Dynamic range estimation for nonlinear systems

It has been widely recognized that the dynamic range information of an application can be exploited to reduce the datapath bitwidth of either processors or ASICs, and therefore the overall circuit area, delay and power consumption. While recent advances in analytical dynamic range estimation can deliver results accurate enough to account for both spatial and temporal correlation, the reported methods are only valid for linear systems. In this paper, we use a powerful mathematical tool, called polynomial chaos, which enables not only the orthogonal decomposition of random processes, but also the propagation of random processes through nonlinear systems with difficult constructs such as multiplications, divisions and conditionals. We show that when applied to interesting nonlinear applications such as adaptive filters, polynomial filters and rational filters, this method can produce complete, accurate statistics of each internal variable, thereby allowing the synthesis of bitwidth with the desired tradeoff between circuit performance and signal-to-noise ratio.