Abstract

A new approach to generate 2-D filters having variable magnitude characteristics has been proposed. In this work, 2-D digital filters starting from a singly terminated network is generated. A new type of Continued Fraction Expansion obtained from a singly terminated network is considered, its stability defined and stable 2-D analog lowpass filters have been generated. The 2-D analog lowpass filters have been transformed to digital domain by applying generalized bilinear transformation. The 2-D digital lowpass filters give rise to 2-D digital highpass, bandpass and bandstop filters. The 2-D highpass and bandstop filters have been generated from 2-D lowpass filters using appropriate transformations. The 2-D bandpass filter has been obtained by a combination of lowpass and highpass filters. The 2-D digital filters are classified into four sets. The classification of four sets is based on the coefficients of the Continued Fraction Expansion. Each set is further classified into four cases. The classification of four cases in each set is based on the coefficients of the generalized bilinear transformation. The effects of the coefficients of the generalized bilinear transformation in each case and the effects of the coefficients of the Continued Fraction Expansion (CFE) in each set are studied. In the end, some basic examples of implementation of 2-D digital lowpass filters in image processing are illustrated. The examples include reducing added Gaussian noise from images by using 2-D lowpass filtering.

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