Linear Fm Wave Detection And Estimation Simplify The Discussion

The Linear Frequency-Modulated signal (LFM) has been applied widely to many fields of information system, such as communications, radar, sonar, earthquake recognition etc. In these systems, the Detection and Parameter Estimation of the Multi-Linear Frequency Modulated signals was an important research problem all the times. As the Fourier Transform couldn't solve the LFM signals, multifarious methods based on maximum likelihood estimation were the main ways. These methods could be come down to an optimization of multi-variant hypostatically, the computational cost is too big to offer the possibility of project application. Recently, sundry time-frequency analysis such as Short Time Fourier Transform (STFT), Wigner-Ville Distribution (WVD), Wavelet Transform (WT), Fractional Fourier Transform (FRFT) based on time-frequency analysis has been applied in Detection and Parameter Estimation of LFM. The FRFT has a chirp element in the kernel function, so it was especially propitious to deal with Linear Frequency-Modulated signal. This paper mainly concerned in the process of Linear Frequency-Modulated signal based on Fractional Fourier Transform, and the main works are as the follows: 1. Analysis of the FRFT's property in the application of chirp detectionThe most important things in chirp detection were the abstraction of frequency characteristic—the chirp ratio and the starting frequency. The characteristic of its chirp element in the kernel function brings the success into chirp detection. And its property of linearity could separate the Multi-Linear Frequency Modulated signals without cross term. But the properties of rotation addition and conservation norm have no help for chirp detection. As a result, the FRFT has redundancy in the chirp detection, and there may be some reduced transforms usable for chirp detection.2. Present a New Time-Frequency TransformThis thesis derived the Reduced Transform (RT) from Linear Canonical Transform (LCT). Using RT instead of FRFT, it could obtain good effect in the Detection and Parameter Estimation of the LFM signal which has a large chirp ratio, also could reduce the computational cost.3. Present a FRFT or RT based Pre-Estimation Algorithm for chirp signals The thesis proposes a FRFT or RT based pre-estimation algorithm (PEA) for Linear Frequency Modulation (LFM) signal detection, which can be used to estimate the value of chirp ratio approximately. The corresponding FRFT rotation angle could be derived from this value. By this, the accurate value of the maximal amplitude and some other parameters of the signal can be determined by using FRFT or RT with the rotation angle. Both the theoretic analysis and simulation results have proved that, comparing with the original FRFT, the PEA method can reduce the computational cost and offer the possibility of real-time signal processing for LFM signal, while keeping the advantage of original FRFT. Additionally, the PEA can avoid the disturbances from the fake peaks in the angle-frequency domain that the original FRFT method can not.