The Research Of Signal Processing In Alpha Stable Distribution Noise Environments

The non-Gauss signal processing is the new realm of signal processing which develops quickly in recent years. As the only one type distribution which satisfy the broad sense center extreme limit axioms, alpha stable distribution was first used in signal processing at 1993, and then large numbers of researchers domestic and overseas pay attention to it. As the broad sense turns Gauss distribution, alpha stable distribution has characteristics of itself. How to do the theory study of the distribution under these restrict and expand it to the signal processing has very important meanings.This text mainly studies the properties of the alpha stable distribution and the time delay estimation and the adaptive filter arithmetic under the noise which satisfy the alpha stable distribution. the main work is generalized as follows.This text reviews the history of the alpha stable distribution at first, and then introduces the actuality and the meaning of the research of alpha distribution.As a typical non-Gauss signal model, the properties of alpha stable distribution are very different from Gauss distribution. This text gives the relational definitions, properties, theorems, and detailed analyzes the interrelated statistics of stable distributions. The parameters estimation is introduced too.The time delay estimation is always the important topic in signal processing. The performance of the traditional time delay estimation methods degenerate under stable distribution noises. Several time delay methods based on fractional lower order statistics are introduced. The text analyzes and compares these methods. A new time delay estimation method based on arc tangent is proposed. The text analyzes it and compares it with the methods forementioned.Under the alpha stable distribution noises, the traditional adaptive filter methods are not applied. Several adaptive filter methods apply to alpha stable distribution are introduced. The text analyzes and compares these methods. A new LMS ADF based on arc tangent is proposed. The text analyzes it and compares it with the methods forementioned.Finally, the text gives a brief summary of the job as well as the future expectations.