  Using a prime element of a local field K of positive characteristic p, the
concepts of multiresolution analysis (MRA) and wavelet can be generalized to
such a field. We prove a version of the splitting lemma for this setup and
using this lemma we have constructed the wavelet packets associated with such
MRAs. We show that these wavelet packets generate an orthonormal basis by
translations only. We also prove an analogue of splitting lemma for frames and
construct the wavelet frame packets in this setting.
