I reread carefully your last post as well as the original. I am not a physicist or an engineer, but what I gleaned from your more recent post is that you will attempt to show objectively that there are differences in cables along the lines of whatever you intend to measure or observe with your computer methodology. Then you intend to observe and compile the statements of a panel of listeners regarding what the cables under test "sound" like. I am sure your listening panel will say that the cables sound different and you seem fairly sure that you will be able to show that the cables impart some changes in spectral balance or timing or harmonics which can be measured using your computers. In your original post you say:
We are postulating that the distortion, with certain component/cable combinations, results in the,(excuse this word), recovery of lost waves. This does not mean that the resulting signal is exactly the same, or that there is not some unwanted stuff in there. We merely suggest that it is the missing waves(distortion) that give music its "real" quality.
Let me assume that your computer analysis, if it demonstrates a difference between the two signals (prior to the cable and after the cable), can attribute this difference to "lost waves".
If the listeners identify any differences in cables, as I think they will since I hear them, I don't think there is anything in the way this experiment is designed that will allow you to attribute the differences which the listeners describe to the "lost waves".
My last statement, I think, is the point of your last post. But it seems to me that all scientific experimentation starts with a hypothesis or, as you described it in the paragraph which I excerpted from you, a postulation. Yours is contained in the last sentence of that which I excerpted. Hopefully you will get there, perhaps with follow-on experiments, but what we really need in audio is not simply more standardized testing as you state in your last post, but more proof that the characteristics being measured, varied or "improved" do contribute significantly to our perception of the quality of the sound. If you can demonstrate that, your contribution to audio will be quite significant and the industry will likely adopt your standards for measuring cables as well as other audio equipment.
I do wish you luck, not because I am tired of listening to cables in order to determine which I think is best. That is, after all, my hobby. I am tired however, of the pseudoscience and advertising "rhetoric" which exists in the audio industry and anyone who is seeking to establish any objective measure of what we agree sounds correct, no matter how difficult this is to accomplish, has my support.