Design of Q-shift filters with flat group delay

Q-shift filters have been proposed by Kingsbury for DTCWTs (Dual Tree Complex Wavelet Transforms), and are required to have linear phase responses. This paper proposes a new method for designing Q-shift filters with flat group delay responses. The proposed design method make use of the transfer function proposed by Gopinath, which satisfies both the specified degree of flatness for the group delay and the specified number of vanishing moments, i.e., the specified number of zeros at z = -1. Therefore, the design is reduced to how to force the filter to satisfy the condition of orthogonality. The design problem is linearized, and then an iterative procedure is used to obtain the filter coefficients. Finally, some examples are presented to demonstrate the effectiveness of the proposed design method.