On Numerical Robustness of Bi-quad Structures using Fixed-Point Approximate Multiplication

Peter Koch, Jan Østergaard, Ove Andersen

Abstract: Digital filters are key components in many applications related to wireless personal communication and multimedia devices, some even portable and battery powered. The ability to design and implement cost efficiently such filters is therefore of significant importance. Recursive filters are known to have low computational complexity (number of multiplication and addition) but at the same time they are numerically sensitive due to their feedback loop. Therefore, using arithmetic functional units with reduced accuracy might introduce some challenges, despite their proficiency in physical size, execution time, and power consumption. We are therefore interested in investigating to what extent approximate multiplication can be used in different types of bi-quad sections, which is the fundamental building block in higher order IIR filter systems. We found that it is possible to operate three selected types of such implementation structures in the presence of additive noise from multipliers with different degree of approximation, and we show that there are significant performance differences of the structures, both in the time- and in the frequency domain.