Abstract:

When the Difference Theorem is applied to calculating the derivative of discrete data, the measure-error can lead to inaccurate result or some of the data having no result. To resolve these problems, the necessary and sufficient conditions for identifying approximative inflexions of the difference-curve are obtained by analyzing and deducing applying conditions of the Difference Theorem on condition that the data are at equal intervals. In the condition of measure-error existing, the applying conditions of the Difference Theorem are obtained by analyzing, and test and verified by using test-function. The results are compared with those from center-smoothing algorithm, cubic spline algorithm and different fitting models. The factors which can affect application effects of the Difference Theorem are analyzed and validated by using measurement data. The detailed method of calculating second order derivative with the Difference Theorem and it's deduction is put forward.

Key words: The difference theorem, Derivative, Digital filtering, Truncation error, Inflexion