Fast design of 2D fully oversampled DFT modulated filter bank using Toeplitz-block Toeplitz matrix inversion

• The stopband energy matrix is a Toeplitz block Toeplitz matrix.
• The algorithm complexity of is largely reduced via matrix inverse lemma..
• The proposed algorithm is suitable for designing 2D high-complexity DMFB.

This letter presents a low-complexity algorithm to design two-dimensional (2D) DFT modulated filter bank (DMFB) with nearly perfect reconstruction (NPR). The design problem is formulated into an unconstrained optimization problem whose cost function consists of the overall distortion and stopband energy. By exploiting the gradient information, the prototype filter (PF) coefficients are iteratively optimized with closed-form formula. At each iteration, the computational complexity is dramatically reduced by evoking Toeplitz-block Toeplitz matrix inversion and matrix inversion lemma, which makes the algorithm suitable for design 2D DMFB with a large number of channels and PF coefficients. Numerical example and comparison are included to show the effectiveness of the proposed design algorithm.