Publication

Abstract : A filter structure that can realize 2D circular filters of different bandwidths, which can be controlled by any arbitrary rational values without changing the overall architecture and without having the prior knowledge of the bandwidths to be realized, is the main contribution of this work. Here, a multiplier-less transformation is made use of to obtain the two dimensional (2D) filter from its one dimensional (1D) counterpart. The first stage of the work involves the design of a Farrow structure based variable bandwidth 1D filter. The Farrow filter obtained is of non-linear phase and since the transformation based methods to design the 2D filters can be applied only to the linear phase 1D filter, a fold and average block are employed to convert the 1D Farrow filter into linear phase. Finally, to map the coefficients from 1D to the 2D domain, a multiplier-free transformation is employed. Thus, by cascading a 1D Farrow filter with a fold and average block and transformation block, different circular filters with a wide range of bandwidths decided by tuning a single parameter in the 1D domain are obtained. Hence, the complexity of implementation of this proposed arbitrarily variable circular filter involves only the complexity of realizing a 1D Farrow filter, a fold and average block and the transformation block. The fine adjustability in bandwidths and the performance parameters of the 2D filters resulting from the proposed architecture are illustrated with the help of variable low-pass and band-pass circular filters.