Multiwavelets possess some nice features that
uniwavelets do not. A consequence of this is that
multiwavelets provide interesting applications in
signal processing as well as in other fields. As
is well known, there are perfect construction
formulas for the orthogonal uniwavelet. However,
a good formula with a similar structure for
multiwavelets does not exist. In particular,
there are no effective methods for the
construction of multiwavelets with a dilation
factor
(, ). In this paper, a procedure for constructing
compactly supported orthonormal multiscaling
functions is first given. Based on the
constructed multiscaling functions, we then
propose a method of constructing multiwavelets,
which is similar to that for constructing
uniwavelets. In addition, a fast numerical
algorithm for computing multiwavelets is given.
Compared with traditional approaches, the
algorithm is not only faster, but also
computationally more efficient. In particular,
the function values of several points are
obtained simultaneously by using our algorithm
once. Finally, we give three examples
illustrating how to use our method to construct
multiwavelets.
