Design of symmetric orthonormal wavelet filters using a single complex allpass filter

This paper gives a new class of real-valued symmetric orthonormal wavelet filters by using a single complex allpass filter. Firstly, the conditions that the complex allpass filter has to satisfy are derived from the symmetric and orthonormal conditions of wavelets. Then, from the viewpoint of the wavelet regularity, a new method is proposed for designing the proposed symmetric orthonormal wavelet filters with maximal flatness. In the proposed method, the maximally flat solutions can be easily obtained by solving a set of linear equations only