First off, interesting read, thanks, Anaxilus.
Originally Posted by Pio2001
Is IMD with three frequencies more than the sum of IMD for each pair of frequencies, and if so, does it make a significant difference, or is it just 0.1 % of 0.1 %, and IMD with four frequencies 0.1 % of 0.1 % of 0.1 % ?
Transient IMD asks the same question. If you measure IMD on a fixed frequency sine plus a transient burst, will you get more than the total IMD for all frequencies contained in the burst associated with your sine ? If so, is it significantly more, or just 0.1 % more ?
I don't know.
And just in case you couldn't tell, I was being facetious with the 4D, 5D, etc., but I think it got the point across. In general for a linear system, if you have input frequencies A, B, C, and D, the output will only have frequencies A, B, C, and D (may have different amplitude and phase, but frequencies do not change). For a nonlinear system, intermodulation results in output frequencies at different sums and differences of the inputs. Sums and differences of A, B, C, and D as seen in an IMD graph for those four inputs would be would include IMD frequencies seen whenever any pair of A, B, C, and D (e.g. A with D only) are input as well as others from triple and quadruple combinations. The distortion from A, B, C, and D should be at least the distortion with A and B plus the distortion with C and D. I'm not quite sure what the order of magnitude of the distortion in these cases would be, though.
For one example, ryumatsuba has IMD graphs with test tones of 100, 1000, and 10000 Hz. http://www.geocities.jp/ryumatsuba/review.html. Here is the graph for the AKG K101.
Note that the IMD graphs from test tone measurements will include other harmonic distortion too. What's being measured is all frequencies, which include the test tones, IMD, harmonic distortion in multiples of the test tones, harmonic distortion in multiples of the resultant intermod products, other distortion, noise, etc. For characterizing IMD in general, the Volterra series model is used and the parameters estimated, but I couldn't tell you much more than that about the process. There are different numerical methods to solve a problem like that, and I don't even know if people use this tool in audio. About transient IMD and the rest, I'm not sure either. I'm leaving it out there as an open question.
Originally Posted by mike1127
Some people claim the concept "accuracy" is inherently empirical (measurable or numerical). But one of the definitions of accuracy is "true to a standard." No one said that standard had to be empirical. I would wager that in English, the word is used more often non-empirically.
I think "accuracy" in the sound science forum when discussing measurements would imply the numerical definition by default, but maybe that's just me. I would use "perceived accuracy" or "subjective accuracy" for the other definition. The Mona Lisa example explained what you really meant, thanks.
Originally Posted by mike1127
Since art is about the experience of looking at the painting, the accuracy of a copy can only be judged by experiencing it. If someone wants to say: "Look, measure the shapes and colors and find the student who is closest," I would point out that every student deviates from the original more in some places and less in others. How do you quantify each deviation (turn it into a single number)? How do you weight the series of numbers that results? And if you find one student that is generally closer than others, you still have to ask: does that student capture the feeling of the painting? We don't know without looking at the painting and making a subjective judgment. If a student is the best one at copying shapes but doesn't create an artistic experience in the viewer, then I'm not very interested in that student's work. I would say he's on the wrong track.
On a side note, I must mention that a lot of people in DSP, video/image transmission, etc. would point out that they do scan the image and "turn it into a number(s)." There are many algorithms for this that a lot of people work with. Applications include robot vision, detection of objects from photographs, and the like. However, I do agree that from an artistic point of view, the "best" (which is subjective, though experts may be able to agree on this) portrayal may not have the highest "closeness" score from whatever algorithm you apply. You could say that the algorithms are not measuring the right thing.
Often in evaluating image compression, coding, transmission, and the like, researchers use both empirical measures from algorithms as well as human responses to "rate how good picture B is compared to picture A" or "is there a difference between A and B", or something like that. Both are important if the end image or audio signal is meant to be processed by humans. Machine algorithms are more useful at determining absolute differences, especially when differences are smaller. If the goal is for the end product to be processed by a human, you want to know what differences can be discerned by humans. And this is determined through the usual blinded testing. Well, blind in the sense of eliminating biases wherever possible, not that you test people blindfolded when asking them to compare images.
Originally Posted by mike1127
This seems like the most useless measurement of all, because it gives you an infinity of numbers. What do you do with those numbers? As soon as you try to collapse them into a meaningful single number, then you've used a model, which is not reality.
Cancellation is most useful when the difference is zero, or at least close to it: hence canceling. Then you don't need to do anything with those numbers. If you record the output using interconnect X and record it again with interconnect Y and find that the difference between the two recordings is zero, there was no difference between the two interconnects (that could be picked up by the measuring equipment, which is more empirically accurate than human hearing).
Let me wrap up this post by reiterating that the models used are close enough to reality for our purposes in audio. Particularly, they are great for interconnect cables, which are very linear. I think one thing you're trying to say is that perceived accuracy in music reproduction is more important than empirical accuracy. e.g. a higher THD score from a system that only produces second harmonics is better than a lower THD score from a system that produces all sorts of unrelated frequencies -- this being the extreme case. However, the most obvious and relevant measures can be related to experience. You just need to interpret the measurement data differently in a known way to conclude what might have been determined subjectively. Even if you focus on what is perceived as best to you (not a bad choice), I think that a reasonably comprehensive set of measurements would give a better understanding of the system than you give it credit for.
Edited by mikeaj - 8/30/10 at 11:12pm