Normalizing the polynomial-match for the non-linear signal in transducers

A polynomial y = y0 + α1x + α2x2 + α3x3 + … can be used for matching a non-linear function y = f(x). The key is how to obtain its coefficients. In this paper, a normalized method is presented for matching any non-linear functions. There is a corresponding normalized polynomial y = y0 + an + bn2 + cn3 + …, n = x/x1, n1 = x1/x1 = 1, nmax = xmax/x1. ni is an integral, x1 is a ratio ruler of the abscissa x, then (α1α2α3…)T=(ax1−1bx1−2cx1−3…)T. a, b, c… can be obtained from the multiplication of normalized matrices. Two examples taken from transducers are presented. When the polynomial matches are used for two different sections in x abscissa, the conditions for continuation of the calculated values for these functions and their derivatives are discussed and the development of sine function in different sections of abscissa is presented as an example.