基于自适应短时Chirplet分解的高性能时频分布重构  

High-Performance Time-Frequency Distribution Reconstruction Based on Adaptive Short-Time Chirplet Decomposition

作　　者：杨阳[1] 程永强 吴昊[1] 杨政 王宏强[1] YANG Yang;CHENG Yongqiang;WU Hao;YANG Zheng;WANG Hongqiang(College of Electronic Science and Technology,National University of Defense Technology,Changsha,Hunan 410073,China)

机构地区：[1]国防科技大学电子科学学院,湖南长沙410073

出　　处：《信号处理》2023年第11期1943-1956,共14页Journal of Signal Processing

基　　金：国家自然科学基金(61921001);湖南省杰出青年基金(2022JJ10063)。

摘　　要：通过傅里叶变换得到的频谱能够反映信号所包含的频率成分,但无法揭示瞬时频率随时间的变化特性。为满足工程应用中大量非平稳信号的分析需求,能够同时描述信号时域和频域特征的时频分析方法得到了广泛关注和深入研究。然而,传统时频分析方法所得到的时频分布往往具有较低的能量聚集性和较强的交叉项干扰,难以支撑信号时频特征的准确表达和提取。通过对信号内在稀疏特性进行挖掘和利用,能够有效提升信号时频分布的质量。本文通过对信号的相位函数进行泰勒展开,阐述了信号稀疏时频分解的实质,并分析了现有稀疏类时频分析的方法不足。在此基础上,提出了一种基于自适应短时Chirplet分解的高性能时频分布重构方法。首先,利用与信号时频特性自适应的窗函数为每一时刻生成了具有最强拟平稳性的最优短时信号;其次,提出了一种Chirplet字典的简化设计方法,利用得到的Chirplet字典对上述短时信号进行稀疏分解,基于分解结果实现了短时信号中心时刻瞬时频谱的参数化重构;最后,按时间顺序排列所有时刻的瞬时频谱,得到了信号能量聚集性高且不含任何交叉项干扰的高性能时频分布。仿真实验表明,所提方法有效改善了传统稀疏类时频分析方法结果中时频曲线畸变的问题,同时在计算效率上具有较大优势。此外,本文还利用所提方法处理了实际雷达系统所采集的微动目标回波,进一步验证了所提方法的有效性和应用潜力。The spectrum obtained by Fourier transform(FT)could clearly reflect the frequency component contained in the signal,but was not able to reveal the time-varying characteristics of the instantaneous frequency function.In order to meet the analysis requirements of a large number of non-stationary signals in engineering applications,time-frequency(TF)analysis(TFA)methods,which could simultaneously describe the characteristics of signals in the time domain and the frequency domain,had been widely concerned and deeply studied.However,the TF distribution(TFD)obtained by traditional TFA methods were difficult to express the signal’s TF feature precisely due to the poor energy concentration and serious cross-term interference.The quality of the signal’s TFD could be effectively improved by utilizing the inherent sparsity of the signal.In this paper,the essence of the sparse TF decomposition was clarified through the Taylor expansion of the signal’s phase function,and the shortcomings of existing sparsity-based TFA algorithms were fully analyzed.On this basis,a reconstruction method of the high-performance TFD based on the adaptive short-time Chirplet decomposition(ASTCD)was proposed.Firstly,the optimal short-time signal segment with the strongest quasi-stationary property was generated for each time instant by using the window whose width had been set to be adaptively varying with the signal’s TF feature.Secondly,a simplified design scheme of the Chirplet dictionary was proposed and the obtained Chirplet dictionary was employed for the sparse decomposition of the above-mentioned short-time signal segments.Moreover,the results of the sparse decomposition were further employed to realize the parametric reconstruction of the instantaneous spectrum of the short-time signal’s center time instant.Finally,the high-performance cross-term-free TFD with high energy concentration was generated by arranging all instantaneous spectra in chronological order.Simulation results confirmed that the proposed method can effectively

关 键 词：时频分析 非平稳信号 稀疏表示 Chirplet字典 字典设计 

分 类 号：TN911.7[电子电信—通信与信息系统]