The Generalizing Theory Of Wavelet And Its Analytic Analysis

Wavelet analysis is an effective tool to analyze non-stationary signal in modern signal processing theory, which is of adjustive time-frequency window, namely, is characteristic of multi-resolution analysis. However, classical wavelets such as Daubechies wavelet, BL wavelet, Meyer wavelet and so on, don't satisfy all engineering applications. So it is necessary that we should not only inherit many excellent properties of these classical wavelets, but also improve some performance for these classical wavelets, such as regularity, symmetry etc. In terms of generalizing theory of classical wavelet presented by Yuan Xiao, we could construct a series of such wavelet bases named generalized classical wavelet that provide new approach for the construction of complex analytic wavelets and other applications.As we know, it is very difficult that we directly extract phase information that is a key to calculate transient parameters and identify singularity signal from real signal. Because analytic wavelet can connect wavelet with complex analysis, we can use analytic wavelet established by generalized wavelets to extract phase information of component parts of signal which are important to analyze non-stationary signal characteristic. For an example of application, identification of modulation type such as MPSK, MFSK in communication is studied. In the master thesis, the main work and obtained results can be summarized as follows:1. Analyzed the generalizing theory in detail and studied properties of generalized wavelet function and scale function.2. Based on double-scales equations, discussed iterative algorithm of forming wavelet functions including scale function and wavelet function.3. Studied constructing conditions of analytic wavelet and analyzed qualities of analytic wavelet. For decreasing computation complexity, fast analytic wavelet transform algorithm are given.4. Comparison between analytic wavelet transform and real wavelet transform in signal processing is done. Results show that phase analysis of analytic wavelet transform (CWTP) is of better performance. At the same time, anti-noise capacity of CWTP algorithm is simulated for evaluation.5. Aiming at identification problem of modulation type, CWTP algorithm is employed to identify MPSK and MFSK.