基于短时分数阶傅里叶变换的谱分割算法

多分量非线性调频信号在现代通信和雷达系统中应用越来越广泛，而对其进行有效分析识别的常用算法就是短时分数阶傅里叶变换（Short Time Fractional Fourier Transform，STFRFT）.文章首先讨论了STFRFT的圆特性，证明了它基于高斯旋转窗的非圆性并给出了修正的圆的STFRFT定义；在此基础上研究了时频变换后不同时频点的谱峭度，进而推导出了区域集的谱峭度，并将该区域谱峭度作为谱图上某区域内是否含有信号点的检测因子；最后基于区域集谱峭度的区域增长算法被用于从谱图中盲分割识别出各个非线性调频分量信号.仿真实验验证了所提算法的有效性和鲁棒性.

A new spectral segmentation algorithm based on short time fractional Fourier transform

The short time fractional Fourier transform (STFRFT) is a useful tool for the research on analysis and recognition of multi-component non-linear frequency modulation (NLFM) signals,which have been presented on a lot of communication systems and radar systems.This paper investigates the non-circularity of STFRFT coefficients,and proposes a modified STFRFT such that all coefficients coming from white Gaussian noise are circular.In order to use the spectral kurtosis (SK) as a Gaussian test to check if signal points are present in a set of STFRFT points,we study the SK of different points in the time-frequency transform figure,and propose the definition of the local SK.Finally,a time-frequency segmentation algorithm based on the region growing by the local SK is proposed to separate the multicomponent NLFM signals.The effectiveness and robustness of this algorithm are evaluated via simulations.