  Delay coordinates are a widely used technique to pass from observations of a
dynamical system to a representation of the dynamical system as an embedding in
Euclidean space. Current proofs show that delay coordinates of a given
dynamical system result in embeddings generically over a space of observations
(Sauer, Yorke, Casdagli, J. Stat. Phys., vol. 65 (1991), p. 579-616). Motivated
by applications of the embedding theory, we consider the situation where the
observation function is fixed. For example, the observation function may simply
be some fixed coordinate of the state vector. For a fixed observation function
(any nonzero linear combination of coordinates) and for the special case of
periodic solutions, we prove that delay coordinates result in an embedding
generically over the space of flows in the $C^{r}$ topology with $r\geq2$.
