Efficient Design Procedure for Circular Filter Banks

Abstract

In this work an efficient analytic design method for 2D zero-phase circular filter banks is described. They are obtained from 1D prototype filters with specified bandwidth, to which a particular frequency transformation is applied. The filters resulted through this procedure have a precise circular shape even close to frequency plane margins and they have a very steep transition for relatively a low order, thus being very efficient. The frequency response results directly factored, thus the large filter matrices are decomposed as a convolution of smaller sixe matrices, which simplifies the implementation and allows to realize the filtering sequentially, in several steps. A design example is provided for a circular filter bank with eight components. The proposed method is based entirely on accurate approximations and frequency mappings, without resorting to any global numerical optimization algorithms. Simulation results of filtering on test images are also provided.