Orthogonal two-direction compactly supported wavelet packets

Orthogonal two-direction wavelet packets with dilation α are introduced and discussed their properties by means of matrix theory and operator theory. A new approach for constructing orthogonal two-direction wavelet packets is developed. The formulas for performing iterations and decomposition are established. New Riesz bases for L²(R) are obtained by constructing a series of subspaces of the given orthogonal two-direction wavelet packets. As application, an example is given.