Filtering error estimates and order of accuracy via the Peano Kernel Theorem
The Peano Kernel Theorem is introduced and a frequency domain derivation is given. It is demonstrated that the application of this theorem yields simple and accurate formulas for estimating the error introduced into a signal by filtering it to reduce noise. The concept of the order of accuracy of a filter is introduced and used as an organizing principle to compare the accuracy of different filters. (C) 2010 Elsevier B.V. All rights reserved.
filtering error order of accuracy peano kernel theorem equivalent nise bandwidth