The main aim of signal analysis is to research and represent the basic property of the analyzed signal. The representation form of the signal affect the result of the signal analysis directly. We want to find the representation form which is the most efficient in reflecting the intrinsic characteristics of the analyzed signal. Usually, signal is a function which varies with time. we are accustomed to research the values of the varying signal, but the frequency of a signal can also varies with time. For this reason, the time-frequency analysis is an important and difficult research field. The aim of the time-frequency analysis is to analysis how the frequency components vary in local time or local space and utilize these time-frequency features to accomplish signal processing assignments. The instantaneous frequency is exactly the quantity which can reflect the varying rules of different frequency components, and it is an important research object in time-frequency analysis domain. Complicated signal often consists of many different frequency components. It is difficult to analysis this signal directly. The decomposition of these components is also an important step before we analysis the origin signal. This thesis researches the time-frequency of analysis one-dimension signal and two-dimension image based on the idea of signal decomposition. In the first two chapters, this thesis researches the empirical mode decomposition (EMD) based on the discussion about instantaneous frequency. At first, many signal decomposition algorithms are reviewed. Then, many questions about instantaneous frequency are researched, such as the definition of instantaneous frequency, the interpretation of the instantaneous frequency and some paradoxes about it. And then, the EMD algorithm proposed to deal with these paradoxes is introduced. This thesis also represents many improved EMD algorithms. At last, a new EMD algorithm based on bandwidth is proposed, and the physical interpretation and the convergence of the algorithm are also discussed. This thesis also does some research in domain of two-dimensional signal time-frequency analysis. At first, some two-dimensional EMD algorithm are introduced, and the drawback of them is discussed. Then the two-dimensional instantaneous frequency is researched. At last, the bandwidth based two-dimensional EMD algorithm is proposed. Simultaneously, This thesis bring out a Gabor filter bank based IMF decomposition algorithm. The combination of two-dimensional EMD and Gabor filter bank composes an image decomposition and representation framework. Theory analysis and experiment results indicate that the algorithms proposed in this thesis have respective advantages, such as innovation, accuracy, simplicity, applicability, etc. This thesis explores a reasonable way to improve EMD, to research time-frequency analysis, and to represent signal adaptively.
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