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



On May 6, 6:42 pm, Surfer <wbb...@xxxxxxxxx> wrote:
On May 6, 8:22 pm, Jerry <Cephalobus_alie...@xxxxxxxxxxx> wrote:

On May 6, 3:02am, Surfer <n...@xxxxxxxx> wrote:

Here are some counter examples:

Averaged raw data =
{10, 90, 10, 90, 10, 90, 10, 90, 10, 90, 10, 90, 10, 90, 10, 90, 10}
Output =
{10., 90., 10., 90., 10., 90., 10., 90., 10.}

Pathetic. This is simultaneously periodic over 1/2, 1/4,
and 1/8 turn.

So is the raw data. The point is the processing has NOT produced any
EXTRA component periodic in half a turn.

Averaged raw data=
{10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150,
160, 170}
Output=
{10., 10., 10., 10., 10., 10., 10., 10., 10.}

Big swings in raw data values, but they do not cause outputs periodic
in half a turn.

Doubly pathetic.

The point is a linear temperature drift does not produce any EXTRA
component periodic in half a turn.

Here is a simulated linear temperature drift plus signal.

Averaged data=
{19, 20, 39, 40, 59, 60, 79, 80, 99, 100, 119, 120, 139, 140, 159,
160, 179}

Output =
{10.`, 90.`, 10.`, 90.`, 10.`, 90.`, 10.`, 90.`, 10.`}

Again nothing EXTRA periodic in half a turn has been added by the
processing.

Here is a counter example:

Averaged raw data =
{30, 20, 10, 0, 10, 20, 30, 40, 30, 20, 10, 0, 10, 10, 20, 30, 30}
Output =
{30., 20., 10., 0., 10., 15., 25., 35., 30.}

Despite your carefully engineered "raw data", note the beautiful
periodicities:

35 35
30--------------30--------------30--
25 25
20 20
15 15
10 10 10 10

00 00

This would simulate a case where the velocity vector happened to have
the same value when measurements were made at Marker 1, Marker 9 and
at Marker 1 again. Unusual but not impossible.

The point is, contrary to Tom Robert's claim, the zero is NOT
constrained to be near the end points.


Your claim that nothing "EXTRA periodic" can be added by the
algorithm is easily refuted.

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.

000 195 383 556 707 831 924 981 1000 981 831 707 556 383 195 000

1000 981000981
950
900 924 924
850 831 831
800
750
700 707 707
650
600
550 556 556
500
450
400 383 383
350
300
250
200 195 195
150
100
050
000 000 000
. . . . . . . . . . . . . . . . .

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

APPLY THE ALGORITHM ONCE.


000 195 383 556 707 831 924 981 1000
1000 981 924 831 707 556 383 195 000
--------------------------------------------
1000 1176 1307 1387 1414 1387 1307 1176 1000

1425 1414 1414
1400
1375 1387 1387 1387 1387
1350
1325
1300 1307 1307 1307 1307
1275
1250
1225
1200
1175 1176 1176 1176 1176
1150
1125
1100
1075
1050
1125
1000 1000 1000 1000
. . . . . . . . . . . . . . . . .

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

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

APPLY THE ALGORITHM AGAIN.

1000 1176 1307 1387 1414
1414 1387 1307 1176 1000
------------------------
2414 2563 2614 2563 2414

2625 2614 2614 2614 2614
2600
2575 2563 2563 2563 2563 2563 2563 2563 2563
2550
2525
2500
2475
2450
2425 2414 2414 2414 2414 2414
2400
. . . . . . . . . . . . . . . . .

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

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

APPLY THE ALGORITHM AGAIN.


2414 2563 2614
2614 2563 2414
--------------
5028 5126 5028

5125 x x x x x x x x
5100
5075
5050
5025 x x x x x x x x x
5000
. . . . . . . . . . . . . . . . .

AN EIGHTH-ROTATION PERIODICITY IS NOw PRESENT WHERE NONE EXISTED
BEFORE.

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

Jerry
.

Relevant Pages

  • Re: continued fractions
    ... > Although the periodicity of a cf is nice to find quadratic ... > roots, the cf's for cubic and higher roots are not periodic, ... > But to know the coefficients of a cf for an irrational means ... you can perform Euclid's algorithm on r,1 ...
    (sci.math)
  • Re: Analysis of gas mode MM interferometer operation using standard SR formulae.
    ... So is the raw data. ... the same value when measurements were made at Marker 1, ... My claim was that the averaging would not add anything extra. ... APPLY THE ALGORITHM ONCE. ...
    (sci.physics.relativity)
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