Band-limited wavelet packets (Q2737609)

Properties of (band-limited) wavelet packets are studied in this paper. For example, the authors give necessary and sufficient conditions for the system \(\{\omega_{lnk}: n=2^p, 2^p +1, \dots, 2^{p+1}-1\), \(l=j-p, j,k\in {\mathbb Z}\}\) generated by a wavelet packet \(\{\omega_n: n=0,1,2,\dots\}\) to be orthonormal, where \(p=0\) if \(j<0\) and \(p=0,1,\dots,j\) if \(j>0\). They also give necessary and sufficient conditions for this system to be complete in \(L^2(R)\) when \(\omega_n\) are band-limited to some intervals. Some other necessary conditions for (band-limited) wavelet packets can also be found in this paper.NEWLINENEWLINEFor the entire collection see [Zbl 0960.00033].