More on the world above 20 KHz - a reference

[Mike Sulzer]

Because I'm talking about big samples. Lots of unipolar distributions became gaussian in some limit.

And because the original question arose from comparing the spectrum of an impulse to that of white noise.

You do not understand the difference between the power spectrum of a sample of a random process, and the spectrum of the process. I cannot explain it to you even after so long trying. I suggest that you take one of those books you mentioned above and just start over.

[Joe Gwinn]

You do not understand the difference between the power spectrum of a sample of a random process, and the spectrum of the process. I cannot explain it to you even after so long trying. I suggest that you take one of those books you mentioned above and just start over.

Ad hominem.

[Mike Sulzer]

Ad hominem.

Not at all. It is just the truth. It is time for you to recognize that you do not know what you are talking about, and make some effort to learn if find it worthwhile to comment on matters such as this.

[Joe Gwinn]

You do not understand the difference between the power spectrum of a sample of a random process, and the spectrum of the process. I cannot explain it to you even after so long trying. I suggest that you take one of those books you mentioned above and just start over.

If you insist.

You are falling into a common error of thought by believing that if I only understood the difference between a the full (infinite) population from a process, and a perhaps small sample taken from that population, that I would agree with the original proposition. When I disagreed, you repeated the bit about the sample, only louder. This went on for a number of cycles, each louder and nastier than the last. The words limit or limiting came up often.

I understood the difference between a sample and a population from decades before, but disagreed with the conclusion you were trying to draw, that the power density distribution of white gaussian noise differed from the power density distribution of an impulse; it has been known since the 1940s (when the theory was developed) that these power density distributions are the same in the limit.

And yes, the standard analyses always use the limiting case, precisely because if one uses small samples, one will get a slightly different answer every time the analysis is performed. And there may be bias effects afflicting small samples. Nuisances all.