传感器与固体电子学中非线性函数多项式拟合的规范化

Normalizing the Polynomial-Match for a Non-Linear Function in Sensors and Solid Electronics

多项式可用于非线性信号的拟合,关键在于求解其各项系数。对于任何非线性函数,文中提出都有一个规范化的拟合方法。相应有一个规范化的多项式。该规范化多项式是以整数n为底的幂级数,最大幂次n_(max)是x坐标区间的等分数,其系数可用一个规范化的矩阵积得到。我们给出了固体电子学中的两个应用实例。当x坐标区间分段拟合应用时,还讨论了函数及其导数计算值的连续性条件,并以正弦函数不同区间的展开为例,作了演示。

A polynomial can be used for matching a non-linear function.The key is how to obtain its coefficients.A normalized polynomial method is presented here for matching any non-linear function. There is a corresponding normalized polynomial which consists of a power series with the integral n as base. The maximum base nmax is the division number within range of x abscissa. The coefficients of this normalized polynomial can be obtained from the multiplication of normalized matrixes. One example used in solid electronics are presented. When the polynomial match are used for two different sections in x abscissa, the conditions for continuation of the calculated values for these functions and their conductive are discussed and the development of sine function in different sections of abscissa is presented as an example.