Up: On the automatic folding
Subsections
7 The Mk II autofolder
Whilst the logical development of the Mk I autofolder appears to preclude
any possibility of refinement, the noisiness of the data raises the possibility
that the best fold of any given rotation curve is not necessarily the fold which
uses the maximal number of Fourier modes possible for the rotation curve.
Thus, for example, the algorithm of Sect. 6.2 might indicate
the use of five Fourier modes whilst, in practice, the noisiness of the data
might allow a better fold with three Fourier modes.
Thus, given a rotation curve for which a maximum of N Fourier modes are
indicated by the data, then the logic of this latter argument forces us to consider
a set of potential solutions consisting of the 1mode fold, the 2mode fold, ..., the Nmode
fold; we must then choose the "best'' solution from this set of N possibilities.
Naturally, since the objective quality of the folding process over the whole PS sample
is to be judged against the PS solution represented by Fig. 3 left, then
the means by which we select between these N folds must be independent
of this latter figure.
The means by which this is done is described in the following.
7.1 Choosing between Fourier modes
The logic of the modechoosing strategy is rooted in the result of Roscoe 1999A that
optical rotation curves are described by the power law
so that
and
are in a linear relation:
Suppose that, for any given rotation curve, we have a choice between Nfolds, consisting of the 1mode fold, the 2mode fold, ..., the Nmode fold.
For each of these N folds we compute
as described in Sect. 3
(and applying the holecutting algorithm described Roscoe 1999A) and,
at the same time, record the residual mean square (rms) arising from the
regression. We then simply choose the mode which has the least rms
associated with it.
In other words, we simply choose the mode that provides the tightest
linear fit between
and
after the holecutting
algorithm has been applied.
Applying the Mk II autofolder described above to the PS sample we find
that it gives the
distribution of Fig. 4 right.
Comparison with the Mk I solution (Fig. 4 left), shows that the
Bpeak has strengthened considerably, the Cpeak is moreorless unchanged,
the Dpeak has weakened slightly whilst the Epeak has strengthed considerably.
Thus, the overall impression is that the Mk II autofolder represents an
improvement over the Mk I autofolder.

Figure 4:
Comparison of Mk I and Mk II autofolder solutions.
The vertical lines indicate the positions of the A, B, C, D and E peaks in
the PS solution 
Up: On the automatic folding
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