M带N周期多尺度分析

N Periodic Multiresolution Analysis with Band M

引入了M带N周期多尺度分析的概念,将传统的周期多尺度分析进行了推广。利用傅立叶变换和函数内积研究了M带N周期正交多尺度分析,得到了M带N周期多尺度分析的尺度函数空间的频域表示,以及高通滤波器系数与低通滤波器系数之间的关系和面具的初等性质。结论表明,周期小波的滤波器系数和面具是具有周期性的一族系数。

N periodic multiresolution analysis with band M was introduced. By means of Fourier transformation and inner-product, N periodic orthogonal muhiresolution analysis with band M was studied. Expression of its scaling function space in frequency domain is obtained, the coefficients relationship of lowpass filter and highpass filter is investigated, and the elementary property of its mask is worked out. The results show that filter and mask of periodic wavelet is a series of coefficients.