A new class of complex compact-supported orthonormal symmlets

This paper presents a new class of complex-valued compact-supported orthono rmal symmlets. Firstly, some properties of complex-valued compact-supported orthonormal symmlets are investigated, and then it is shown that complex-v alued symmlets call be generated by real-valued half-band filters. Therefor e, the construction of complex-valued symmlets can be reduced to the design of real-valued half-band filters. Next, a design method of real-valued hal f-band FIR filters with some flatness requirements is proposed. For the max imally Bat half-band filters, a closed-form solution is given. For the filt er design with a given degree of flatness, the design problem is formulated in the form of linear system by using tilt: Remez exchange algorithm and c onsidering the given flatness condition. Therefore, a set of filter coeffic ients can be easily computed by solving a set of linear equations, and the optimal solution is obtained through a few iterations. Finally, some design examples are presented to demonstrate the effectiveness of the proposed me thod.