Inverse Taylor series problem in linear filtering and related conjectures

This paper considers an inverse Taylor series problem and some related conjectures which arise in considering linear integral filters from a new viewpoint. The inverse Taylor series problem is defined as expanding a Lebesgue measurable function into a Taylor series by integration, which is an estimation problem.

[1]  R. E. Kalman,et al.  A New Approach to Linear Filtering and Prediction Problems , 2002 .

[2]  Xiao-Yun Lu,et al.  Integral filters from a new viewpoint and their application in nonlinear control design , 2000, Proceedings of the 2000. IEEE International Conference on Control Applications. Conference Proceedings (Cat. No.00CH37162).

[3]  W. Tranter,et al.  Signals and Systems: Continuous and Discrete , 1983 .

[4]  Van Valkenburg,et al.  Analog Filter Design , 1982 .

[5]  R. E. Kalman,et al.  New Results in Linear Filtering and Prediction Theory , 1961 .