Why Some Audiophiles Fear Measurements
- Thread starter Jeff Fritz
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An interesting demonstration of how FFTs can be mis-applied:
This is an example of two chirp sounds - the top one going from low frequency to high & the bottom one from high frequency to low. We can easily hear the difference between them (as can birds or they would be in severe trouble) but an FFT freq domain, power spectrum for the two are identical
http://zone.ni.com/devzone/cda/tut/p/id/3548
So, when using measurements we have to be careful about what is used & how it's interpreted. Indeed, this may be the crux of the OPs thread title - there is a general misconception that measurements "prove" something & therefore lack of measurements "disprove" it. There is also a pervasive attitude to science as a god replacement - the comfort of infallibility perhaps? People often forget that science is very fallible & indeed is based on the notion of fallibility - it advances by proving the fallibilty of a previous experiment/theorem. Making demands of someone to "prove" that what they hear is "true" is in a lot of instances misguided & adversarial. It would be a better use of everyone's time to work on a more accurate model of the ear & psychoacoustics' complexities.
I'm also reminded of the old adage by the above example (& my recent experiences on this forum), "To a man with a hammer, everything looks like a nail".
This is an example of two chirp sounds - the top one going from low frequency to high & the bottom one from high frequency to low. We can easily hear the difference between them (as can birds or they would be in severe trouble) but an FFT freq domain, power spectrum for the two are identical
http://zone.ni.com/devzone/cda/tut/p/id/3548
So, when using measurements we have to be careful about what is used & how it's interpreted. Indeed, this may be the crux of the OPs thread title - there is a general misconception that measurements "prove" something & therefore lack of measurements "disprove" it. There is also a pervasive attitude to science as a god replacement - the comfort of infallibility perhaps? People often forget that science is very fallible & indeed is based on the notion of fallibility - it advances by proving the fallibilty of a previous experiment/theorem. Making demands of someone to "prove" that what they hear is "true" is in a lot of instances misguided & adversarial. It would be a better use of everyone's time to work on a more accurate model of the ear & psychoacoustics' complexities.
I'm also reminded of the old adage by the above example (& my recent experiences on this forum), "To a man with a hammer, everything looks like a nail".
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Yes, well said. It's the illusion of audio that we are interested in - trying to measure this is probably futile! We can measure & improve elements that might bring us closer to the successful creation of the illusion but ultimately our ears tell us what works & what doesn't. Some people try to deny this illusion & even suggest that what we hear is a placebo but placebos work!
jkeny,
Thanks for bringing some fresh air to this well worn subject. Some manufacturers, such as Soulution or Spectral openly refer to temporal resolution in audio.
Yes, it's well worn if people continually plough the same furrow with their arguments. Some fresh thinking is needed. I'm not saying I have that fresh thinking but I appreciate what Kunchur is doing in looking afresh at the issue with a new perspective. One of the problems is that it requires someone with muti-discipline expertise to grapple with the subject in a meaningful manner. Even taking the subset of digital audio - real expertise in it requires someone with both digital & analogue expertise. In these days of extreme specialisation, that's a rare enough being.
The FFT has both an amplitude and a phase spectrum. When both are retained, one can uniquely determine the corresponding time function from the FFT. That's how software like Room EQ Wizard works to compute system impulse response. When the FFT phase is discarded, it is no longer possible to uniquely compute the corresponding time function. The power spectrum shown discards the phase, making the corresponding time function non-unique. The two signals they chose have identical amplitude spectra but different phase spectra, and thus have different FFTs. The power spectrum doesn't show that, because it throws away the phase.
So this NI marketing literature is an example of misuse of the FFT. This is not a problem with the FFT itselt, but rather a misapplication of it by throwing away the FFT phase iniformation, then making the false assumption that the time function can be uniquely recovered.
For any given measurement technique, one could likely concoct many ways to do it wrong, but these are user errors, not problems with the measurement technique itself.
Keep in mind that this is marketing literature for a product that forgoes the FFT in favor of wavelets.
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Perhaps, Andy you are correct - I did say how FFTs are mis-applied. I seldom if ever see an FFT for a device measurement (speakers aside) where the FFT phase is shown, do you? It might boil down to people not using FFTs correctly or misinterpreting the results. You already pointed out recently on another thread 
, the common mistake of mis-interpreting the FFT power spectrum plot's grass as the noise floor. How many other common mistakes are made with this powerful tool? So yes FFTs are maybe not at fault but then they might not be the best tool suitable for the type of time-domain analysis needed. So let me ask you some questions, in the interest of learning & nothing more - can FFTs (as commonly used) :
- give us the full information needed for impulsive signals?
- give us the full information of how frequencies evolve over time?
, the common mistake of mis-interpreting the FFT power spectrum plot's grass as the noise floor. How many other common mistakes are made with this powerful tool? So yes FFTs are maybe not at fault but then they might not be the best tool suitable for the type of time-domain analysis needed. So let me ask you some questions, in the interest of learning & nothing more - can FFTs (as commonly used) : - give us the full information needed for impulsive signals?
- give us the full information of how frequencies evolve over time?
Perhaps, Andy you are correct - I did say how FFTs are mis-applied. I seldom if ever see an FFT for a device measurement (speakers aside) where the FFT phase is shown, do you? It might boil down to people not using FFTs correctly or misinterpreting the results. You already pointed out recently on another thread
- give us the full information needed for impulsive signals?
- give us the full information of how frequencies evolve over time?
Yes it can, provided one retains the phase information. In fact, Room EQ Wizard uses a frequency-modulated sine wave as the system input for computing system impulse response. There's a paper showing how this works that I talked about in this post and this one. The article by Farina referenced in the second post describes in detail how the impulse response is calculated.
I think what NI is referring to is benchtop FFT analyzers, which in some cases replace traditional analog spectrum analyzers. These instruments only show the amplitude spectrum of the FFT. It's been years since I've done test engineering though, so I'm not sure what instruments are currently available and what their capabilities are.
I luv what I'm reading, especially from the last couple pages.
Thanx John and Andy (among others). :b
Thanx John and Andy (among others). :b
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Andy, doesn't an FFT operate on the basis of periodic signal & analyses the power spectrum of that signal into frequency bins? Does this not mean that a single impulse completed in less time than the width of the bin frequency will not be picked up by the FFT? Is it not a time-frequency trade-off? Example - take a 4K FFT bin - this equates to a 100mS grab @44.1KHz so if anything dynamic completes in that 100mS window it will be missed by that FFT?
If I follow, you are close. FFT's are based upon samples in time, and the frequency of samples (fs) sets the upper frequency bound (as determined by Nyquist) that can be accurately captured (without playing other games). The record length dictates (among other things) the lower-frequency limit that can be properly captured since the lowest frequency bin is related to 1/record length. Anything within the time window is captured. A signal that falls between samples, such as an impulse, can be missed. A signal that spans multiple samples but fits within the record length will be fully captured ("seen"). A signal too long (low in frequency) will be lumped into the lowest bin (and d.c. component, natch), so is seen but not fully resolved (max error ~= sampling period).
Thus, the impulse that might be missed (depending upon it's timing with the sampler) must be less than 1/44.kHz, or about 23 us, not 100 ms. In fact, due to aliasing (Nyquist again), we can't accurately resolve frequencies equal to or higher than 22.05 kHz, 45 us, 1/2 the sampling frequency.
I think... - Don
p.s. There are vector analyzers that output magnitude and phase, but the vast majority of times we look at an FFT we are only looking at the magnitude response (amplitude) because that's what the display shows us.
Thus, the impulse that might be missed (depending upon it's timing with the sampler) must be less than 1/44.kHz, or about 23 us, not 100 ms. In fact, due to aliasing (Nyquist again), we can't accurately resolve frequencies equal to or higher than 22.05 kHz, 45 us, 1/2 the sampling frequency.
I think... - Don
p.s. There are vector analyzers that output magnitude and phase, but the vast majority of times we look at an FFT we are only looking at the magnitude response (amplitude) because that's what the display shows us.
Just for the record, James Johnston (JJ) and others at the Hydrogen Audio forum debunked Kuncher's paper soundly:
http://www.hydrogenaudio.org/forums/index.php?showtopic=88874
www.hydrogenaudio.org/forums/index.php?showtopic=73598
JJ goes by the screen name Woodinville in that forum. If you Google "kuncher debunked" you'll find many other such debunkings.
--Ethan
http://www.hydrogenaudio.org/forums/index.php?showtopic=88874
www.hydrogenaudio.org/forums/index.php?showtopic=73598
JJ goes by the screen name Woodinville in that forum. If you Google "kuncher debunked" you'll find many other such debunkings.
--Ethan
Thanks Don, yes, that's a much more accurate description of what I'm getting at Small correction - I was talking about a 4K bin so 4096*22.6uS = 100mS. I used this example to highlight the seemingly common mis-use of FFTs - it's an example from this paper http://www.scalatech.co.uk/papers/jaes496.pdf by Dunn & Sandler "A comparison of Dithered & Chaotic Sigma-Delta Modulators"
I guess my wider point is that there is an over-reliance on FFTs in general & maybe they have been mis-used leading us up a blind alley that we are beginning to emerge from? A bit like the decade of THD?
Small correction - I was talking about a 4K bin so 4096*22.6uS = 100mS. I used this example to highlight the seemingly common mis-use of FFTs - it's an example from this paper http://www.scalatech.co.uk/papers/jaes496.pdf by Dunn & Sandler "A comparison of Dithered & Chaotic Sigma-Delta Modulators"I guess my wider point is that there is an over-reliance on FFTs in general & maybe they have been mis-used leading us up a blind alley that we are beginning to emerge from? A bit like the decade of THD?
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No, a dynamic signal impulse of less than 100mS. In the case of the paper I referenced it's their use of this bin size & their following statement that noise modulation distortion is absent.
I'm not quite sure I fully understand your question. An analog unit impulse can be represented as a signal with a duration of t0 and a height of 1/t0 (area = 1). Then you let t0 become infinitesimally small, so you get a signal with amplitude that approaches infinity for a time duration that approaches zero. The spectrum of this, computed with the continuous-time Fourier transform, is a constant over all frequency. Such a signal violates the sampling theorem, so you can never recover it from digital samples. You have to first bandlimit the signal with an anti-aliasing filter, and you end up with a sinc function in the time domain at the output of this filter. This spreads out the signal in time.
The context of the FFT is a sequence of samples in the time domain, possibly created by sampling an analog signal, but not necessarily so. If you compute its FFT, then its inverse FFT, you get the original sequence back. It's actually a periodic repetition of the sequence, so you have to know about that and account for it.
When I said "recover the time function" with the inverse FFT, I was speaking loosely. The inverse FFT actually recovers a sequence of samples. If we assume that set of samples came from an analog signal, whether we can get the original analog signal back depends on whether the sampling theorem has been violated in obtaining those samples. The sampling theorem only says that you can recover a strictly bandlimited signal from its samples, not an arbitrary signal. But that's a requirement of the sampling theorem, and unrelated to the FFT.
Another potential point of confusion is the impulse in the continuous-time domain as I've described above (the Dirac delta function) vs. what's sometimes called a "unit pulse" in a discrete-time system. The latter is just a discrete-time sequence of values that are all zero except for one non-zero element.
All very interesting, Andy but my example is still correct, right? The 4K bin size will miss any impulse with a less than 100mS duration! Now, this suggests, as you have already pointed out, that bin size is critical in FFT use & determines much about the FFT & it's correct analysis. I have seen a contention, with which I tend to agrre, that in this audio field, there is a group-think mentality about FFTs.
You mean short in the audibility stakes? Yes, for one such impulse signal but multiples of such impulses would still be missed by this FFT, I believe! The authors of that paper were analysing noise modulation & this could easily not be visible to them using this FFT.
