分数傅里叶变换域的调频信号稀疏性研究

Research on sparsity of frequency modulated signal in fractional Fourier transform domain

调频信号广泛应用于声纳、雷达、激光和新兴光学交叉研究领域,其紧致性(稀疏性)是调频信号采样、去噪、压缩等研究中面临的共性基础问题。本文致力于研究调频信号在分数傅里叶变换域的稀疏性,提出了一种最大奇异值法来估计调频信号的紧致分数傅里叶变换域。该方法利用调频信号幅度谱的最大奇异值来度量其紧致域,并应用鲸鱼优化算法来搜寻紧致域,有效改善了现有方法的不足。与MNM和MACF方法相比,本文方法给出了调频信号在分数傅里叶变换域更加稀疏的表征,具有更少的重要振幅数。最后,给出了该方法在调频信号滤波中的初步应用。

Frequency modulated(FM)signal is extensively applied in sonar,radar,laser and emerging optical cross-research,its sparsity is a common basic issue for the sampling,denoising and compression of FM signal.This paper mainly studies the sparsity of FM signal in the fractional Fourier transform(FRFT)domain,and a maximum singular value method(MSVM)is proposed to estimate the compact FRFT domain of FM signal.This method uses the maximum singular value of amplitude spectrum of FM signal to measure the compact domain,and WOA is used to search the compact domain,which effectively improves the shortcomings of the existing methods.Compared with MNM and MACF,this method gives a sparser representation of FM signal in the FRFT domain,which has less number of significant amplitudes.Finally,the primary application of this method in the FM signal filtering is given.