A Algebraic Construction Method Of M-band Semi-orthogonal Wavelet

In this paper, algebraic construction of M-band semi-orthogonal wavelet and its application in decomposition and reconstruct signal are researched.At first, the history of development of the theory of wavelet has been introduced, and the resource of the basic idea of wavelet transform which is the method of flex and translation has been clarified. As the shortage of the consecutive Fourier transform, incompact supported analysis theory can not be well applied in practical research. From the introduction, basic conception of consecutive wavelet transform and the deformation of it have been given, and the character of them has also been discussed. At the base of the thought of the consecutive wavelet transform, the form of the discrete wavelet transform and its deformation can be easily got. The utility and convenience in processing the discrete signal and the digital signal have also been discovered.Because different wavelet has different time-frequency character, there exists a problem in the choosing and optimizing of the base of wavelet and wavelet function. Continuity, orthogonality, symmetry, linearity phase and the center, radius and area of time-frequency window of the base of wavelet and wavelet function become the wavelet function character when using it in practice. Of course, the theory of the wavelet analysis is choosing appropriate base of wavelet according to time-frequency character of discrete signal .Recently, the construction of semi-orthogonal wavelet and M-band semi-orthogonal wavelet has become a focus of the research of wavelet theory. The orthogonal wavelet of compact supported wavelet doesn't have symmetry and dissymmetry generally, while the base of semi-orthogonal wavelet can possess symmetry and compact support. Similarly, the extension from 2-band wavelet to M-band wavelet can make us analyze the area of frequency character more clearly, and it can be conceived that M-band semi-orthogonal wavelet will be the better choice of digital signal processing. However, this paper presents an algebraic construction method which is based on the idea of M-band semi-orthogonal wavelet,Concrete construction method of diagonal intersection when stressly discussing M=3(The scale function is hill shape function and two appearance strips),and apply it in the signal checkout with going chirp,by the test of the computer,We found that the method is very active, and we also use it to test unsteady signal and remove the noises of signal.The arithmetic of the paper is carried out by programming in matlab, and is verified very effective.