Re: Analysis of gas mode MM interferometer operation using standard SR formulae.

On May 7, 2:54 am, Surfer <n...@xxxxxxxx> wrote:
On Tue, 6 May 2008 21:16:04 -0700 (PDT), Jerry

My claim was that the averaging would not add anything extra.
I did not claim that combining two half turns would never do it,
although I gave some examples for which it wouldn't happen.

(SNICKER)

When I wrote up my example, I made an intentional mistake for you
to find, confident that you wouldn't find it.

I was right.

YOU FAILED.

Begin with a sine curve.
1000*sin(n*pi/16) where n = 0 to 16

It should of course be obvious that the curve generated by this
function will not exhibit any half period harmonics.

Since you didn't catch my inaccuracy, it is perfectly evident
that you know nothing about Fourier Analysis except a few catch-
phrases. Anybody who knows anything at all about FA knows that
a half-cycle sine wave curve -will- have harmonics!

The important point I wanted to make, though, is that the half-
turn averaging procedure does absolutely nothing to reveal the
Fourier components but throws away data and introduces artifact.

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============================================================

APPLY THE ALGORITHM ONCE.

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A HALF-ROTATION PERIODICITY IS NOw PRESENT WHERE NONE EXISTED
BEFORE.

That is a good example. But note that if a signal with such a period
appeared in the raw data, multiple periods of it would be recorded in
the raw data during the twenty turns.

EVEN AS THE HALF-TURN AVERAGING PROCEDURE THROWS AWAY DATA AND
INTRODUCES ARTIFACT, THE TWENTY-TURN AVERAGING PROCEDURE ALSO
THROWS AWAY DATA AND INTRODUCES ARTIFACT.

Since the period in the example you gave is two turns, the half period
that appeared in each alternate turn would cancel when the turns were
averaged.

So you would end up with zero in the averaged data.

If you choose a signal with a period that was not divisible into 20
turns, eg one with a period of 3 turns, then a portion of it would
remain uncanceled when the 20 turns were averaged. However, the
uncanceled portion would be reduced in magnitude by the division by 20
used in the averaging.

In contrast, if a genuine signal with period of half a turn appeared
in the raw data, it would retain its full value during the averaging
process.

So I would say the full algorithm with the averaging is fairly
resistent to the problem you are worried about.

So you guess.

So you guess.

So you guess guess guess guess guess...

Surfer, three points:

1) In defending Miller, you have completely lost sight of the
real question. The real question is NOT whether ANY half-rotation
component can be extracted from the data. The plain fact of the
matter is that even the frequency spectrum of PURE NOISE will
contain every frequency component, whether the noise be white,
pink, red, or any other "color." Rather, the real question is,
does the half-rotation component of the frequency spectrum show
any significant excess over its expected level? This question
cannot be answered using data preprocessed using an algorithm
that throws away 95% of the available information by averaging,
then distorts the shape by subtracting a modeled background that
demonstrably does not match the observed systematic error.

2) I had earlier shown how Miller's data processing algorithm,
applied to a Markov chain generated using the digits of pi,
ALWAYS results in a periodic half-rotation curve, MOST of the
curves resembling sine waves. When Dirk suggested that I try out
the algorithm on e, two out of four "looked like" good sine waves
and the other two, even though they didn't "look like" good sine
waves, were nevertheless periodic half-rotation curves because
they were FORCED TO BE SO by Miller's algorithm.

3) We don't use mechanical harmonic analyzers anymore to analyze
signals. We have things called "computers" that can perform a
full 320 point DFT on the unprocessed, unaveraged, undistorted
data. When Tom Roberts performed a 320 point DFT on Miller's
published Fig. 1, which Miller claimed represented a "typical"
run (but as we all know, "typical" data is never published, only
"good" data), he found an STATISTICALLY INSIGNIFICANT excess in
bin 40 corresponding to the half-rotation. This INSIGNIFICANT
excess was matched by a corresponding deficit in bin 20 pointing
to the excess being due to a systematic bias in Miller's data
collection procedures or instrumentation. Robert's analysis of
many more of Miller's UNPUBLISHED runs did not show even THAT
miniscule amount of seemingly excess signal.

Jerry
.

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