  Laplacian pyramid based Laurent polynomial (LP$^2$) matrices are generated by
Laurent polynomial column vectors and have long been studied in connection with
Laplacian pyramidal algorithms in Signal Processing. In this paper, we
investigate when such matrices are scalable, that is when right multiplication
by Laurent polynomial diagonal matrices results in paraunitary matrices. The
notion of scalability has recently been introduced in the context of finite
frame theory and can be considered as a preconditioning method for frames. This
paper significantly extends the current research on scalable frames to the
setting of polyphase representations of filter banks. Furthermore, as
applications of our main results we propose new construction methods for tight
wavelet filter banks and tight wavelet frames.

Functional Analysis;Numerical Analysis