基于线性正则变换与短时傅里叶变换联合的时频分析方法

A Time-frequency Analysis Method Based on Linear Canonical Transform and Short-time Fourier Transform

线性正则变换作为傅里叶变换、分数阶傅里叶变换更为广义的形式,已经在光学和信号处理等领域得到了应用.短时傅里叶变换是一种线性时频分布,避免了其他双线性时频分布中出现的交叉项干扰,是分析时频信号的有力工具.本文从线性正则变换的定义和性质出发,研究了线性正则变换与短时傅里叶变换的时频关系,提出了基于线性正则变换与短时傅里叶变换联合的时频分析方法,避免了交叉项问题能够实现chirp信号干扰抑制和多分量时频信号分离.最后用仿真实例表明,该方法是分析时频信号的有效手段.

The linear canonical transform（LCT）,which is a generalization of the Fourier transform and the fractional Fourier transform,has been used in many fields of optics and signal processing.The short-time Fourier transform（STFT） is a kind of linear Time-Frequency Representations（TFRs）.Compared with many bilinear TFRs,the STFT does not have the cross-term problem.Because of this advantage,the STFT becomes an important time-frequency analysis tool.Starting with the LCT＇s definition and its properties,many useful relations between the LCT and the STFT have been derived.Based on these relations,we present a new time-frequency signal analysis method,which has no cross-terms problem.It can be used to realize interference suppression of chirp signals and separate components from a time-frequency signal.Finally the simulation results illustrate the validity of the proposed method.