Study And Application Of Time-Frequency Analysis And Cyclic Statistics Under Alpha-stable Noises

There are strong impulse noise and same frequency band interference in communications, remote sensing, radar and sonar signal processing and many other areas. Many of the signals we encountered in these systems are cyclostationary signal, which is a special kind of non-stationary signal with periodic or multi-periodic stable transform statistics. The noises which overlap with the signal both in the time-domain and frequency-domain can be effectively smoothed by the use of the cyclostationary properties. Only its second order characteristics are needed to carry out the separation, and other signal processing. We can only use the second-order cyclostationary to fulfillment the signal separation examination and so on. But, in fact there are a lot of non-Gaussian signals and noises with notable pulse characteristic, so people usually use alpha-stable distribution model to depict stochastic signals with a remarkable impulsive characteristic. Because of the second-order statistics of the alpha-stable distributed noise doesn't exist, which result in noticeable degradation or even failure of the performance of algorithms based on the second-order statistics. Focusing on this question, the thesis combines the fractional lower-order theory and cyclic statistics theory, and the new fractional lower-order cyclic statistics was given, which can restrain both the same frequency band interference and alpha-stable distributed noise.The main work of this paper is as follows:(1) The time-frequency problem under alpha-stable distributed noises has been studied. The definitions of Fractional lower-order Fourier transform(FSTFT) and Fractional lower-order Ambiguity function(FA) based on fractional lower-order statistics are proposed.(2) Use the second-order cyclic correlation and fractional lower-order correlation statistics, deduced the formula of fractional lower-order cyclic correlation and fractional lower-order cyclic covariance, examples shows that their cyclic frequency is equal to the cyclic frequency of second-order cyclic correlation. On this foundation, a MUSIC algorithm based on the fractional lower order cyclic correlation and a new DS-SS signal detection method based on the fractional lower order cyclic covariance are proposed. It shows that these new algorithms are robust for both Gaussian and non-Gaussian impulsive noise environment through theoretical analysis and computer simulations.(3) The concept of Fractional lower-order Cyclic Spectrum was given. Make a research in the application in the estimation of cyclic frequency and mechanical fault diagnosis through simulations. The experiments' result shows the effectiveness and wide application outlook.