| Along with high-tech development increasing, request of people for the signals analysis is more and more complicated, analytic signal objects are more and more wide. In the past people mainly process and analyze the stationary signals. The main investigative tool is Fourier analysis method. People even also suppose nonstationary signals as linearity, Gaussian feature and stationary objects to process. These methods have more and more localizations. People regard nonlinearity,no-Gaussian feature and nonstationary signals as objects of modern nonstationary signals. In analyzing signals, analysizing and processing the nonstationary signals methods not only are the new technique in the development and applying of information science and technology numerous courses, but also cause extensive research and application interest in physics, mechanics, earth physics, living creature medical science, astronomy, hydrology etc, for example processing speech signals with short time Fourier transform, processing picture and identifying mode with small wave analysis etc. On the basis of Fourier analysis, people put forward and develop a series of new signals analysis theories: short time Fourier analysis, time-frequency analysis, Gabor transform, small wave transform, Radon-Wigner transform, Fractional Fourier transform, linearity modulation frequency small wave transform and so on.In practical application, such as correspondence signals, some radars signals, seismic wave, sonar etc, all are nonstationary signals. The traditional Fourier analysis is a full domain transformation in time or frequency domain, it can't describe time domain and frequency domain characteristics at the same time, namely it can't describe the relation between different time with different frequency. However, this kind of relation property justly is the most important and key property of the nonstationary signals. Fractional Fourier transform is a kind of improved method of the classic Fourier analysis method. Fractional Fourier transform is found on the rotation of coordinate axis. It can manifest time and frequency property of signals at the same time, and it makes up Fourier analysis that can't manifest time and frequency property at the same time. V.Namias first put forward Fractional Fourier transform at 1980'. Several years of Recent, Fractional Fourier transform has applying Extensively in differential calculus, quantum mechanics theories and optics deliver, optical system and optical signals processing, filter wave of time varying and deliver along many roads, filter of scanning frequency, artificial nerve network, small wave transform, time-frequency analysis etc. It is emerging vaster applied foreground.In the thesis, the main aim is discussing the frequency separation, filter and interference functions of LFM signals in the nonstational signals analysis and processing. The research objects are LFM signals in the nonstationary signals. LFM signal is a kind of typical nonstationary signals that is the most suitable for making the frequency gathering evaluation, this kind of signals is used extensively in radar, sonar and seismic signals etc exploring systems. This thesis researches the following aspects and obtains some valuable results:Firstly, this thesis introduces the basic theories principle of Fractional Fourier transform, respectively explaining its variable causes from the mathematics, optics and others aspects. It realizes number computing of Fractional Fourier transform, computes Fractional Fourier transform of rectangle wave, Gaussian signals and two kinds of actual time signals. It explains that Fractional Fourier transform converts rectangle wave when , while converts square signals when. Also, it proves that Gaussian signal is Gaussian signal in any p domain. So it shows that Fractional Fourier transform is another improvement method of the classic Fourier analysis through diagram, and Fractional Fourier transform can manifest signals and frequency property at the same time. The main property of Fraction...
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