Error analysis of FIR filters implemented with 1-digit 2-dimensional logarithmic number systems

Multi-dimensional logarithmic number system (MDLNS) is a recently developed number representation that is very efficient for implementing the inner product step processor (IPSP). The effects of data mapping and conversion in finite-impulse response (FIR) digital filters implemented with 1 digit 2-dimensional logarithmic number (2-DLNS) are examined. Expressions for the ratio of output variance with errors to output variance without errors are derived. The simulation results indicate that the experimental results are in good agreement with the theoretical results. It is shown that the FIR filters implemented using 2-DLNS result in lower error-to-signal variance than that implemented using LNS and FPNS as well as potential hardware reduction of the entire filter