Closed-form and real-time wordlength adaptation

FPGA and configurable computing-based DSP algorithms have demonstrated significant performance improvements over software implementations. This has caused renewed interest in developing or mapping DSP algorithms to custom hardware. An algorithm will be successfully mapped if the intermediate wordlengths can be reduced to maintain reasonable hardware size. We consider linear hardware cost functions, for which we can derive closed-form expressions for the reduced wordlengths. We then apply these results to an adaptive LMS filter, where we adapt not only the tap weights, but also the wordlengths as a function of the data in real-time.