Dynamic-range estimation

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 application-specific integrated circuits and, therefore, the overall circuit area, delay, and power consumption. While recent proposals of analytical dynamic-range-estimation methods have shown significant advantages over the traditional profiling-based method in terms of runtime, it is argued here that the rather simplistic treatment of input correlation and system nonlinearity may lead to significant error. In this paper, three mathematical tools, namely Karhunen-Loegraveve expansion, polynomial chaos expansion, and independent component analysis are introduced, which enable not only the orthogonal decomposition of input random processes, but also the propagation of random processes through both linear and nonlinear systems with difficult constructs such as multiplications, divisions, and conditionals. It is shown 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 trade off between circuit performance and signal-to-noise ratio