  In the framework of wave packet analysis, finite wavelet systems are
particular classes of finite wave packet systems. In this paper, using a
scaling matrix on a permuted version of the discrete Fourier transform (DFT) of
system generator, we derive a locally-scaled version of the DFT of system
genarator and obtain a finite equal-norm Parseval wavelet frame over prime
fields. We also give a characterization of all multiplicative subgroups of the
cyclic multiplicative group, for which the associated wavelet systems form
frames. Finally, we present some concrete examples as applications of our
results.
