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Application of linear canonical transform correlation for detection of linear frequency modulated signals

机译：线性典范变换相关在线性调频信号检测中的应用

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摘要

Linear canonical transform (LCT), which can be deemed to be a generalisation of the fractional Fourier transform, has been used in several areas, including signal processing and optics. Motivated by the operator theory, a new unitary operator associated with the LCT is introduced. This new operator generalises the unitary fractional operator which is proposed by Akay et al. recently. Via operator manipulations, the authors also derive a new definition, the LCT correlation operation, and present an alternative and efficient implementation of it. It is shown that the proposed LCT autocorrelation corresponds to radial slices of the ambiguity function in the ambiguity plane. On the basis of this relationship, an application of the fast LCT autocorrelation for detection and parameter estimation with respect to the chirp rates of linear frequency modulated signals corrupted by noise is proposed. Finally, the validity of the proposed method is verified by simulation results.
机译：线性规范变换（LCT）被认为是分数阶傅里叶变换的概括，已在包括信号处理和光学在内的多个领域中使用。受算子理论的启发，引入了一种与LCT相关的新型unit算子。这个新的运算符归纳了Akay等人提出的the式分数运算符。最近。通过操作员操作，作者还得出了一个新的定义，即LCT相关运算，并提出了它的另一种有效选择。结果表明，所提出的LCT自相关对应于歧义平面中歧义函数的径向切片。基于这种关系，提出了一种快速LCT自相关技术在检测和参数估计中针对被噪声破坏的线性调频信号的线性调频率的应用。最后，仿真结果验证了该方法的有效性。

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