Analysis of the coefficients of generalized bilinear transformation in the design of 2-D band-pass and band-stop filters and an application in image processing

Due to rapid progress in the field of speech and image processing, there is a greater need of a digital filter which possesses variable magnitude characteristics; one such filter is proposed in this paper. The proposed 2-D band-pass and band-elimination filters are designed from a 1-D low-pass Butterworth filter by applying a low-pass to band-pass and low-pass to band-stop transformations respectively. The resulting structure is converted to 2-D analog filter by making the series arm having impedances in s₁-domain and the shunt-arm impedances in the s₂-domain. The filters so obtained are digitized using the generalized bilinear transformations, thereby giving eight variables to be adjusted, giving a large number of possible magnitude characteristics. It is further shown how these filters can be utilized in reducing the noise content in images