二元信号线性滤波的完整框架
A complete framework for linear filtering of bivariate signals
摘要：
基于裁剪四元数傅里叶变换，提出了一个完整的二元信号线性时不变滤波理论框架。这个框架的特点是直接描述的LTI滤波器的本征特性，使紧凑的演算和物理上可解释的频域滤波关系。具有偏振光学基本特性（双折射、双衰减）的滤光片的设计是简单的。它产生了一个有效的频谱合成方法和新的见解维纳滤波的双变量信号与规定的频率相关的偏振特性。这个通用的框架有利于原始描述的双变量信号在两个组件与特定的几何或统计特性。数值实验支持我们的理论分析，并说明合成数据的方法的相关性。
英文摘要：
A complete framework for the linear time-invariant (LTI) filtering theory of bivariate signals is proposed based on a tailored quaternion Fourier transform. This framework features a direct description of LTI filters in terms of their eigenproperties enabling compact calculus and physically interpretable filtering relations in the frequency domain. The design of filters exhibiting fondamental properties of polarization optics (birefringence, diattenuation) is straightforward. It yields an efficient spectral synthesis method and new insights on Wiener filtering for bivariate signals with prescribed frequency-dependent polarization properties. This generic framework facilitates original descriptions of bivariate signals in two components with specific geometric or statistical properties. Numerical experiments support our theoretical analysis and illustrate the relevance of the approach on synthetic data.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
