四元数和超复数在二维二次非线性相位耦合分析中的应用

针对二维二次非线性相位耦合分析中的分维配对问题,本文首先对一般二维谐波信号模型进行变换,构造了符合四元数结构的新的信号模型.接着讨论了Hamilton四元数、三维超复数及"新四元数"在估计二维谐波频率中的可能性.最后根据上述模型利用特殊的三阶累积量切片分析了加性高斯有色噪声中二维二次非线性相位耦合及联合Hamilton四元数和超复数在二维二次非线性相位耦合中的应用前景.此方法避免了在复数模型的二维二次非线性相位耦合分析中构造复杂的增广矩阵,并从根本上解决了通过分维求取频率之后,频率配对中所有可能产生的错误频率对,以及有可能产生的两维频率估计精度的不平衡性.仿真实验验证了本文的理论.

Quadratic nonlinear coupling analyse of two-dimensional harmonics in Gaussian noise with quaternion and hypercomplex

The pairing steps are always needed when we estimate the frequency pairs of quadratic nonlinear coupling which is described by complex signals. Here the quaternion and hypercomplex is applied to the quadratic nonlinear coupling analyse. First we construct the quaternion signal model through the separated signal and its Hilbert transform. Then we define the corresponding three order cumulant to restrain the addition Gauss coloured noise and extract the coupling and coupled frequency using the properties of Hamilton quaternion and hypercomlex. This method avoids constructing complicated extended matrix, and accounts for the error frequency pairs and the imbalance of the two frequencies of the frequency pairs. Some simulations are given to verify the algorithm in this paper.