Design of two-dimensional large-scale DFT-modulated filter bank

This study presents a novel property of the two-dimensional DFT-modulated filter bank and an efficient algorithm for designing the filter bank with large scale (with a large number of subbands and filters of large spatial support). It is firstly shown that the overall transfer function and aliasing transfer functions can be simply represented with the multiplication of the prototype filters and their modulated filters; a new property used to remarkably reduce the calculation of these functions. On the other hand, the design problem of the filter bank is formulated into an unconstrained optimisation problem. Based on the gradient vector, the conjugate gradient method is utilised to solve the design problem. The convergence of the proposed algorithm is analysed. Numerical examples and comparisons with other methods are included to show the performance of the algorithm.