2-D digital filters using logarithmic number systems

Procedures for the design of 2-D digital filters for real-time image processing using logarithmic number systems are explored. The analysis is limited to logarithmic systems having only nonnegative exponents; reliance is placed on computation of the filter coefficients on a uniform grid of feasible points. It is shown that the maximum quantization error depends on the size of the filter coefficient, and the maximum useful word length is obtained. An alternative procedure is outlined which can be iterated if an unsatisfactory solution is found. Tables of limiting values, error functions, and filter coefficients are provided.