The Properties of a Class of Two-Direction Compactly Supported Wavelet Packets with a Positive Integer Dilation Factor

In this article, the notion of biorthogonal two-directional compactly supported wavelet packets with a positive integer dilation factor is introduced. A new approach for constructing biorthogonal two-directional wavelet packets is developed and their properties is investigated by means of time-frequency analysis method, matrix theory and operator theory. The formulas for performing iterations and decomposition are established. Finally, two new Riesz bases of space L²(R) are derived.