, then compute the DFT of this extended sequence.. The resulting spectrum of the zero-padded sequence will be more densely sampled than without the time-domain padding. This is analogous to the conventional sampling theorem, except it's a kind of "frequency domain sampling theorem".
So the practical solution is simple: just pad the time-domain signal with as many zeros as needed so the calculated spectrum no longer changes when more zeros are added.
where f = frequency in Hz and T = 1/(sample frequency in Hz) and j = sqrt(-1)
The DFT ends up being a sequence which consists of samples of the DTFT. And the FFT is just a specific algorithm for computing the DFT. In order for this frequency-domain sequence to give an accurate representation to the continuous-frequency spectrum of the time-domain sequence, the frequency points of the DFT must be chosen to be dense enough so they don't miss the needed detail of the spectrum. If, for example, we had a very short time-domain sequence, say 4 samples, this might seem to be an obstacle. But the answer is to pad the sequence with many zeros, then compute the DFT of this extended sequence.. The resulting spectrum of the zero-padded sequence will be more densely sampled than without the time-domain padding. This is analogous to the conventional sampling theorem, except it's a kind of "frequency domain sampling theorem".
So the practical solution is simple: just pad the time-domain signal with as many zeros as needed so the calculated spectrum no longer changes when more zeros are added.
Now that I'm finished saying that, I have a question to ask. After all, why should I only answer questions, and not ask ones of my own?
This is my question for jkeny.
Have you learned to use an oscilloscope yet?.
This is my question for jkeny.
Have you learned to use an oscilloscope yet?.
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Haha, Andy - if you do your research adequately, as I know you can, you can answer your own question. As they say "go figure" !
You are agreeing then that the example I gave from that AES paper illustrates that a 4K FFT bin size will miss noise transients of <100ms in the signal they are investigating. This was not stated as a limitation by the authors (presumably because it was not understood) & was not picked up by peer reviewers (Agenda One types?). it makes me wonder how common are similar mistakes in the use of FFT analysis in audio? If it is found that these types of mistakes are commonly made in audio, then are we not blindly following a particular erroneously partial view of the audio field?
Edit: It's really just a question which I find interesting, no need for anyone to get defensive about the tool - it's the usage of the tool in audio that I'm wondering about
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Great - much appreciate your analysis! Now can you link to examples of such a practical solution of FFT usage with a music signals when analysing audio equipment? As I said, it's an area I'm currently very interested in & it will help my further education
There seems to be many papers addressing transient analysis in audio but I have not seen many applications of these techniques to analysing audio equipment - some example papers:
A TRANSIENT DETECTION ALGORITHM FOR AUDIO USING ITERATIVE ANALYSIS OF STFT
IMPROVED MODELING OF AUDIO SIGNALS BY MODIFYING TRANSIENT LOCATIONS
A review of techniques for the extraction of transients in musical signals
A conclusion from the last 2005 paper
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I'm sure you understood the example given & because of the 4k bin size chosen that a signal transient of <100ms duration may not be revealed by the FFT? Now are you saying that his transient somehow violates the sampling theorem?
So will this impulse of 100ms will be spread out by an A/D? - by how much? - I think you need to clarify this statement with some values and maybe give us some transient timings for the attack signal on cymbals, etc
If you deal with real world examples rather than theoretical ones, that would be helpful?
But we are talking about analysing audio reproduction systems which are non-linear?
Anyway, what he said was in relation to analysis of a speech wave - "Well, I see this looks quite like a linear system." Well, that's all you can see through those tools. You've got to have a different tool to see the modulations in detail that abound in the speech wave."
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Part of a signal transient greater than 100 ms will missed due to the record size (4096 * 1/44.1kHz = 92.9 ms). To capture longer transients (or lower frequency signals) in their entirety you need a longer record. FWIWFM, I rarely use a record as small as 4K.
The highest signal you can capture at 44.1 kS/s is about 22 kHz. The shortest pulse that can be captured is thus about 1/22 kHz ~ 45 us. Shorter pulses might be captured poorly (aliased) or ultimately not at all (depending upon the sampler architecture).
An FFT (or DFT, or just FT) does not care if if the system is linear.
I must confess I am having trouble with the relevance of all this...
The highest signal you can capture at 44.1 kS/s is about 22 kHz. The shortest pulse that can be captured is thus about 1/22 kHz ~ 45 us. Shorter pulses might be captured poorly (aliased) or ultimately not at all (depending upon the sampler architecture).
An FFT (or DFT, or just FT) does not care if if the system is linear.
I must confess I am having trouble with the relevance of all this...
Don,
My question was "is the frequency domain rather than temporal domain the predominant analysis in audio & is this a mistake? Secondly, is this the result of the predominance of FFTs as the audio measurement tool of choice?"
My question was "is the frequency domain rather than temporal domain the predominant analysis in audio & is this a mistake? Secondly, is this the result of the predominance of FFTs as the audio measurement tool of choice?"
Still struggling how that relates to why audiophiles fear measurements...
Most of the measurements taken and reported in a typical spec sheet are frequency-domain, e.g. frequency response, harmonic and intermodulation distortion, signal-to-noise ratio, etc. It is fairly easy to create the test signals and these are well-understood. There are (were) standards established by e.g. the IHF for distortion, noise and such. Time-domain analysis is less common but is used to test transient response of components and loudspeakers. In fact, many of the room and speaker analysis programs I have used derive time-domain information (reverb, decay, etc.) from a pulse measurement. And, most of the reviews of CD/BD/etc. players I have seen now include time-domain (pulse) response to look at things like filter ringing in the time domain.
I believe both are useful and agree I would like to see much more time-domain analysis. I am not sure there are as many standards for test signals and such for time-domain analysis.
Most of the measurements taken and reported in a typical spec sheet are frequency-domain, e.g. frequency response, harmonic and intermodulation distortion, signal-to-noise ratio, etc. It is fairly easy to create the test signals and these are well-understood. There are (were) standards established by e.g. the IHF for distortion, noise and such. Time-domain analysis is less common but is used to test transient response of components and loudspeakers. In fact, many of the room and speaker analysis programs I have used derive time-domain information (reverb, decay, etc.) from a pulse measurement. And, most of the reviews of CD/BD/etc. players I have seen now include time-domain (pulse) response to look at things like filter ringing in the time domain.
I believe both are useful and agree I would like to see much more time-domain analysis. I am not sure there are as many standards for test signals and such for time-domain analysis.
I don't think audiophiles fear measurements. They just find less utility in them than those that have to design and build the equipment.
Just to add one only needs to see that the majority here do not fear measurements but are sceptical in how a few others present them as absolutes for all things relating to audio, appreciate there are a few who are aggressive in being anti-measurement as well.
Here is an interesting audio measurement none of us touched upon yet in this thread and talk about often.
Speaker sensitivity; from an objectivists perspective this is a conundrum because this will differ each time when using the industry standard/pink noise/music, on top of this it is far from linear across the frequency range.
So in this case it is not an absolute and goes against the grain that we measure all audio products accurately (key is both the measurement and test process combined with focusing on what we capture in terms of data and understanding its scope-limitations) nor do we have one for speaker sensitivity -Keith Howard has done some great articles on this subject in the past.
Another interesting one is inverted polarity, which will not show a difference in FR-distortion-etc that many use to state whether an amp/preamp sounds different, however changing polarity (quite a few products allow this) may be heard pretty clear with around 15-20% of music when played through the whole system with speakers.
I appreciate this last one is pretty contentious and may only noticable with certain albums-music, may being the keyword.
Anecdotally so IMO I have experienced inverted polarity with around 5% to 10% of my albums, and in reality only would bother me with a few of them.
Hope this adds a different dimension to the many pages we have discussed so far.
Cheers
Orb
Here is an interesting audio measurement none of us touched upon yet in this thread and talk about often.
Speaker sensitivity; from an objectivists perspective this is a conundrum because this will differ each time when using the industry standard/pink noise/music, on top of this it is far from linear across the frequency range.
So in this case it is not an absolute and goes against the grain that we measure all audio products accurately (key is both the measurement and test process combined with focusing on what we capture in terms of data and understanding its scope-limitations) nor do we have one for speaker sensitivity -Keith Howard has done some great articles on this subject in the past.
Another interesting one is inverted polarity, which will not show a difference in FR-distortion-etc that many use to state whether an amp/preamp sounds different, however changing polarity (quite a few products allow this) may be heard pretty clear with around 15-20% of music when played through the whole system with speakers.
I appreciate this last one is pretty contentious and may only noticable with certain albums-music, may being the keyword.
Anecdotally so IMO I have experienced inverted polarity with around 5% to 10% of my albums, and in reality only would bother me with a few of them.
Hope this adds a different dimension to the many pages we have discussed so far.
Cheers
Orb
Yes, that was partly my point & FFT was the ubiquitous tool which, it seems to me, is so easy to misuse or interpret results incorrectly. I also agree with Orb - I am sceptical of those who use measurements as absolutes & wanted to point out instances where they are used incorrectly. I gave an example of an AES paper & what was wrong with their interpretations & use of FFT in that particular instance.
As James Kaiser said "The most widely used signal processing tool is the FFT; The most widely misused signal processing tool is also the FFT".
So maybe we have to be careful of quoted measurements, not fear them!
Someone also once said - the important measurements on a datasheet are the ones that are left out!
What color do you like? Do you like blond people or dark haired people? These are subjective and personal choices. Why is 1080p clearer then 480i? More pixels, or whatever I read. Makes sense, even if my parents cannot tell the difference. Measurements on my gear? Bring it on! The measurements say my gear is garbage (hypothetically)? I do not care. I only care about the emotional connection my system gives me. Am I always trying to improve my system? Yes, of course, I can't help it. Measurements are great for marketing and proving engineers can validate their degrees. Otherwise who needs them? 
If you love your partner, do you need to know her bra size?
If you love your partner, do you need to know her bra size?
jkeny
I am not sure I get your insistence on FFT.. A scalpel can be either a life saver or the most lethal object .. it depends on the use... It depends of the hands, the intention and qualification of who's holding it... Same with FFT or any other measurements or other measurement protocol .. Any tool ...
Measurements are an important parts of the scientific method . it is what insure that the experience is repeatable. if it is not, we do have a problem, an observation which cannot be explained by science or whose existence is at least suspect.
We, audiophiles have a vested interest in our gear. The investment is not only financial but in many ways emotional. Our gear is in some way a mirror of what we believe in. It is always a problem for human beings to see the object of their belief destroyed or shaken or proven wrong. We will resist and push back.. When confronted with findings or studies that invalidates our beliefs, the easiest path is to try to find flaws in the findings or to utterly reject it often with no ways of proving it wrong; for some it is then time to gather the obfuscation weapons and invoke interesting but flawed rationale including paradoxically and ironically Science. That will not change in the here and now and certainly not in this forum or in this thread...
I am not sure I get your insistence on FFT.. A scalpel can be either a life saver or the most lethal object .. it depends on the use... It depends of the hands, the intention and qualification of who's holding it... Same with FFT or any other measurements or other measurement protocol .. Any tool ...
Measurements are an important parts of the scientific method . it is what insure that the experience is repeatable. if it is not, we do have a problem, an observation which cannot be explained by science or whose existence is at least suspect.
We, audiophiles have a vested interest in our gear. The investment is not only financial but in many ways emotional. Our gear is in some way a mirror of what we believe in. It is always a problem for human beings to see the object of their belief destroyed or shaken or proven wrong. We will resist and push back.. When confronted with findings or studies that invalidates our beliefs, the easiest path is to try to find flaws in the findings or to utterly reject it often with no ways of proving it wrong; for some it is then time to gather the obfuscation weapons and invoke interesting but flawed rationale including paradoxically and ironically Science. That will not change in the here and now and certainly not in this forum or in this thread...
Frantz,
I agree with your psychological analysis of our "investment bias".
What I'm asking is:
- is FFT a dangerous tool as it is often misused?
- Does it have some inherent shortcomings/bias which leads measurements more focused towards frequency domain rather than the time domain?
- As it uses averaging of many samples does this favour oversampling/noise shaping in DACs & is this the direction that we should be going in?
So is this measurement tools actually leading us in a useful direction? It may be a bit tangential to the thread title but I thought it in the same ballpark & probably is a genuine reason why we should be afraid of these measurements.
I agree with your psychological analysis of our "investment bias".
What I'm asking is:
- is FFT a dangerous tool as it is often misused?
- Does it have some inherent shortcomings/bias which leads measurements more focused towards frequency domain rather than the time domain?
- As it uses averaging of many samples does this favour oversampling/noise shaping in DACs & is this the direction that we should be going in?
So is this measurement tools actually leading us in a useful direction? It may be a bit tangential to the thread title but I thought it in the same ballpark & probably is a genuine reason why we should be afraid of these measurements.
I, for one, do not mind being shown the right path to heaven's door. Not in an article, but right here, right now. Maybe that is why I have gone through such a gear metamorphosis. I love to be proven not wrong, but shown a different and substantial option.
I dunno jkeny, you're making FFT sound like it should be included in gun control legislation.
The danger isn't in it's generated measurements much less it's use rather than the sometimes overreaching conclusions derived from them. These are two separate things.
FFTs don't kill people, People kill poeple.
I don't know the numbers, but I doubt that many people have killed other people by their bare hands, if you know what I mean. That is the real raw "people killing people". So yes, I believe guns kill people. It makes it too convenient.
You might mean easy and not convenient, that is unless you wanna put guns in the ipod and instant coffee category.
