On efficient implementations of 2-D digital filters using logarithmic number systems

The implementation of 2-D digital filters using logarithmic number systems (LNS's) is discussed in detail. The properties of such systems are derived with reference to an iterative rounding scheme, which allows increasing the accuracy of the filter coefficient representation by using more than one power of the base a. The optimization of the base is proposed as an efficient tool for the design of accurate 2-D filters. Different design strategies are considered, together with a discussion of the degree of precision required for the circuits which determine the base of the LNS. The efficiency and versatility of this approach are demonstrated with several design examples in 2-D.