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线性可逆变换在信号分析与信号处理领域有着广泛的应用,其中有一类线性可逆变换将连续变量(离散变量)的函数变换为连续变量(离散变量)的函数。本文讨论了这样一类线性可逆变换的对偶性,给出了正反变换之间对偶关系的一般表示式;得出了这类线性可逆变换存在对偶性的充分必要条件。利用信号变换中的对偶性,有利于更深入地揭示信号特性在时域与变换域的内在联系;并能方便地从信号的时域特性直接导出信号在变换域的相应特性,这在信号分析与信号处理中具有一定意义。
Linear reversible transform has a wide range of applications in signal analysis and signal processing. There is a class of linear reversible transformations that transform the continuous variable (discrete variable) function into a continuous variable (discrete variable) function. In this paper, we discuss the duality of such a class of linear reversible transformations, and give the general expression of the duality relationship between the forward and inverse transformations. We obtain the necessary and sufficient conditions for the duality of such linear reversible transformations. Utilizing the duality of the signal transformation, it is helpful to reveal the intrinsic relationship between the signal characteristics and the transform domain in more depth; and it is convenient to directly derive the corresponding characteristics of the signal in the transform domain from the time domain characteristics of the signal, And signal processing has a certain meaning.