Short Time Lv Transform Research For Nonlinear Frequency Modulated Signal Sensing

Frequency modulation(FM)signal refers to the signal whose frequency changes with time during the duration.It is widely used in various information systems including radar,sonar and communication.According to the different law of frequency variation,frequency modulation signal can be divided into linear frequency modulation(LFM)signal and nonlinear frequency modulation signal.The nonlinear frequency modulation signal is a kind of non-stationary signal.It is difficult to obtain the accurate information directly by the traditional analysis method.As a powerful tool for analyzing time-varying non-stationary signals,time-frequency analysis,short for time-frequency joint domain analysis,has become a hot topic in modern signal processing research.The time-frequency analysis method provides joint distribution information of time domain and frequency domain,and clearly describes the relationship between signal frequency and time.Short Time Lv Transform(STLVT)is an important time-frequency analysis method,and its basic idea is to segment the signal with windows and each segmented signal is analyzed respectively and finally summarized.STLVT has advantages over other time-frequency analysis methods that it has a high resolution in the processing of nonlinear FM signals and can eliminate cross-term interference when processing multi-component nonlinear FM signals.However,STLVT has two defects: first,it cannot determine the optimal window length.Second,the same window length must be used for the entire signal and the window length cannot be adjusted.Therefore,this thesis focuses on these two defects of STLVT.The specific contents of this thesis are as follows:(1)Aiming at STLVT's inability to determine the optimal window length,this thesis proposes the optimal Lv transform,OWLT for short,to optimize the window length.In OWLT,skewness is used as the standard to measure the performance of the algorithm,and the optimization model is designed based on the random approximation method.OWLT will calculate the optimal window length to maximize the energy aggregation degree of short-time Lv transform,and then perform window segmentation with the optimal window length to complete short-time Lv transform.(2)Aiming at STLVT's defect of not being able to adjust the window length,this thesis proposes an adaptive window length Lv transform(Adaptive Window Lv Transform,AWLT for short).AWLT will use a longer window length where the signal frequency function waveform is nearly linear,and a shorter window length where the signal frequency function waveform has obvious nonlinear characteristics.AWLT uses skewness as a measure of algorithm performance to determine whether to continue the adaptive process based on the size of the skewness.Compared with the original STLVT and OWLT,AWLT can make the time-frequency information obtained by time-frequency analysis more accurate and have higher energy aggregation degree,but the calculation of AWLT is more complex and slower.(3)This thesis will add digital watermarks to the images using the nonlinear frequency modulation signals,analyze the images using the OWLT and AWLT methods,and determine whether there is a target watermark in the image.The results of digital watermarking perception using OWLT and AWLT are presented and compared with the results of the original STLVT method,so as to reflect the advantages of OWLT and AWLT and the application value of the research content of this thesis.