Arithmetic in the Design of Linear Time-Invariant Filters

This chapter provides an arithmetic-centered point of view on the construction of hardware digital filters. Such filters combine arithmetic components (adders and multipliers) with memory. The design of the arithmetic must take into account this memory. This chapter introduces the relevant concepts and then provides two definitions of faithfulness for hardware digital filters: faithful to an ideal linear time-invariant filter and faithful to a frequency specification. With these definitions, filter design and implementation become a single global optimization problem.