Gaussian Circular 2D FIR Filters Designed Using Analytical Approach

Abstract

This paper proposes an analytical design procedure for a particular class of 2D filters, namelyGaussian-shaped, circularly-symmetric FIR filters. We approach both low-pass and band-pass circular filters,which are adjustable in selectivity and peak frequency. The design starts from a given 1D Gaussian prototypefilter, approximated using the Chebyshev series. A frequency transformation is applied to derive the circularfilter. Several design examples are provided for both types of filters. The filters designed through this methodare efficient, their frequency response results in a factored or nested form, convenient for implementation.