A study of the effects of the coefficients of generalized bilinear transformations in design of two-dimensional variable recursive digital filters

Two-dimensional variable recursive digital filters are applied in signal processing and communication systems where the frequency-domain characteristics of digital filters are required to be adjustable. The main objective of this thesis is to propose a new technique of designing 2-D recursive digital filters with variable characteristics. From a 1-D second order Butterworth low-pass analog ladder structure, 2-D low-pass and high-pass digital filters can be obtained through the application of double generalized bilinear transformations when the coefficients of the transformations are chosen in their specified ranges. And when one or more these coefficients are changing, the resulting 2-D low-pass and high-pass filters possess variable magnitude responses. Another two important types of 2-D digital filters, 2-D band-pass and band-elimination filters, can also be obtained by properly combining a 2-D low-pass filter and a 2-D high-pass filter. When the coefficients used to obtain the 2-D low-pass and high-pass filters are changeable, the resulting 2-D band-pass and band-elimination filters also possess variable magnitude characteristics. The manner how each coefficient of generalized bilinear transformation affects each type of desiring 2-D recursive digital filters is investigated in detail. Stability is always an important issue in 2-D recursive digital filter design. The stability conditions of generalized bilinear transformation and the stability conditions of the 2-D digital filters having a denominator with single degree of each variable are discussed in detail here.