Design of Q-shift filters with improved vanishing moments for DTCWT

Q-shift filters have been used in the Dual Tree Complex Wavelet Transform (DTCWT), and are required to have a well-controlled group delay. This paper proposes a new method for designing Q-shift filters with improved vanishing moments. The proposed design method allows the flatness condition of the group delay response to be included along with the vanishing moments and orthogonality of wavelets. Therefore, the resulting Q-shift filters possess flat group delay responses. Moreover, the number of vanishing moments can be arbitrarily specified by locating the desired number of zeros at z = -1. Finally, one example is presented to demonstrate the effectiveness of the proposed design method.