The Principle Of Multi-resolution Analysis And Its Applications

This paper first gives a little prior knowledge, it is is helpful for understanding of the paper.Secondly this paper introduces the continuous wavelet, the wavelet transform of a function, in some ways can reflect some of the properties of the original function, and the function with wavelet transform has a good property, such as continuity. It is similar with the Fourier transform, but a little more complex than Fourier transform.Thirdly it introduces discrete wavelet transform,orthogonal wavelets. This chapter introduces the multiresolution analysis, describes some of the properties and theorems associated, For example, the scaling function on multi-resolution analysis have a decisive role. Through multiresolution analysis, it gives a general method for constructing orthogonal wavelets. This can also be said to give by the scal-ing function constructed orthogonal wavelet methods. When constructing orthog-onal wavelet with compact support, The first step is constructing scaling function through the scaling filter, and then by the scaling function to construct the orthog-onal wavelet.Finally, the use of multiresolution analysis gives the mathematical form Mallat algorithm.