Application Of Physics Wavelet Transform On Acoustic Signal Processing

Wavelet transform is a popular method which is more and more used in many fields such as signal processing and physics and so on recent twenty years.The conception of'physical wavelets'was first introduced by Gerald Kaiser, who had expended real signal to complex Hilbert space by analytic signal transform. However, this method is not applied on practical signal processing, but just deduced mathematically by G. Kaiser. And analytic signal transform, a critical transform, is introduced at the same time. It is concerned whether a signal that satisfies wave equation could be used as a'mother wavelet'to analyze the progress of wave spread.Several new signal processing methods are mentioned in this article. They are used to give a deeper understanding of physical wavelets, which the physical meaning is not much clear yet. Physical wavelets are used to analyze practical signal acquired by experiments. The possibilities of applications ,numerical simulations of Fast Arithmetic Transform are discussed at the end part of this article.Acoustics wavelet is used to analyze both broad band and narrowband acoustic echo signals. With different parameters, the physical meanings of physical wavelets and Analytic Signal Transform are discussed. It is proved that the physical wavelets have general physical meanings. It can be used in two kinds of different signals.General analytic signal transform is used to deal with the integral equation of acoustic problem. The applications of AST in source localization and scattering are discussed at the same time. It is proved that AST could be identified as a beam forming method with scale-changed and direction-selectivity.A new algorithm which called Fast Arithmetic Transform is introduced at last part of this article. It is proved theoretically that FAT has superiority over other fast algorithms in algorithm complexity. It may improve the speed of operation, and the spectrums of several basic functions are listed at last.