Optimal Design of Multiplierless Second-Order Infinite Impulse Response Digital Filters
Rémi Garcia, Alexandre Goldsztejn, Jonas Kühle, Martin Kumm, Anastasia Volkova · HAL (Le Centre pour la Communication Scientifique Directe) · 2021
In this work we solve the problem of design of optimal multiplierless second-order Infinite Impulse Response (IIR) filters. Given a frequency specification, we design a filter with fixed-point coefficients yielding minimal number of adders when evaluated with Direct Form. The coefficient design and quantization steps, typically conducted independently, are now gathered into one global optimization problem, modeled through mixed integer linear programming and efficiently solved using generic solvers. Moreover, we guarantee the frequency-domain stability of the filter, increasing the confidence in the result. The generated filters are implemented and synthesized using our new operators within FloPoCo IP core generator for Field Programmable Gate Arrays (FPGA). With respect to state-of-the-art two-step filter design methods our one-step optimal design approach achieves, on average, 42% reduction in number of lookup tables (LUT) and 21% improvement in delay.