A non-parametric approach for dynamic range estimation of nonlinear systems

ABSTRACT

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. Recent advances in analytical dynamic range estimation methods indicate that by systematically decomposing the system inputs into orthonormal random variables using a mathematical procedure called polynomial chaos expansion (PCE), output statistics of interest can be obtained for both linear and nonlinear systems. Despite its power for capturing both spatial and temporal correlation, the application of this method has been limited only to near-Gaussian inputs. In this paper, we propose the first algorithm with the capacity of handling both near-Gaussian and non-Gaussian input signals. Our method is based on the use of independent component analysis (ICA). Our experiments show that the new algorithm can reduce the original relative errors of 2nd order moments from 25% - 65% to 1% - 2%.

REFERENCES

• 1: Bin Wu , Jianwen Zhu , F. N. Najm, Dynamic range estimation for nonlinear systems, Proceedings of the 2004 IEEE/ACM International conference on Computer-aided design, p.660-667, November 07-11, 2004 [doi>10.1109/ICCAD.2004.1382658]
• 2: Roger G. Ghanem , Pol D. Spanos, Stochastic finite elements: a spectral approach, Springer-Verlag New York, Inc., New York, NY, 1991
• 3: R. G. Ghanem. The nonlinear gaussian spectrum of lognormal stochastic processes and variables. ASME Journal of Applied Mechanics, 66(4):964--973, 1999.
• 4: A. Hyvarinen, J. Karhunen, and E. Oja. Independent Component Analysis. John Wiley & Sons, New York, 2001.
• 5: A. Hyvarinen. Fast and robust fixed-point algorithms for independent component analysis. IEEE Transactions on Neural Networks, 10(3):626--634, 1999.

INDEX TERMS

Primary Classification:
  B. Hardware
  B.7 INTEGRATED CIRCUITS

General Terms:
Algorithms, Design, Theory

Keywords:
dynamic range estimation, independent component analysis, non-gaussian, non-parametric, nonlinear