Filter realization structures are synoptic diagrams that plot the way different arithmetical operations such as additions, multiplications, and shifts are connected.
When we are operating in infinite precision – that is, when there are no quantification errors – all structures will yield the same results. However, quantification errors and coding of different parameters on processors operating in fixed-point will affect structures, which then will not yield the same filtering results. In this way, an IIR filter assumed to be stable can, during its implantation, lead to unstable filters if the appropriate realization structure has not been chosen. This is due to the fact that the structures do not have the same sensitivity to quantification, truncation, and round of errors.
This chapter is organized as follows: first, we will present structures dedicated to FIR and IIR filters. We will look closely at direct and cascade structures. We will discuss second-order cells. Then, we will present ways of choosing finite precision structures by lowering sensitivity through manipulating quantification error.
Chapter written by Mohamed NAJIM and Eric GRIVEL.