振幅指数衰减正弦干涉信号线性预测模型的求解

Linear prediction of exponential decaying sinusoidal superposition signal

在光谱成像的光谱分辨率增强技术中,对振幅衰减干涉信号的线性预测是其中的关键之一.文中在已知振幅指数衰减正弦干涉信号的个数、波数和衰减率的前提下,给出了线性预测系数直接计算公式及其前向线性预测系数与后向线性预测系数之间的关系;定义了该类正弦迭加信号的前向和后向线性可预测性条件.研究结果表明,振幅指数衰减的正弦迭加信号的前向和后向线性预测系数不再是简单的共轭对称关系了,但是二者依然是有联系的.该研究为一般的衰减干涉信号的光谱分辨率增强算法提供了理论基础.

In spectral resolution enhancement the linear prediction of exponentially decaying sinusoidal superposition signal is one of the key technologies.In this study,the direct calculating equations of forward and backward linear prediction coefficients,the relationship between forward and backward linear prediction coefficients,and the forward and backward linear predictability conditions are derived.It is shown that,for exponential decaying sinusoidal superposition signal,there is not simple conjugate symmetry between forward and backward linear prediction coefficients, but they are still related. This research provides a theoretical basis for spectral resolution enhancement about decaying interference signals.