论文部分内容阅读
引入了一类新的积分变换，即对称变换．这类变换在空间域和空间频率域中实现的变换操作是相同的．换句话说，如果一个积分变换器对信号本身及其Ｆｏｕｒｉｅｒ频谱作相同的变换操作，那么这种变换即为对称变换．给出了对称变换的成立条件，即当积分变换核是所谓的类自Ｆｏｕｒｉｅｒ变换函数时，此变换即为对称变换．并提出了类自Ｆｏｕｒｉｅｒ变换函数的一种构造方式．同时还指出，光学中的分数Ｆｏｕｒｉｅｒ变换即是一种对称变换
A new type of integral transformation is introduced, that is, symmetric transformation. The transformations implemented in this type of transformation are the same in the spatial and spatial frequency domains. In other words, if an integral transformer performs the same transformation on the signal itself and its Fourier spectrum, then this transformation is a symmetric one. The conditions for the establishment of symmetric transformation are given. That is, when the integral transformation kernel is a so-called self-Fourier transformation function, the transformation is symmetric transformation. And a class of self-Fourier transform function is proposed. It is also pointed out that the fractional Fourier transform in optics is a kind of symmetric transformation