Generation of all-pole two-dimensional digital filters from the combination of all-pass filters

Two-dimensional digital filters are applied in signal processing and pro-imaging process, as well as 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 for designing all-pole 2-D digital filters with variable magnitude characteristics. In this thesis, 2-D digital filters starting from the identical analog 1-D second-order Butterworth lowpass filter are generated through the combination of all-pass filters in Category A and Category B. A new type of all-pole 2-D analog lowpass filter is designed through the combination of all-pass filters. The transfer functions of these filters are verified for stability. The 2-D analog lowpass filter has been transformed to the digital domain by applying generalized bilinear transformation. The design of the 2-D digital lowpass filter gives rise to 2-D digital highpass, bandpass and bandstop filters in Category A and Category B. The 2-D digital highpass and bandstop filters have been designed from the 2-D lowpass filter using appropriate generalized bilinear transformation in both the categories. The 2-D digital bandpass filter has been obtained by a combination of the 2-D digital lowpass and highpass filters in both the categories.;The effect of the coefficients of the generalized bilinear transformation on the 2-D digital filter's transfer function is studied in detail for Category A and Category B. In the end, an application of the proposed 2-D lowpass filter in Category A and Category B is illustrated in image processing. The designed 2-D low-pass filter has been used to reduce the effect of additive white Gaussian noise on digital images in both the categories.