Lms Adaptive Filtering Algorithm Based On Fractional Fourier Transform

Filter technology always plays a part in electronic information processing domain, especially the digital filter technology, which is used widely and is paid more attention to by many countries. In recent years, the adaptive filtering algorithm research is one of the active tasks in adaptive signal processing domain. The Least Mean Square algorithm is one of two basic linear adaptive filtering algorithms. It mainly is based on The Least Mean Square criterion, and makes the mean error smallest between the output signal and the expected output signal. The LMS algorithm is widely applied in many domains such as the system identification, the echo eliminates, the adaptive spectral line strengthens, the adaptive channel balanced and so on, because it is simple, effective, easy to realize and has good robustness.The Fractional Fourier Transform (FRFT) is a newly developed time-frequency analysis tool, and it receives growing attention in the signal processing domain, especially in the non-stationary signal processing. Because The Fractional Fourier Transform has fine characteristics for analyzing and processing the non-stationary signal, this dissertation is focused on the LMS adaptive filtering algorithm in FRFT domain for the non-stationary signal while statistical property of the signal and the noise is not request to be known. The main contributions and innovations of the dissertation are:1. A lot of literatures are read and the research of the LMS adaptive filtering algorithm are made the quite thorough analysis, especially the LMS adaptive filtering algorithm in transform domain are made the detailed analysis comparison and the summary.2. The LMS adaptive filtering algorithm based on fractional Fourier transform is analyzed and verified by simulations. In this paper, the simulations show the LMS adaptive filtering algorithm will be more effective when the fractional Fourier transform is matched with the signal parameters. This conclusion gives the reference for the best filtering in fractional Fourier transform domain.3. Basing on the standard LMS algorithm in FRFT domain, the dissertation combines the Genetic Algorithm and presentes a new LMS adaptive filtering algorithm based on FRFT and Genetic Algorithm, which realizes the synchronous adaptive search of the fractional number in FRFT and the weighting factor in LMS algorithm. The new LMS algorithm has the quicker convergence rate and conforms to the practical application.4. Basing on the above works, this dissertation combines the LMS adaptive filtering algorithm in transform domain with the changeable step size LMS algorithm, and presents a new LMS adaptive filtering algorithm with the changeable step size in FRFT domain. It has better performances.