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Design and Properties of Two-direction Compactly Supported Wavelet Packets with an Integer Dilation Factor

In this article, the notion of biorthogonal two-direction compactly supported wavelet packets with a positive integer dilation factor \alpha is introduced. A new approach for constructing biorthogonal two-direction 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 L^2(R) are obtained.