基于多项式插值的小波变换预滤波器设计
Wavelet Tramsform Prefilter Design Based on Polynomial Interpolation
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摘要: 该文提出了基于多项式插值的预滤波器设计方法， 这种方法从分析尺度函数出发设计预滤波器。信号均匀采样时, 预滤波器是时不变滤波器, 其系数是分析尺度函数各阶矩的线性组合。预滤波器的逼近阶取决于分析尺度函数的支撑集长度而不是正则阶。该设计方法有两个突出的优点：可以设计比传统预滤波器更高逼近阶的预滤波器,如综合尺度函数整数点的值构成的特殊预滤波器和由预尺度函数法产生的预滤波器等，可以很自然地推广到信号非均匀采样的情况, 相应的预滤波器是时变滤波器, 逼近阶依赖于分析尺度函数的支撑集长度和采样点的分布。数值结果表明, 利用基于多项式插值的小波变换预滤波器可以得到逼近效果更好的初始尺度系数。Abstract: This paper presents a novel method to design prefilters starting from analysis scaling functions and utilizing the algebraic polynomial interpolation. In the case of uniform sampling, the obtained prefilters are time-invariant and its coefficients are linear combinations of the moments of the analysis scaling function. Its approximate order is dependent on the support length of analysis scaling function rather than its degree of regularity. This method provides two outstanding advantages: the prefilters can be designed with higher approximate orders than the existing prefilters, e.g., the special prefilters from the values at integer points of the synthesis scaling function and the prefilters from prescaling function method; moreover, the method is easy to be extended to the case of nonuniform sampling, in which the prefilters are time-variant and their approximate order is dependent on the support length of analysis scaling function as well as the distribution of sample points.
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