Sum-of-products evaluation schemes with fixed-point arithmetic, and their application to IIR filter implementation

The signal processing and control algorithms are widely based on sum-of-products evaluation. In fixed-point arithmetic, the roundoff errors and coefficient quantization may have an important effect on the application´s performance and characteristics. As part of a global methodology on optimal fixed-point implementation of filters/controllers, this paper formalizes the various implementation schemes for sum-of-products in fixed-point arithmetic and automates the fixed-point code production. The order of the operations are considered, as their bit-width and the fixed-point representation of the coefficients, variables and partial results. Applied to linear filters, the output roundoff noise error is then evaluated and used as a criteria to find out interesting evaluation scheme. An example illustrates the approach.