Self-Adapted Wavelet Construction And Its Application To Signal Processing

Wavelet analysis is an efficient method in signal processing after Fourier Transform. It can provide excellent time and frequency localization. The different wavelet base corresponds with different processing results, so the choice of the wavelet bases is highly important.The paper introduces the developing process of wavelet theory, researches the property, construction method of wavelet bases and multiresolution analysis, penetrates the essential influence by selecting suitable wavelet bases in signal processing. The focus is set on the method and theory of selecting optimal wavelet bases according to practice signal.Most of the constructing optimal wavelet bases method is to select relative optimal bases from the constructed ones. It is limited by the constructed wavelets and a great deal of calculation is needed. Another method is to construct a wavelet base according to practice signal. So the wavelet base is interrelated to the signal.In the frame of multiresolution, according to the property and construction method of band limited orthonormal wavelet bases, the validity that optimal scale functions and wavelet bases can be constructed according to the power spectra of practice signal in the limit of orthonormal condition is proved with functional analysis theory precisely. The self-adapted scale functions and wavelet bases can lock the frequency band of learning signal, the shape is self-adapted modulated. Self-adapted matching construction algorithm are designed. In the simulating experiment about radar, earthquake, normal and disease electroencephalogram signal, optimal scale and wavelet is generated, the frequency component that concentrated the main energy is picked up in one level decomposition and reconstruction. The self-adapted matching construction algorithm is inosculated with the two dimensitional wavelet theory, suitiable two dimensitional scale function and wavelet are constructed according to learning image. Application to SAR oil spill image shows that the oil spill domain is filterd out efficiently. The signal and image are processed in real time.