The Description of Two-Direction Biorthogonal Finitely Supported Wavelet Packets with Poly-Scale Dilation
Wavelet analysis has become a popular subject in scientific research during the past twenty years. In this paper, the notion of biorthogonal two-direction compactly supported wavelet packets with poly-scale is developed. A new method for designing two-direction biorthogonal wavelet packets is proposed and their properties is investigated by algebra theory, means of time-frequency analysis methodand, operator theory. The direct decomposition relationship is provided. Finally, new Riesz bases of space are constructed from these wavelet packets. Three biorthogonality formulas regarding these wavelet packets are derived.
S. D. Du and D. Y. Yuan, "The Description of Two-Direction Biorthogonal Finitely Supported Wavelet Packets with Poly-Scale Dilation ", Key Engineering Materials, Vols. 439-440, pp. 1171-1176, 2010