Characteristics of Higher-dimensional Two-directional Wavelet Packets

Abstract-In this article, the notion of biorthogonal two-direction finitely supported wavelet packets with three-scale is introduced. A new approach for designing two-direction biorthogonal wavelet packets is developed and their properties is investigated by means of time-frequency analysis method, matrix theory and operator theory. The decomposition relationship is established. Lastly, two Riesz bases of space L² (R) are drawn from these wavelet packets.