Hilbert pair of almost symmetric orthogonal wavelets with arbitrary center of symmetry

This paper proposes a new method for designing a class of Hilbert pairs of almost symmetric orthogonal wavelets with arbitrary center of symmetry. Two scaling low-pass filters are designed simultaneously to satisfy the specified degree of flatness of group delays, vanishing moments and orthogonality condition of wavelets, along with improved analyticity. Therefore, the resulting scaling low-pass filters have flat group delay responses and the specified number of vanishing moments. Moreover, the difference of the frequency responses between two scaling low-pass filters can be effectively minimized to improve the analyticity of complex wavelets. The condition of orthogonality is linearized, and then an iterative procedure is used to obtain the filter coefficients. Finally, several examples are presented to demonstrate the effectiveness of the proposed design procedure.