no ensemble FT update edit log

Major Problem with FT, New Edit Log PhL 8.2.13 Well, this was my Big Nightmare, and it has finally soaked in that I have a huge problem. Xiong I guess was the last straw. Everything I have done starting from Section 32, although not strictly WRONG, is done in a completely stupid way which makes the whole paper stupid. I am now of the feeling that there is no need for any kind of "ensemble" in this document, so all those <...> averages are unnecessary. Using a very simple method involving R"(z), you can compute P(ω) for any pulse train with no need for ensembles. This then relieves me of the task of jumping through hoops in order to create an ensemble with the right properties! I must admit, I have spent many days trying to "tune" this ensemble. All that time is wasted in retrospect, and I doubt now I can meet my Aug 12 Cod departure deadline. This problem is a LARGE problem and permeates everything after Section 32 which is a lot of the doc. We are talking here about rewriting at least half of this entire document! Edit Log So I will now start a new folder called "no ensemble FT update" and start editing sections one at a time and see if I run into trouble. This then is the new edit log. Reflection rules update: I added stuff to the short section 7 and changed the equation numbers. I will now do a global cross reference repair: DONE, took a while. I start by making a copy of Section 32 and trying to edit that copy to see what will happen. Section 32 (a) OK (b) OK (c) OK, major repair here to account for complex x(t) and be parallel with later (d) OK (e) OK, major repairs here due to new and more correct definition of autocorrelation (f) OK, showed this for both infinite and finite! So the edited result sits for now in a file section 32.doc. I will not install, but will for now move on to the next section. Section 33 -- no changes needed whatsoever, so no section 33 file created. Got off light here! Section 34 -- no changes needed whatsoever, so no section 33 file created. Got off light here! I will now install my repaired Section 32: I really have done no changes regarding the "no ensemble" aspect of things, so I will back up the current state of FT as today's date 5PM which is right now. Section 35 (starts page 166 out of 323 pages! ) This is where major changes will begin!!! I got well underway, have a conflict between δ5 and δ6 and will resume tomorrow. Shutting down tat 9:30 PM, good progress today on this painful task. Sat Aug 3 2013. I got the finite train result wrong yesterday, will try to fix now at 6:20AM. But as I try to "fix" this little problem, I see that something major is wrong with the no-ensemble picture. Statement of the problem: Problem with the No Ensemble Picture of Scenario #1. I defined a set of random variables Yn and drew this picture: The problem is this: Every single Yn is associated with exactly the same distribution of its yn values, these being the xi of the passing pulse train. Thus, for example, Y0 and Y2 cannot be independent as I conjectured. In fact, I now think that all these "random variables" are the SAME random variable. That is why we have "stationary" ! So now I think this no-ensemble scenario #1 is complete and utter nonsense devoid of any meaning. So the ship bounced off one reef and is not foundering on another reef. I then considered these three possibilities 1) Y1 and Y2 are the same random variable 2) Y1 and Y2 are different random variables 3) Y1 and Y2 are not random variables. I decided that (2) cannot be true since E(Y1Y2) = sum xixi+1 differs from E(Y12) = sum xi2. Then I decided that 3) is true and here is the reason. A RV must be associated with an outcome of some experiment that you repeat many times, and in Scenario #1 there is no experiment you can name whose outcome is associated with Y1. If the experiments are a generator creating different pulse trains, then what outcome is associated with Y1 ? For Scenario #2, the outcome of interest is the value of position 1 in an ensemble of pulse trains, so you CAN answer this question. For Scenario #1 you cannot answer this question, and therefore Y1 is an ill-defined RV. It is not a RV at all! Therefore this edit log is closing down. It was a path that went wrong. I will maintain the directory and I will now copy the bu saved version back to my old directory.