Iterative design of two-dimensional critically sampled MDFT modulated filter banks

• The PR condition in spatial-domain is firstly derived for 2D MDFT modulated filter bank.
• An efficient algorithm is proposed to design the filter bank by using the PR condition.
• Numerical examples verify the effectiveness of the proposed algorithm.

In this paper, an efficient design algorithm is proposed to design the recently introduced two-dimensional (2D) critically sampled modified DFT (MDFT) modulated filter bank. First of all, the original perfect-reconstruction (PR) condition in frequency-domain of the filter bank is transformed into a spatial-domain condition, which is a set of quadratic equations with respect to the prototype filter (PF). Then, with the derived PR equations, the design problem is formulated into an unconstrained optimization problem that involves PR condition and stopband energy of the PF. An iterative algorithm is proposed to solve the optimization problem. The convergence of the algorithm is proved. Numerical results and comparison with existing method are included to show the effectiveness of the proposed design algorithm.