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本文讨论了A题给出的一类非线性交调的频率设计问题。首先根据题中给出的数据用最小二乘法求出适合本题要求的输入输出函数,设计出一种简洁算法用计算机求出了适合要求的解,然后对解的稳定性进行了讨论。本文的最后一部分,对解的各种数学性质做了进一步讨论,证明了本文主要结果:给出了适合本题要求的解的充分必要条件(定理1)。应用这一结果可以直接求出适合本题的频率约束的解。
In this paper, we discuss the frequency design of a class of nonlinear crosstalk given in Problem A. First of all, based on the data given in the title, we find the input / output function that fit the requirements of this project by using the least square method. We design a simple algorithm to find the suitable solution by computer, and then discuss the stability of the solution. In the last part of this paper, the further discussion on various mathematical properties of the solution proves the main result of this paper: a sufficient and necessary condition for the solution to the problem is given (Theorem 1). Application of this result can be directly obtained for the problem of frequency constraint solution.