Please continue on, Ed, if you will, with your experience with CEPSTRUM analysis. This is just out of my experience, but I am willing to learn, and I probably have the equipment to do it, as well.
What does FFT miss? Plenty.
Here's a quick tutorial.
http://www.ele.uri.edu/~hansenj/projects/ele436/fft.pdf
As the tutorial shows, the number of points N determines how badly FFT misses the mark compared to the Continuous Time Fourier Transform. As N increases, FFT approaches the correct continuous time answer asymptotically. For precision, depending on how large N is, that may not be good enough.
The one exception I take to the tutorial is that the transform does not have to be applied from T=-infinity to T=+ infinity. If it did, the measurement would have had to have begun at the big bang and continue to the end of the universe. Continuous Fourier analysis gives the right answer for any waveform capture in the time domain between two arbitrary points T1 and T2.
The use of spectrum analyzers where band limited noise is used as the test signal is another perversion of Fourier Theory. A real spectrum analyzer uses a sweep generator, the slower the sweep the more accurate the results. The use of a tracking filter to eliminate spurious noise may be of value if it is absolutely flat within the required precision of measurement over its required range. If it is not, then it will distort the results unacceptably.
The measurement of frequencies beyond the capabilities of human hearing is a rejection of the very concept of Fourier analysis itself. Measurement of the noise floor below the threshold of hearing is also a canard. The information window for audibility is the limits of frequency and amplitude of human hearing, the required resolution no greater than the ability of human hearing to distinguish between differences in frequency and loudness. To be valid, any test should be at least one order of magnitude greater in resolution.
The AIA design criteria for an absolutely quiet concert hall where live music performed with the greatest dynamic range is NC 25 which I think is C weighted. In the real world with a real audience, the noise floor is much higher.
It's not that the FFT "misses" anything, it's just that if the process isn't understood and appropriate parameters chosen for the specific things you're looking for, you won't get a valid measurement. No different than any other measuring tool (e.g., a voltmeter used to measure a high impedance node) used incorrectly.
JC: CEPSTRUM is a tool to find periodicity in the SPECTRUM, not sure if it helps in a link level audio design at all.
Take a look at Bill Waslo's excellent article "Reflecting on Echoes and the Cepstrum: A look at Quefrency Alanysis and Hearing" in Speaker Builder, Aug 1994. Bill also had a very nice paper on cepstral theory on his website, but it doesn't appear to still be there. It's an interesting technique- we played around with this during my Nicolet days.
It is clear from the tutorial that when N is low, FFT gives grossly invalid results in the frequency domain in exaclty the same way digitizing an amplitude gives invalid results depending on what level of resolution you require compared to what the measuring instrument is capable of. Thus for example if you need to measure voltage to six places and your DVM only resolves to two places the measurement will be unsatisfactory.
This is not a comment about the adequacy of what FFT is being used to measure, it is a comment about the technique of FFT itself within the context of approximating the correct values obtainable by continuous fourier transform. It seems odd to me that those who are so vocally adamant about quantization errors of an insignificant order in RBCD have so completely missed the obvious potential flaw in FFT measurements. For those who use FFT, what is N in your measurement? FFT is certainly much cheaper than a real time analog spectrum analyzer. Are there computer programs which perform the equivalent of continuous fourier transform from an analog data capture device? Even using a very high number for N such as say 10,000 or 1,000,000 would be better than using a low number.
Dude, it's the 21st century, not 1980. For even cheap analyzers, N can easily be set to 1M or higher. I can't remember the last time I used N smaller than 64k or so. Higher when I need to resolve closely spaced sidebands or drop the measurement floor. Add in the multiplex and throughput advantages, and you can see why the swept tone stuff is a relic.
Ed, your EXPERIENCE with Cepstrum analysis, and where you have found it important. I agree that it can be most useful in loudspeaker analysis. I like understanding loudspeaker problems, as I have measured them myself, in the long past.
Agreed. Non-linear and/or multi-modal systems behave differently if the excitation frequency moves by too fast.
Actually, if one intends to measure a system's impact on localization in the 2 to 5 uSec range, there are not many options available.
I'd add interchannel criteria as well, but that is not within the scope of what you've been stating...a scope which I do generally agree with.
This is perhaps the most important statement in your post.
Cheers, John
ps..welcome back
"Actually, if one intends to measure a system's impact on localization in the 2 to 5 uSec range, there are not many options available."
The critical importance of the ability to hear difference of arrival of the same sound between two ears of 2 to 5 uSec demonstrates that there is at the very least a fatal gap in the conventional understanding of sound localization, in fact the accepted model may be dead wrong. I am not at liberty to tell you what is lacking but its implications go far beyond localization. The proof that the theory is wrong is the fact that binaural sound recording/reproduction doesn't work. That system meets every criteria of the model, if the model was right it would work perfectly.
The frequency of a sound wave with a period of 5 uSec is 200 Khz, the frequency of one with a period of 2 uSec is 500 Khz. The limit of human hearing is in the vascinity of 20 khz. The understanding of how the human brain interprets the neural information it gets from the ears determines not only what is and is not important in accurate sound reproduction but the specification criteria for performance of a sound system intended to reproduce it accurately. The two go hand in hand. Between lack of knowledge of how sound works and lack of knowledge of how the brain hears means that current sound systems cannot be designed with the expectation of reproducing the subjective experience of a live musical performance. Until that gap is closed, investment in expensive sound reproducing equipment is a waste of money and trying to perfect a failed paradigm is a waste of time and effort. Meanwhile the claims of vast superiority for the most expensive equipment and technological breakthroughs never lets up. The reaons are not only commercial but also relate to egos.
We're talking about audio. You want to talk about spectral analysis at RF, start a new thread- it's an interesting subject in and of itself.
It depends on what one considers the "accepted" model. IID based pan only, pffft. I do not subscribe to the old model.
I can tell ya, but then I'd hafta kill ya..
It's top secret, so I can't tell ya.
Please spare us statements such as that. We get enough of that from the purveyers of that "quantum" device. Either spill your guts, or allude to nothing.
Inverted bandwidth is important if you're buying a scope probe. It is a meaningless reference with respect to the audibility of specific frequencies on a per channel basis.
It has meaning only for ITD.
Cheers, John
Hit your head against the same wall. I don't care, the wall doesn't care either. It still won't budge.
If it ain't broken, don't fix it.
If the shoe fits, wear it.
If pigs had wings...
S... or get off the bowl.
Quippy phrases bring nothing to the table.
Either engage the discussion or not.
"I am not at liberty to tell you"....
More often than not, that phrase is used to imply understanding beyond the grasp of others, a tool of denigration. Often used on the target market with the intent of bamboozling them into purchasing.
It is meaningless to me. Bring knowledge to the table, or punt.
Cheers, John
Well, I guess I will have to ask Ed Simon, directly. It is his EXPERIENCE that I hoped to learn from.
I have no products to offer the market...yet. I may or may not have knowledge you don't. Why should I reveal it if I do? Whatever advantage it might eventually have for me would be lost if I did.
You're smart enough to put the pieces of the puzzle together and figure it out for yourself. They're all there, you've been looking at them for years. Don't see it yet? Too bad.
Protection of IP, especially if it has not been patented, can be a big concern.
You are engaging conversation in a discussion forum... Note the word discussion.
Either discuss, or discontinue. Very simple.
Claims of "you're wrong but I can't tell you why, doesn't float anybody's boat.
I've seen those types of statements before, used to justify things like Q-purifiers, intelligent chips, lifters, dots, green markers..
As I said, you're statement is of little value, and does not distinguish you from some of the people you castigate..
I am sure this was not your initial intent..
Cheers, John
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