Thu Apr 4 14:44:58 EDT 2019

Embedding manifolds

Application domain: I have a system where the central measurement is
phase difference between two oscillators, and I need to continously
trak this difference, keeping track of "wraparound" based on a
well-known initial point.

The main insight is to keep the representation of phase "embedded" in
the representation of a quadrature signal, as opposed to flattening it
out into a single number that cannot represent the idea of rollover in
a continous way.

I think there is a generic field here: e.g. representation of Lie
groups as sets of matices.

Can this be generalized?  I.e. there are more cases where
discontinuities and ambiguities are a consequence of the
representation, and not intrinsic to the problem.

Riemann surfaces come to mind as well.