基于多項(xiàng)式插值的小波變換預(yù)濾波器設(shè)計(jì)
Wavelet Tramsform Prefilter Design Based on Polynomial Interpolation
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摘要: 該文提出了基于多項(xiàng)式插值的預(yù)濾波器設(shè)計(jì)方法， 這種方法從分析尺度函數(shù)出發(fā)設(shè)計(jì)預(yù)濾波器。信號(hào)均勻采樣時(shí), 預(yù)濾波器是時(shí)不變?yōu)V波器, 其系數(shù)是分析尺度函數(shù)各階矩的線性組合。預(yù)濾波器的逼近階取決于分析尺度函數(shù)的支撐集長(zhǎng)度而不是正則階。該設(shè)計(jì)方法有兩個(gè)突出的優(yōu)點(diǎn)：可以設(shè)計(jì)比傳統(tǒng)預(yù)濾波器更高逼近階的預(yù)濾波器,如綜合尺度函數(shù)整數(shù)點(diǎn)的值構(gòu)成的特殊預(yù)濾波器和由預(yù)尺度函數(shù)法產(chǎn)生的預(yù)濾波器等，可以很自然地推廣到信號(hào)非均勻采樣的情況, 相應(yīng)的預(yù)濾波器是時(shí)變?yōu)V波器, 逼近階依賴于分析尺度函數(shù)的支撐集長(zhǎng)度和采樣點(diǎn)的分布。數(shù)值結(jié)果表明, 利用基于多項(xiàng)式插值的小波變換預(yù)濾波器可以得到逼近效果更好的初始尺度系數(shù)。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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