Re: [Phys-l] data manipulation -- analysis

[John Denker <jsd@av8n.com>]

On 04/06/2012 10:28 AM, Bernard Cleyet wrote:
> interrupt time data from a photogate by a clock pendulum is very
> noisy.  In order to analyze and display (graph), it's necessary to
> "smooth" it (Kaleidograph's word for average).   It's intuitive that
> one should square then average instead of the reverse order.
> Otherwise there is a cross product,** no?  Also it's convenient first
> to smooth the speed data.   Should one smooth the raw (interrupted
> time) data before inverting, or invert and then smooth?   The two do
> not result in the same value.  Of course the difference is very
> small, as the difference between successive data is very small
> (otherwise any noise would not be obvious!).

You need to reformulate the approach.

You have a data reduction problem.  In simple cases, this can
be formulated in terms of /curve fitting/.

  To say the same thing the other way:  If you formulate it in 
  terms of "smoothing" you have already lost the game before it 
  begins.

The basic steps include:
 a) figure out what variables are directly observable
 b) figure out what variables describe the physics you are 
  most interested in.  
 c) figure out the relationship between the observable
  variables and the interesting variables.  Typically this
  takes the form of a parameterized model, where the parameters
  are the "interesting" variables.
 d) come up with a model for the noise.
 e) fit the model to the data.

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

Also: Important:  If the photogate data is unduly noisy, maybe
you shouldn't be using a photogate!

If I were doing this, I wouldn't use a photogate.  I might use 
some sort of gray-coded position sensor, as we have discussed
before.  There are lots of other possibilities.
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