Abstract
An expression for the direct convolution of two-dimensional infinite impulse response digital filters, which corresponds to that presented by Gold and Jordan for one-dimensional filters, is derived. Specifically, the output of the filter is given in terms of the input and output values and a set of initial conditions. The analysis is based on the two-dimensional block realization model. The cases of the quarter plane, non-symmetric half-plane and symmetric half-plane, primarily with respect to the required initial conditions, which are given explicitly, are considered.
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