High performance low cost implementation of FPGA-based fractional-order operators

Hardware implementation of fractional-order differentiators and integrators requires careful consideration of issues of system quality, hardware cost, and speed. This paper proposes using field programmable gate arrays (FPGAs) to implement fractional-order systems, and demonstrates the advantages that FPGAs provide. As an illustration, the fundamental operator s to a real power is approximated via the binomial expansion of the backward difference. The resulting high-order FIR filter is implemented in a pipelined multiplierless architecture on a low-cost Spartan-3 FPGA. Unlike common digital implementations in which all filter coefficients have the same word length, this approach exploits variable word length for each coefficient. Our system requires twenty percent less hardware than a system of comparable quality generated by Xilinx's System Generator on its most area-efficient multiplierless setting. The work shows an effective way to implement a high quality, high throughput approximation to a fractional-order system, while maintaining less cost than traditional FPGA-based designs.