Adaptive And Fractional Non-stationary Signal Processing

For a long time, the stationary signals are only considered. Though many nonstationary signals are encountered, the scholars have to suppose that all signals are stationary. Under the hypothesis, the processing effect is acceptable in many scenes. But it isn't acceptable in most of scenes. The purpose of hypothesis is convenience for processing signal. If the hypothesis isn't fit for the ture scene, even it is wrong. It will result in an unreliable conclusion and processing work will be insignificance for anyone. Because of the concept, naturally, the study of nonstationary signal processing becomes a hotspot in modern signal processing domain. A few problom about nonstationary signal is studied deeply by using both adaptive and Fractional Fourier Transform theory as main route. The contributions of this paper are as follows.? Present a modification LMS algorithm based on quadratic cyclostatistic.? Present a kind of struct of period adaptive filter based on filter bank.? Present a kind of struct of period adaptive filter based on time base function expand.? Present an algorithm to estimate the period of LPTV system? Present a time-varying parametric model that is LPTV type, and study the relationship between model parametrics and cyclostatistics of its ouput signal.? Present a whitening signal algorithm based on disordering sequence. One bases on chaos sequence, another bases on pseudo random sequence.? Present a modification LMS algorithm based on whitening input signal.? A Wavelet Neural Network is introduced into a time-varying parametric model. Based on Wavelet Neural Network, an AR time-varying parametric model is present.?Present a Ambiguity Function based on Fractional Fourier Transform. Its properties are studied. The application is discussed carefully that how to extract cube phase information by the Fractional Ambiguity Function.? Present a definition of cepstrum based on Fractional Fourier Transform.? Present a struct and a kind of algorithm for numerical solution of Fractional Fourier Transform that is linear frequency modulation style.There are seven chapters in this paper. The contents of this paper are as follows.Firstly, based on reviewing time-frequency analysis methods, A few background knowledges are mentioned. The main reseach contents are also outlined.Secondly, the cyclostationary property of output signal is discussed, when a stationary (or cyclostationary) signal passes a linear period time-varying (or time invariant) system. Based on these characteristics, a modification LMS algorithm that is fit for cyclostationary input is presented. The modification algorithm performance is discussed on the gradientestimate noise side. In linear period time-varying system, the classical adaptive filter cann't work correctly. Two styles of period adaptive filter are presented, which are fit for this kind of system.Thirdly, many cyclic statistics of cyclostationary signal, such as cyclic spectra, are used to describe cyclostationary signal. The description is also a nonparametric one. The relationship must exist between it and the parametric one, and the relationship is studied in the thesis. A few analytical expressions are presented to bring forth the relationship. A time-varying parametric model of LPTV type is also presented.Fourthly, the time-varying parametric model of nonstationary, especially, decomposing time-varying parametric to linear combination of base function is studied. Based on other scholars' work, the new time-varying model is presented by using wavelet Neural Network as base function. The application of new model is also studied.Fifthly, It is very important to select a base function for time-frequency analysis work. Good choice will be very efficient, because the good base functions can concentrate signal characteristics into a few coefficients. As a representative Transform, the Fractional Fourier Transform is considered as a generalized Fourier Transform. Combining Fractional Fourier Transform and classical quadratic time-frequency analys...