The Design And Analysis Of Multiband Wavelet Filter Banks

The construction of biorthogonal wavelet filter banks containing parameter are discussed by developing the common frame with lifting scheme of the perfect reconstruction fitler banks, and the famous CDF9/7 wavelet is then achieved by choosing a particular parameter. In image compression application, new wavelets with simple integer coefficients and comparable property to CDF9/7 wavelet are easily obtained by proper parameters. The above wavelet can also be easily implemented in hardware circumstance. The superiority with simple coefficients wavelet is analyzed from the viewpoint containing computing and image compression.As a new computational process, known lifting scheme can be used to decrease the complexity, but it cannot be used to construct wavelets efficiently. In this paper, we presented a new kind of lifting scheme, which is obtained by factoring symmetric orthogonal wavelet into lifting steps, the weakness mentioned above is partly overcame, and some examples are given to illustrate it.Because M-band wavelets and filter banks have some unparalleled property as two-band ones, it can analyze and process the signal more precisely. So, it has been a hotspot in research of wavelets' theory and application. At present, there are two main methods in the construction of M-band orthogonal wavelets. The first method is based on lattice structure and constraint of regularity, which is realized by solving a constrained optimization. The second approach is achieved by orthogonalizing the polyphase matrix of M-band wavelets system. Both of them have the defect that either the constraints are too complicated or the process not to keep the linear phase property. In this paper, we present a method to design symmetric orthogonal M-band wavelets with arbitrary regularity by using Grobner basis and syzygy module algorithm in computing algebra to orthogonalize the polyphase matrix. The drawbacks mentioned above are avoided. Simultaneously, the presented wavelet filters contains free variables when the associated scale filter coefficients involve parameters. So, M-band wavelets with free variables via practice requirement are also developed.