A New Phase-Factor Design Method for Hilbert-Pairs of Orthonormal Wavelets

A new method is proposed for designing Hilbert transform pairs of orthonormal wavelet bases with improved analyticity. Selesnick proposed a simple common factor technique for designing the Hilbert transform pairs in [7], where the phase factor is required to satisfy the half-sample delay condition, while the common factor is used to obtain the maximum number of vanishing moments and to satisfy the condition of orthonormality. To improve the analyticity of complex wavelets, we propose a novel method to design the phase factor by using the Remez exchange algorithm, so that the difference in the frequency response between two scaling lowpass filters is minimized. One design example is presented to demonstrate the effectiveness of the proposed method.