  We consider a one-dimensional diffusion whose drift contains a deterministic
periodic signal with unknown periodicity $T$ and carrying some unknown
$d$-dimensional shape parameter $\theta$. We prove Local Asymptotic Normality
(LAN) jointly in $\theta$ and $T$ for the statistical experiment arising from
continuous observation of this diffusion. The local scale turns out to be
$n^{-1/2}$ for the shape parameter and $n^{-3/2}$ for the periodicity which
generalizes known results about LAN when either $\theta$ or $T$ is assumed to
be known.
