Error analysis of FIR filters implemented using logarithmic arithmetic

The principal factors influencing the design and implementation of most real-time digital filters are accuracy, speed, and ease of implementation. In this work, the effects of roundoff noise in finite-impulse response (FIR) digital filters implemented using a logarithmic number system are examined. Expressions for the ratio of output variance with roundoff errors to output variance without roundoff errors are derived. The noise performance of logarithmic FIR filters is compared to that of floating-point FIR filters. Simulation results are provided which confirm the theoretical results of error analysis.