联合分数变换相关器的分数相关特性分析

从分数傅里叶变换（FRFT）的定义出发，理论分析了联合分数变换相关器（JFRTC）的分数相关特性.从所得JFRTC的数学表达式中可以看出，将FRFT应用到联合变换相关器（JTC）中得到的JFRTC具有与传统JTC不同的性质.对于传统JTC，一旦输入平面上参考图像与目标图像之间的距离给定，相关输出峰的位置即确定，而JFRTC的相关输出峰的位置则可以由分数级次p₁和p₂来自由调节，这个特性在实际模式识别中非常有用.另一方面，JFRTC的相关输出峰值在大多数情况下低于传统JTC的相关峰值，却是JFRTC的一大缺点.最后，从FRFT的比例性质出发，给出了FRFT谱畸变不变的实现条件，并由此预言了JFRTC畸变不变模式识别的功能.

Fractional Correlation Properties of the Joint Fractional Fourier Transform Correlator

The mathematical expressions of the joint fractional Fourier transform correlator(JFRTC) are demonstrated,according to which,the properties of the JFRTC are discussed.It is shown that the properties of a JFRTC are different from that of a conventional JTC.In a conventional JTC,the distance between the two desired correlation signals at the output plane is fixed and is depended on the distance between the target and the reference images.However,by shifting the fractional orders,the distance between the two desired correlation signals at the output plane of a JFRTC can be changed larger or smaller than that of a conventional JTC.Besides,when the fractional order is shifted appropriately,the distortion of the fractional spectrum derived from the dimension distortion of the target image can be offset.Thus the JFRTC is predicted having the capability of distortion-invariant pattern recognition.On the other hand,the intensity of the desired correlation signals at the output plane of a JFRTC is always lower than that of a conventional JTC.